- published: 15 Oct 2014
- views: 659
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Leonhard Euler was the greatest mathematician of modern times. His work on pentagonal numbers shows that they connect naturally to sums of divisors of numbers, and also to the partition functions. These are both really surprising facts.
This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. The full playlist is at http://www.youtube.com/playlist?list=PL5A714C94D40392AB&feature;=view_all
- published: 27 Apr 2010
- views: 5700
The patterns formed by triangular numbers and square numbers have generalizations in different directions. One is to three dimensional tetrahedral numbers, and three dimensional pyramidal numbers. Another is to pentagonal numbers, which have a number of interesting features.
This video belongs to Wildberger's MathFoundations series, which attempts to create a coherent and logical framework for modern mathematics.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger. I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?ty=h .
- published: 26 Apr 2010
- views: 5445
Introduction to Java Comprehensive 10th Edition
Chapter 6 Methods
Programming Exercise 6.01 Pentagonal Numbers
- published: 16 Feb 2016
- views: 50
Pentagonal number
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical.The nth pentagonal number pn is the number of distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=pGFDtLYhdao
- published: 22 Jan 2016
- views: 43
Date: September 23, 2010
Speaker: Krishnaswami Alladi, Univeristy of Florida
Title: Some new companions to Euler's pentagonal numbers theorem
Abstract:
We will deduce two new companions to Euler's celebrated
Pentagonal numbers theorem from partial theta identiities of
Ramanujan and Andrews. These companions are acttually stronger
in the sense that they can be refined by the introduction of a
parameter a. The cancellation by parity split is just as strong
as in Euler's theorem even with the parameter a, but for these
companions the role of the pentagonal numbers is replaced by the
squares. It is amazing that even though the weights in the two
companions are different, their sums are the same, and so the
cancellation and the resulting lacunarity are identical.
Finally, from another identity in Ramanujan's Lost Notebook, we
will deduce one more companion to Euler's theorem, this one
involving twice the pentagonal numbers. We will show how these
companions are connected to various fundamental results in the
theory of partitions and q-hypergeometric series. The talk will
be accessible to non-experts.
- published: 13 Oct 2010
- views: 658
Date: September 23, 2010
Speaker: Krishnaswami Alladi, Univeristy of Florida
Title: Some new companions to Euler's pentagonal numbers theorem
Abstract:
We will deduce two new companions to Euler's celebrated
Pentagonal numbers theorem from partial theta identiities of
Ramanujan and Andrews. These companions are acttually stronger
in the sense that they can be refined by the introduction of a
parameter a. The cancellation by parity split is just as strong
as in Euler's theorem even with the parameter a, but for these
companions the role of the pentagonal numbers is replaced by the
squares. It is amazing that even though the weights in the two
companions are different, their sums are the same, and so the
cancellation and the resulting lacunarity are identical.
Finally, from another identity in Ramanujan's Lost Notebook, we
will deduce one more companion to Euler's theorem, this one
involving twice the pentagonal numbers. We will show how these
companions are connected to various fundamental results in the
theory of partitions and q-hypergeometric series. The talk will
be accessible to non-experts.
- published: 13 Oct 2010
- views: 253
Date: September 23, 2010
Speaker: Krishnaswami Alladi, Univeristy of Florida
Title: Some new companions to Euler's pentagonal numbers theorem
Abstract:
We will deduce two new companions to Euler's celebrated
Pentagonal numbers theorem from partial theta identiities of
Ramanujan and Andrews. These companions are acttually stronger
in the sense that they can be refined by the introduction of a
parameter a. The cancellation by parity split is just as strong
as in Euler's theorem even with the parameter a, but for these
companions the role of the pentagonal numbers is replaced by the
squares. It is amazing that even though the weights in the two
companions are different, their sums are the same, and so the
cancellation and the resulting lacunarity are identical.
Finally, from another identity in Ramanujan's Lost Notebook, we
will deduce one more companion to Euler's theorem, this one
involving twice the pentagonal numbers. We will show how these
companions are connected to various fundamental results in the
theory of partitions and q-hypergeometric series. The talk will
be accessible to non-experts.
- published: 14 Oct 2010
- views: 172
We arranged these oranges in triangles and squares, can we go to higher orders.
Why not? We can arrange oranges in pentagons and then we can discover the whole world of pentagonal numbers.
Place an orange and consider it be a pentagon of side 1. Place 4 more oranges to make a pentagon of size 2. The total number of oranges in size 2 pentagon will be 5. Now make a pentagon of size 3. For this you will need 7 more oranges.
For size2 we needed 1 + 4
For size 3 we will need 1 + 4 + 7 = 12
Now make an even larger pentagon of size 4.
For size 4 we will need 1 + 4 + 7 + 10 = 22. So the 4th pentagonal number is 22.
Finally, let’s make a pentagon on size 5. Each of its 5 sides will have five oranges each.
From size 4 pentagons to make size 5 pentagons we will need 13 oranges more.
From size 1 to size 2 we need 3 oranges
From size 2 to size 3 we need 3 more oranges
From size 3 to size 4 we need 3 more oranges
From size 4 to size 5 we need 3 more oranges
These numbers 1, 5, 12, 22 and 35 are called pentagonal numbers and they fit the formula (n) (3n-1)/2 This work was supported by IUCAA and Tata Trust. This film was made by Ashok Rupner
- published: 21 Feb 2015
- views: 114
Pentagonal number
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. The nth pentagonal number pn is the number of distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex. For instance, the third one is formed from outlines comprising 1, 5 and 10 dots, but the 1, and 3 of the 5, coincide with 3 of the 10 – leaving 12 distinct dots, 10 in the form of a pentagon, and 2 inside.
pn is given by the formula:
for n ≥ 1. The first few pentagonal numbers are:
1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287, 330, 376, 425, 477, 532, 590, 651, 715, 782, 852, 925, 1001 (sequence A000326 in OEIS).
The nth pentagonal number is one third of the 3n-1th triangular number.
Generalized pentagonal numbers are obtained from the formula given above, but with n taking values in the sequence 0, 1, -1, 2, -2, 3, -3, 4..., producing the sequence:
This page contains text from Wikipedia, the Free Encyclopedia -
http://wn.com/Pentagonal_number
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
Leonhard Euler
Leonhard Euler (/ˈɔɪlər/ OY-lər;Swiss Standard German [ˈɔɪlər], German Standard German [ˈɔʏlɐ]) (15 April 1707 – 18 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer who made important and influential discoveries in many branches of mathematics like infinitesimal calculus and graph theory while also making pioneering contributions to several branches such as topology and analytic number theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory.
Euler was one of the most eminent mathematicians of the 18th century, and is held to be one of the greatest in history. He is also widely considered to be the most prolific mathematician of all time. His collected works fill 60 to 80 quarto volumes, more than anybody in the field. He spent most of his adult life in St. Petersburg, Russia, and in Berlin, then the capital of Prussia.
This page contains text from Wikipedia, the Free Encyclopedia -
http://wn.com/Leonhard_Euler
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
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12:15Pentagonal numbers
Pentagonal numbersPentagonal numbers
math 211 HW 1.2 -
6:18Pentagonal Numbers
Pentagonal Numbers -
10:05MathFoundations52: Leonhard Euler and Pentagonal numbers
MathFoundations52: Leonhard Euler and Pentagonal numbersMathFoundations52: Leonhard Euler and Pentagonal numbers
Leonhard Euler was the greatest mathematician of modern times. His work on pentagonal numbers shows that they connect naturally to sums of divisors of numbers, and also to the partition functions. These are both really surprising facts. This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. The full playlist is at http://www.youtube.com/playlist?list=PL5A714C94D40392AB&feature;=view_all -
9:54MathFoundations51: More patterns with algebra
MathFoundations51: More patterns with algebraMathFoundations51: More patterns with algebra
The patterns formed by triangular numbers and square numbers have generalizations in different directions. One is to three dimensional tetrahedral numbers, and three dimensional pyramidal numbers. Another is to pentagonal numbers, which have a number of interesting features. This video belongs to Wildberger's MathFoundations series, which attempts to create a coherent and logical framework for modern mathematics. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger. I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?ty=h . -
4:30Java 6.01 Pentagonal Numbers
Java 6.01 Pentagonal NumbersJava 6.01 Pentagonal Numbers
Introduction to Java Comprehensive 10th Edition Chapter 6 Methods Programming Exercise 6.01 Pentagonal Numbers -
6:30Pentagonal number
Pentagonal numberPentagonal number
Pentagonal number A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical.The nth pentagonal number pn is the number of distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex. -Video is targeted to blind users Attribution: Article text available under CC-BY-SA image source in video https://www.youtube.com/watch?v=pGFDtLYhdao -
6:02Some new companions to Euler's pentagonal numbers theorem part1
Some new companions to Euler's pentagonal numbers theorem part1Some new companions to Euler's pentagonal numbers theorem part1
Date: September 23, 2010 Speaker: Krishnaswami Alladi, Univeristy of Florida Title: Some new companions to Euler's pentagonal numbers theorem Abstract: We will deduce two new companions to Euler's celebrated Pentagonal numbers theorem from partial theta identiities of Ramanujan and Andrews. These companions are acttually stronger in the sense that they can be refined by the introduction of a parameter a. The cancellation by parity split is just as strong as in Euler's theorem even with the parameter a, but for these companions the role of the pentagonal numbers is replaced by the squares. It is amazing that even though the weights in the two companions are different, their sums are the same, and so the cancellation and the resulting lacunarity are identical. Finally, from another identity in Ramanujan's Lost Notebook, we will deduce one more companion to Euler's theorem, this one involving twice the pentagonal numbers. We will show how these companions are connected to various fundamental results in the theory of partitions and q-hypergeometric series. The talk will be accessible to non-experts. -
6:02Some new companions to Euler's pentagonal numbers theorem part2
Some new companions to Euler's pentagonal numbers theorem part2Some new companions to Euler's pentagonal numbers theorem part2
Date: September 23, 2010 Speaker: Krishnaswami Alladi, Univeristy of Florida Title: Some new companions to Euler's pentagonal numbers theorem Abstract: We will deduce two new companions to Euler's celebrated Pentagonal numbers theorem from partial theta identiities of Ramanujan and Andrews. These companions are acttually stronger in the sense that they can be refined by the introduction of a parameter a. The cancellation by parity split is just as strong as in Euler's theorem even with the parameter a, but for these companions the role of the pentagonal numbers is replaced by the squares. It is amazing that even though the weights in the two companions are different, their sums are the same, and so the cancellation and the resulting lacunarity are identical. Finally, from another identity in Ramanujan's Lost Notebook, we will deduce one more companion to Euler's theorem, this one involving twice the pentagonal numbers. We will show how these companions are connected to various fundamental results in the theory of partitions and q-hypergeometric series. The talk will be accessible to non-experts. -
6:01Some new companions to Euler's pentagonal numbers theorem part3
Some new companions to Euler's pentagonal numbers theorem part3Some new companions to Euler's pentagonal numbers theorem part3
Date: September 23, 2010 Speaker: Krishnaswami Alladi, Univeristy of Florida Title: Some new companions to Euler's pentagonal numbers theorem Abstract: We will deduce two new companions to Euler's celebrated Pentagonal numbers theorem from partial theta identiities of Ramanujan and Andrews. These companions are acttually stronger in the sense that they can be refined by the introduction of a parameter a. The cancellation by parity split is just as strong as in Euler's theorem even with the parameter a, but for these companions the role of the pentagonal numbers is replaced by the squares. It is amazing that even though the weights in the two companions are different, their sums are the same, and so the cancellation and the resulting lacunarity are identical. Finally, from another identity in Ramanujan's Lost Notebook, we will deduce one more companion to Euler's theorem, this one involving twice the pentagonal numbers. We will show how these companions are connected to various fundamental results in the theory of partitions and q-hypergeometric series. The talk will be accessible to non-experts. -
4:58Pentagon with Oranges | Kannada | Fun with Maths
Pentagon with Oranges | Kannada | Fun with MathsPentagon with Oranges | Kannada | Fun with Maths
We arranged these oranges in triangles and squares, can we go to higher orders. Why not? We can arrange oranges in pentagons and then we can discover the whole world of pentagonal numbers. Place an orange and consider it be a pentagon of side 1. Place 4 more oranges to make a pentagon of size 2. The total number of oranges in size 2 pentagon will be 5. Now make a pentagon of size 3. For this you will need 7 more oranges. For size2 we needed 1 + 4 For size 3 we will need 1 + 4 + 7 = 12 Now make an even larger pentagon of size 4. For size 4 we will need 1 + 4 + 7 + 10 = 22. So the 4th pentagonal number is 22. Finally, let’s make a pentagon on size 5. Each of its 5 sides will have five oranges each. From size 4 pentagons to make size 5 pentagons we will need 13 oranges more. From size 1 to size 2 we need 3 oranges From size 2 to size 3 we need 3 more oranges From size 3 to size 4 we need 3 more oranges From size 4 to size 5 we need 3 more oranges These numbers 1, 5, 12, 22 and 35 are called pentagonal numbers and they fit the formula (n) (3n-1)/2 This work was supported by IUCAA and Tata Trust. This film was made by Ashok Rupner
-
Pentagonal numbers
math 211 HW 1.2 -
-
MathFoundations52: Leonhard Euler and Pentagonal numbers
Leonhard Euler was the greatest mathematician of modern times. His work on pentagonal numbers shows that they connect naturally to sums of divisors of numbers, and also to the partition functions. These are both really surprising facts. This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. The full playlist is at http://www.youtube.com/playlist?list=PL5A714C94D40392AB&feature;=view_all -
MathFoundations51: More patterns with algebra
The patterns formed by triangular numbers and square numbers have generalizations in different directions. One is to three dimensional tetrahedral numbers, and three dimensional pyramidal numbers. Another is to pentagonal numbers, which have a number of interesting features. This video belongs to Wildberger's MathFoundations series, which attempts to create a coherent and logical framework for modern mathematics. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger. I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, b... -
Java 6.01 Pentagonal Numbers
Introduction to Java Comprehensive 10th Edition Chapter 6 Methods Programming Exercise 6.01 Pentagonal Numbers -
Pentagonal number
Pentagonal number A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical.The nth pentagonal number pn is the number of distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex. -Video is targeted to blind users Attribution: Article text available under CC-BY-SA image source in video https://www.youtube.com/watch?v=pGFDtLYhdao -
Some new companions to Euler's pentagonal numbers theorem part1
Date: September 23, 2010 Speaker: Krishnaswami Alladi, Univeristy of Florida Title: Some new companions to Euler's pentagonal numbers theorem Abstract: We will deduce two new companions to Euler's celebrated Pentagonal numbers theorem from partial theta identiities of Ramanujan and Andrews. These companions are acttually stronger in the sense that they can be refined by the introduction of a parameter a. The cancellation by parity split is just as strong as in Euler's theorem even with the parameter a, but for these companions the role of the pentagonal numbers is replaced by the squares. It is amazing that even though the weights in the two companions are different, their sums are the same, and so the cancellation and the resulting lacunarity are identical. Finally,... -
Some new companions to Euler's pentagonal numbers theorem part2
Date: September 23, 2010 Speaker: Krishnaswami Alladi, Univeristy of Florida Title: Some new companions to Euler's pentagonal numbers theorem Abstract: We will deduce two new companions to Euler's celebrated Pentagonal numbers theorem from partial theta identiities of Ramanujan and Andrews. These companions are acttually stronger in the sense that they can be refined by the introduction of a parameter a. The cancellation by parity split is just as strong as in Euler's theorem even with the parameter a, but for these companions the role of the pentagonal numbers is replaced by the squares. It is amazing that even though the weights in the two companions are different, their sums are the same, and so the cancellation and the resulting lacunarity are identical. Finally, from another ... -
Some new companions to Euler's pentagonal numbers theorem part3
Date: September 23, 2010 Speaker: Krishnaswami Alladi, Univeristy of Florida Title: Some new companions to Euler's pentagonal numbers theorem Abstract: We will deduce two new companions to Euler's celebrated Pentagonal numbers theorem from partial theta identiities of Ramanujan and Andrews. These companions are acttually stronger in the sense that they can be refined by the introduction of a parameter a. The cancellation by parity split is just as strong as in Euler's theorem even with the parameter a, but for these companions the role of the pentagonal numbers is replaced by the squares. It is amazing that even though the weights in the two companions are different, their sums are the same, and so the cancellation and the resulting lacunarity are identical. Finally, from another ... -
Pentagon with Oranges | Kannada | Fun with Maths
We arranged these oranges in triangles and squares, can we go to higher orders. Why not? We can arrange oranges in pentagons and then we can discover the whole world of pentagonal numbers. Place an orange and consider it be a pentagon of side 1. Place 4 more oranges to make a pentagon of size 2. The total number of oranges in size 2 pentagon will be 5. Now make a pentagon of size 3. For this you will need 7 more oranges. For size2 we needed 1 + 4 For size 3 we will need 1 + 4 + 7 = 12 Now make an even larger pentagon of size 4. For size 4 we will need 1 + 4 + 7 + 10 = 22. So the 4th pentagonal number is 22. Finally, let’s make a pentagon on size 5. Each of its 5 sides will have five oranges each. From size 4 pentagons to make size 5 pentagons we will need 13 oranges more. From size 1...
Pentagonal numbers
- Order: Reorder
- Duration: 12:15
- Updated: 15 Oct 2014
- views: 659
math 211 HW 1.2
math 211 HW 1.2
wn.com/Pentagonal Numbers
Pentagonal Numbers
- Order: Reorder
- Duration: 6:18
- Updated: 02 Sep 2012
- views: 3694
Try this on your own....
The figures above show the first four pentagonal numbers. What is the 110th pentagonal number?
Ans: 18095
Try this on your own....
The figures above show the first four pentagonal numbers. What is the 110th pentagonal number?
Ans: 18095
wn.com/Pentagonal Numbers
MathFoundations52: Leonhard Euler and Pentagonal numbers
- Order: Reorder
- Duration: 10:05
- Updated: 27 Apr 2010
- views: 5700
Leonhard Euler was the greatest mathematician of modern times. His work on pentagonal numbers shows that they connect naturally to sums of divisors of numbers, ...
Leonhard Euler was the greatest mathematician of modern times. His work on pentagonal numbers shows that they connect naturally to sums of divisors of numbers, and also to the partition functions. These are both really surprising facts.
This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. The full playlist is at http://www.youtube.com/playlist?list=PL5A714C94D40392AB&feature;=view_all
wn.com/Mathfoundations52 Leonhard Euler And Pentagonal Numbers
Leonhard Euler was the greatest mathematician of modern times. His work on pentagonal numbers shows that they connect naturally to sums of divisors of numbers, and also to the partition functions. These are both really surprising facts.
This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. The full playlist is at http://www.youtube.com/playlist?list=PL5A714C94D40392AB&feature;=view_all
- published: 27 Apr 2010
- views: 5700
MathFoundations51: More patterns with algebra
- Order: Reorder
- Duration: 9:54
- Updated: 26 Apr 2010
- views: 5445
The patterns formed by triangular numbers and square numbers have generalizations in different directions. One is to three dimensional tetrahedral numbers, and ...
The patterns formed by triangular numbers and square numbers have generalizations in different directions. One is to three dimensional tetrahedral numbers, and three dimensional pyramidal numbers. Another is to pentagonal numbers, which have a number of interesting features.
This video belongs to Wildberger's MathFoundations series, which attempts to create a coherent and logical framework for modern mathematics.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger. I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?ty=h .
wn.com/Mathfoundations51 More Patterns With Algebra
The patterns formed by triangular numbers and square numbers have generalizations in different directions. One is to three dimensional tetrahedral numbers, and three dimensional pyramidal numbers. Another is to pentagonal numbers, which have a number of interesting features.
This video belongs to Wildberger's MathFoundations series, which attempts to create a coherent and logical framework for modern mathematics.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger. I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?ty=h .
- published: 26 Apr 2010
- views: 5445
Java 6.01 Pentagonal Numbers
- Order: Reorder
- Duration: 4:30
- Updated: 16 Feb 2016
- views: 50
Introduction to Java Comprehensive 10th Edition
Chapter 6 Methods
Programming Exercise 6.01 Pentagonal Numbers
Introduction to Java Comprehensive 10th Edition
Chapter 6 Methods
Programming Exercise 6.01 Pentagonal Numbers
wn.com/Java 6.01 Pentagonal Numbers
Introduction to Java Comprehensive 10th Edition
Chapter 6 Methods
Programming Exercise 6.01 Pentagonal Numbers
- published: 16 Feb 2016
- views: 50
Pentagonal number
- Order: Reorder
- Duration: 6:30
- Updated: 22 Jan 2016
- views: 43
Pentagonal number
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first t...
Pentagonal number
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical.The nth pentagonal number pn is the number of distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=pGFDtLYhdao
wn.com/Pentagonal Number
Pentagonal number
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical.The nth pentagonal number pn is the number of distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=pGFDtLYhdao
- published: 22 Jan 2016
- views: 43
Some new companions to Euler's pentagonal numbers theorem part1
- Order: Reorder
- Duration: 6:02
- Updated: 13 Oct 2010
- views: 658
Date: September 23, 2010
Speaker: Krishnaswami Alladi, Univeristy of Florida
Title: Some new companions to Euler's pentagonal numbers theorem
Abstract:
...
Date: September 23, 2010
Speaker: Krishnaswami Alladi, Univeristy of Florida
Title: Some new companions to Euler's pentagonal numbers theorem
Abstract:
We will deduce two new companions to Euler's celebrated
Pentagonal numbers theorem from partial theta identiities of
Ramanujan and Andrews. These companions are acttually stronger
in the sense that they can be refined by the introduction of a
parameter a. The cancellation by parity split is just as strong
as in Euler's theorem even with the parameter a, but for these
companions the role of the pentagonal numbers is replaced by the
squares. It is amazing that even though the weights in the two
companions are different, their sums are the same, and so the
cancellation and the resulting lacunarity are identical.
Finally, from another identity in Ramanujan's Lost Notebook, we
will deduce one more companion to Euler's theorem, this one
involving twice the pentagonal numbers. We will show how these
companions are connected to various fundamental results in the
theory of partitions and q-hypergeometric series. The talk will
be accessible to non-experts.
wn.com/Some New Companions To Euler's Pentagonal Numbers Theorem Part1
Date: September 23, 2010
Speaker: Krishnaswami Alladi, Univeristy of Florida
Title: Some new companions to Euler's pentagonal numbers theorem
Abstract:
We will deduce two new companions to Euler's celebrated
Pentagonal numbers theorem from partial theta identiities of
Ramanujan and Andrews. These companions are acttually stronger
in the sense that they can be refined by the introduction of a
parameter a. The cancellation by parity split is just as strong
as in Euler's theorem even with the parameter a, but for these
companions the role of the pentagonal numbers is replaced by the
squares. It is amazing that even though the weights in the two
companions are different, their sums are the same, and so the
cancellation and the resulting lacunarity are identical.
Finally, from another identity in Ramanujan's Lost Notebook, we
will deduce one more companion to Euler's theorem, this one
involving twice the pentagonal numbers. We will show how these
companions are connected to various fundamental results in the
theory of partitions and q-hypergeometric series. The talk will
be accessible to non-experts.
- published: 13 Oct 2010
- views: 658
Some new companions to Euler's pentagonal numbers theorem part2
- Order: Reorder
- Duration: 6:02
- Updated: 13 Oct 2010
- views: 253
Date: September 23, 2010
Speaker: Krishnaswami Alladi, Univeristy of Florida
Title: Some new companions to Euler's pentagonal numbers theorem
Abstract:
...
Date: September 23, 2010
Speaker: Krishnaswami Alladi, Univeristy of Florida
Title: Some new companions to Euler's pentagonal numbers theorem
Abstract:
We will deduce two new companions to Euler's celebrated
Pentagonal numbers theorem from partial theta identiities of
Ramanujan and Andrews. These companions are acttually stronger
in the sense that they can be refined by the introduction of a
parameter a. The cancellation by parity split is just as strong
as in Euler's theorem even with the parameter a, but for these
companions the role of the pentagonal numbers is replaced by the
squares. It is amazing that even though the weights in the two
companions are different, their sums are the same, and so the
cancellation and the resulting lacunarity are identical.
Finally, from another identity in Ramanujan's Lost Notebook, we
will deduce one more companion to Euler's theorem, this one
involving twice the pentagonal numbers. We will show how these
companions are connected to various fundamental results in the
theory of partitions and q-hypergeometric series. The talk will
be accessible to non-experts.
wn.com/Some New Companions To Euler's Pentagonal Numbers Theorem Part2
Date: September 23, 2010
Speaker: Krishnaswami Alladi, Univeristy of Florida
Title: Some new companions to Euler's pentagonal numbers theorem
Abstract:
We will deduce two new companions to Euler's celebrated
Pentagonal numbers theorem from partial theta identiities of
Ramanujan and Andrews. These companions are acttually stronger
in the sense that they can be refined by the introduction of a
parameter a. The cancellation by parity split is just as strong
as in Euler's theorem even with the parameter a, but for these
companions the role of the pentagonal numbers is replaced by the
squares. It is amazing that even though the weights in the two
companions are different, their sums are the same, and so the
cancellation and the resulting lacunarity are identical.
Finally, from another identity in Ramanujan's Lost Notebook, we
will deduce one more companion to Euler's theorem, this one
involving twice the pentagonal numbers. We will show how these
companions are connected to various fundamental results in the
theory of partitions and q-hypergeometric series. The talk will
be accessible to non-experts.
- published: 13 Oct 2010
- views: 253
Some new companions to Euler's pentagonal numbers theorem part3
- Order: Reorder
- Duration: 6:01
- Updated: 14 Oct 2010
- views: 172
Date: September 23, 2010
Speaker: Krishnaswami Alladi, Univeristy of Florida
Title: Some new companions to Euler's pentagonal numbers theorem
Abstract:
...
Date: September 23, 2010
Speaker: Krishnaswami Alladi, Univeristy of Florida
Title: Some new companions to Euler's pentagonal numbers theorem
Abstract:
We will deduce two new companions to Euler's celebrated
Pentagonal numbers theorem from partial theta identiities of
Ramanujan and Andrews. These companions are acttually stronger
in the sense that they can be refined by the introduction of a
parameter a. The cancellation by parity split is just as strong
as in Euler's theorem even with the parameter a, but for these
companions the role of the pentagonal numbers is replaced by the
squares. It is amazing that even though the weights in the two
companions are different, their sums are the same, and so the
cancellation and the resulting lacunarity are identical.
Finally, from another identity in Ramanujan's Lost Notebook, we
will deduce one more companion to Euler's theorem, this one
involving twice the pentagonal numbers. We will show how these
companions are connected to various fundamental results in the
theory of partitions and q-hypergeometric series. The talk will
be accessible to non-experts.
wn.com/Some New Companions To Euler's Pentagonal Numbers Theorem Part3
Date: September 23, 2010
Speaker: Krishnaswami Alladi, Univeristy of Florida
Title: Some new companions to Euler's pentagonal numbers theorem
Abstract:
We will deduce two new companions to Euler's celebrated
Pentagonal numbers theorem from partial theta identiities of
Ramanujan and Andrews. These companions are acttually stronger
in the sense that they can be refined by the introduction of a
parameter a. The cancellation by parity split is just as strong
as in Euler's theorem even with the parameter a, but for these
companions the role of the pentagonal numbers is replaced by the
squares. It is amazing that even though the weights in the two
companions are different, their sums are the same, and so the
cancellation and the resulting lacunarity are identical.
Finally, from another identity in Ramanujan's Lost Notebook, we
will deduce one more companion to Euler's theorem, this one
involving twice the pentagonal numbers. We will show how these
companions are connected to various fundamental results in the
theory of partitions and q-hypergeometric series. The talk will
be accessible to non-experts.
- published: 14 Oct 2010
- views: 172
Pentagon with Oranges | Kannada | Fun with Maths
- Order: Reorder
- Duration: 4:58
- Updated: 21 Feb 2015
- views: 114
We arranged these oranges in triangles and squares, can we go to higher orders.
Why not? We can arrange oranges in pentagons and then we can discover the whole ...
We arranged these oranges in triangles and squares, can we go to higher orders.
Why not? We can arrange oranges in pentagons and then we can discover the whole world of pentagonal numbers.
Place an orange and consider it be a pentagon of side 1. Place 4 more oranges to make a pentagon of size 2. The total number of oranges in size 2 pentagon will be 5. Now make a pentagon of size 3. For this you will need 7 more oranges.
For size2 we needed 1 + 4
For size 3 we will need 1 + 4 + 7 = 12
Now make an even larger pentagon of size 4.
For size 4 we will need 1 + 4 + 7 + 10 = 22. So the 4th pentagonal number is 22.
Finally, let’s make a pentagon on size 5. Each of its 5 sides will have five oranges each.
From size 4 pentagons to make size 5 pentagons we will need 13 oranges more.
From size 1 to size 2 we need 3 oranges
From size 2 to size 3 we need 3 more oranges
From size 3 to size 4 we need 3 more oranges
From size 4 to size 5 we need 3 more oranges
These numbers 1, 5, 12, 22 and 35 are called pentagonal numbers and they fit the formula (n) (3n-1)/2 This work was supported by IUCAA and Tata Trust. This film was made by Ashok Rupner
wn.com/Pentagon With Oranges | Kannada | Fun With Maths
We arranged these oranges in triangles and squares, can we go to higher orders.
Why not? We can arrange oranges in pentagons and then we can discover the whole world of pentagonal numbers.
Place an orange and consider it be a pentagon of side 1. Place 4 more oranges to make a pentagon of size 2. The total number of oranges in size 2 pentagon will be 5. Now make a pentagon of size 3. For this you will need 7 more oranges.
For size2 we needed 1 + 4
For size 3 we will need 1 + 4 + 7 = 12
Now make an even larger pentagon of size 4.
For size 4 we will need 1 + 4 + 7 + 10 = 22. So the 4th pentagonal number is 22.
Finally, let’s make a pentagon on size 5. Each of its 5 sides will have five oranges each.
From size 4 pentagons to make size 5 pentagons we will need 13 oranges more.
From size 1 to size 2 we need 3 oranges
From size 2 to size 3 we need 3 more oranges
From size 3 to size 4 we need 3 more oranges
From size 4 to size 5 we need 3 more oranges
These numbers 1, 5, 12, 22 and 35 are called pentagonal numbers and they fit the formula (n) (3n-1)/2 This work was supported by IUCAA and Tata Trust. This film was made by Ashok Rupner
- published: 21 Feb 2015
- views: 114
-
Lecture 9 . Enumerative Combinatorics (Federico Ardila)
We prove several partition identities, including Euler's pentagonal number theorem. Lecture notes at: http://math.sfsu.edu/federico/ec.html San Francisco State University (San Francisco, USA) Universidad de Los Andes (Bogota, Colombia) Fall 2013 Partially supported by: US National Science Foundation CAREER Award DMS-0956178 US National Science Foundation Grant DMS-0801075 SFSU-Colombia Combinatorics Initiative. -
John Baez on the number 5
This ain't Sesame Street. The Rankin Lectures 2008, My Favorite Numbers, were given by John Baez of the University of California at Riverside. Baez is well-known for, among other things, his long-running web column This Week's Finds in Mathematical Physics and the research blog The n-Category Café. Different numbers have different personalities. The number 5 is quirky and intriguing, thanks in large part to its relation with the golden ratio, the "most irrational" of irrational numbers. The plane cannot be tiled with regular pentagons, but there exist quasiperiodic planar patterns with pentagonal symmetry of a statistical nature, first discovered by Islamic artists in the 1600s, later rediscovered by the mathematician Roger Penrose in the 1970s, and found in nature in 1984. The Greek ... -
How to solve a megaminx
This a tutorial on how to solve a Megaminx, which is a 12 sided rubix puzzle. Most of the algorithms are the same as a 3X3X3. The Megaminx is a dodecahedron-shaped puzzle similar to the Rubik's Cube. It has a total of 50 movable pieces to rearrange, compared to the 20 of the Rubik's cube. Algorithms: U, R, Ui, Ri, Ui, Fi, U, F Ui, Fi, U, F, U, R, Ui, Ri F,R,U,Ri,Ui,Fi R, U, Ri, U, R, UUU, Ri or R, U, Ri, U, R, Ui Ui, Ri same thing Ui, Ri, U, R Ri, Di, R, D and after that either Di, Ri, D, R or Ri, Di, R, D -
MathHistory29: Combinatorics
We give a brief historical introduction to the vibrant modern theory of combinatorics, concentrating on examples coming from counting problems, graph theory and generating functions. In particular we look at partitions and Euler's pentagonal theorem, Fibonacci numbers, the Catalan sequence, the Erdos Szekeres theorem, Ramsey theory and the Kirkman Schoolgirls problem. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwild... -
First Contact Radio 9/17/14 - Esoteric Science, UFOs, US Constitution, Atlantis, Daily Meditation
First Contact Radio 9/17/14 Show #1230 hosted by Joshua Poet COSMIC WEATHER Astrology http://www.mooncatsastrology.com/calendar/9-14.htm Numerology http://www.numerology.com/number-6 Highlights of Tarot http://www.botaineurope.org/index.php?id=17&L;=0 Tree of Life http://www.bota.org/images/treeclr-7.jpg Moon Phase http://www.calculatorcat.com/moon_phases/phasenow.php This Week’s Sky at a Glance, September 12–20 http://www.skyandtelescope.com/observing/weeks-sky-glance-september-1220/ Mayan Oracle http://www.starroot.com/cgi/daycalc.pl Spaceweather.com http://www.spaceweather.com Jewish Calendar http://www.chabad.org/calendar/view/month.htm UFO NEWS Fast UFOs filmed over Mexico 11-Sep-2014 http://www.latest-ufo-sightings.net/2014/09/fast-ufos-filmed-mexico-11-sep-2014.html Multip... -
LSU Number Theory Lecture 20 primitive roots
-
Ep. 173 - Rent a Gaijin
http://badcommunicationjapan.com - Coming up on this week's show we talk about an exam taking robot, the new rent a 'gaijin' service, cats and sightseeing, the resignation of Osaka Mayor Hashimoto, a record high number of foreign employees and pentagonal oranges that will help you pass your next exam! All that and more on this week's Bad Communication! Exam Taking Robot [Telegraph] http://www.telegraph.co.uk/news/worldnews/asia/japan/10474490/Japanese-researchers-develop-exam-taking-robot.html Rent a Gaijin [Tofugu] http://www.tofugu.com/2014/01/24/rent-a-gaijin-for-all-your-temporary-gaijin-needs/ Cats are the Cutest Guides to Japan [Kotaku] http://kotaku.com/cats-are-the-cutest-guides-to-japan-1510546846 Osaka Mayor Hashimoto to Resign [News on Japan] http://newsonjapan.com/html/news... -
Quadratic residues: The Legendre symbol
-
-
A Case Study In Early 21st-Century Mathematical Narrow-Mindedness Part 1
Date: February 23, 2012 Speaker: Doron Zeilberger, Rutgers University Title: A Case Study In Early 21st-Century Mathematical Narrow-Mindedness: How a "Non-Rigorous", but ABSOLUTELY CERTAIN Disproof of a 45-Year Old Conjecture Made by One of the Greatest Number Theorists of the 20th Century Got Rejected By Three Journals Abstract: I will tell the sad (but funny!) story how the beautiful refutation by Drew Sills and myself, of a long-standing conjecture by Hans Rademacher, got rejected by three journals. First we (naively!) submitted it to George Andrews, Rademacher's "Benjamin" (see the bottom of this page) for the Proceedings of the National Academy of Science, who rejected it because it was "only experimental". Then we submitted it to Mathematics of Computation (see its editoria...
Lecture 9 . Enumerative Combinatorics (Federico Ardila)
- Order: Reorder
- Duration: 76:01
- Updated: 03 Oct 2013
- views: 901
We prove several partition identities, including Euler's pentagonal number theorem.
Lecture notes at: http://math.sfsu.edu/federico/ec.html
San Francisco Sta...
We prove several partition identities, including Euler's pentagonal number theorem.
Lecture notes at: http://math.sfsu.edu/federico/ec.html
San Francisco State University (San Francisco, USA)
Universidad de Los Andes (Bogota, Colombia)
Fall 2013
Partially supported by:
US National Science Foundation CAREER Award DMS-0956178
US National Science Foundation Grant DMS-0801075
SFSU-Colombia Combinatorics Initiative.
wn.com/Lecture 9 . Enumerative Combinatorics (Federico Ardila)
We prove several partition identities, including Euler's pentagonal number theorem.
Lecture notes at: http://math.sfsu.edu/federico/ec.html
San Francisco State University (San Francisco, USA)
Universidad de Los Andes (Bogota, Colombia)
Fall 2013
Partially supported by:
US National Science Foundation CAREER Award DMS-0956178
US National Science Foundation Grant DMS-0801075
SFSU-Colombia Combinatorics Initiative.
- published: 03 Oct 2013
- views: 901
John Baez on the number 5
- Order: Reorder
- Duration: 63:57
- Updated: 16 May 2012
- views: 18996
This ain't Sesame Street.
The Rankin Lectures 2008, My Favorite Numbers, were given by John Baez of the University of California at Riverside.
Baez is well-kn...
This ain't Sesame Street.
The Rankin Lectures 2008, My Favorite Numbers, were given by John Baez of the University of California at Riverside.
Baez is well-known for, among other things, his long-running web column This Week's Finds in Mathematical Physics and the research blog The n-Category Café.
Different numbers have different personalities. The number 5 is quirky and intriguing, thanks in large part to its relation with the golden ratio, the "most irrational" of irrational numbers. The plane cannot be tiled with regular pentagons, but there exist quasiperiodic planar patterns with pentagonal symmetry of a statistical nature, first discovered by Islamic artists in the 1600s, later rediscovered by the mathematician Roger Penrose in the 1970s, and found in nature in 1984.
The Greek fascination with the golden ratio is probably tied to the dodecahedron. Much later, the symmetry group of the dodecahedron was found to give rise to a 4-dimensional regular polytope, the 120-cell, which in turn gives rise to the Poincaré homology sphere and the root system of the exceptional Lie group E8. So, a wealth of exceptional objects arise from the quirky nature of 5-fold symmetry.
Text taken from http://www.maths.gla.ac.uk/~tl/rankin/
wn.com/John Baez On The Number 5
This ain't Sesame Street.
The Rankin Lectures 2008, My Favorite Numbers, were given by John Baez of the University of California at Riverside.
Baez is well-known for, among other things, his long-running web column This Week's Finds in Mathematical Physics and the research blog The n-Category Café.
Different numbers have different personalities. The number 5 is quirky and intriguing, thanks in large part to its relation with the golden ratio, the "most irrational" of irrational numbers. The plane cannot be tiled with regular pentagons, but there exist quasiperiodic planar patterns with pentagonal symmetry of a statistical nature, first discovered by Islamic artists in the 1600s, later rediscovered by the mathematician Roger Penrose in the 1970s, and found in nature in 1984.
The Greek fascination with the golden ratio is probably tied to the dodecahedron. Much later, the symmetry group of the dodecahedron was found to give rise to a 4-dimensional regular polytope, the 120-cell, which in turn gives rise to the Poincaré homology sphere and the root system of the exceptional Lie group E8. So, a wealth of exceptional objects arise from the quirky nature of 5-fold symmetry.
Text taken from http://www.maths.gla.ac.uk/~tl/rankin/
- published: 16 May 2012
- views: 18996
How to solve a megaminx
- Order: Reorder
- Duration: 27:25
- Updated: 26 Dec 2010
- views: 87275
This a tutorial on how to solve a Megaminx, which is a 12 sided rubix puzzle.
Most of the algorithms are the same as a 3X3X3.
The Megaminx is a dodecahedron...
This a tutorial on how to solve a Megaminx, which is a 12 sided rubix puzzle.
Most of the algorithms are the same as a 3X3X3.
The Megaminx is a dodecahedron-shaped puzzle similar to the Rubik's Cube.
It has a total of 50 movable pieces to rearrange, compared to the 20 of the Rubik's cube.
Algorithms:
U, R, Ui, Ri, Ui, Fi, U, F
Ui, Fi, U, F, U, R, Ui, Ri
F,R,U,Ri,Ui,Fi
R, U, Ri, U, R, UUU, Ri or R, U, Ri, U, R, Ui Ui, Ri same thing
Ui, Ri, U, R
Ri, Di, R, D and after that either Di, Ri, D, R or Ri, Di, R, D
wn.com/How To Solve A Megaminx
This a tutorial on how to solve a Megaminx, which is a 12 sided rubix puzzle.
Most of the algorithms are the same as a 3X3X3.
The Megaminx is a dodecahedron-shaped puzzle similar to the Rubik's Cube.
It has a total of 50 movable pieces to rearrange, compared to the 20 of the Rubik's cube.
Algorithms:
U, R, Ui, Ri, Ui, Fi, U, F
Ui, Fi, U, F, U, R, Ui, Ri
F,R,U,Ri,Ui,Fi
R, U, Ri, U, R, UUU, Ri or R, U, Ri, U, R, Ui Ui, Ri same thing
Ui, Ri, U, R
Ri, Di, R, D and after that either Di, Ri, D, R or Ri, Di, R, D
- published: 26 Dec 2010
- views: 87275
MathHistory29: Combinatorics
- Order: Reorder
- Duration: 41:01
- Updated: 03 Jun 2015
- views: 19370
We give a brief historical introduction to the vibrant modern theory of combinatorics, concentrating on examples coming from counting problems, graph theory and...
We give a brief historical introduction to the vibrant modern theory of combinatorics, concentrating on examples coming from counting problems, graph theory and generating functions. In particular we look at partitions and Euler's pentagonal theorem, Fibonacci numbers, the Catalan sequence, the Erdos Szekeres theorem, Ramsey theory and the Kirkman Schoolgirls problem.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .
wn.com/Mathhistory29 Combinatorics
We give a brief historical introduction to the vibrant modern theory of combinatorics, concentrating on examples coming from counting problems, graph theory and generating functions. In particular we look at partitions and Euler's pentagonal theorem, Fibonacci numbers, the Catalan sequence, the Erdos Szekeres theorem, Ramsey theory and the Kirkman Schoolgirls problem.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .
- published: 03 Jun 2015
- views: 19370
First Contact Radio 9/17/14 - Esoteric Science, UFOs, US Constitution, Atlantis, Daily Meditation
- Order: Reorder
- Duration: 63:27
- Updated: 17 Sep 2014
- views: 131
First Contact Radio 9/17/14 Show #1230 hosted by Joshua Poet
COSMIC WEATHER
Astrology
http://www.mooncatsastrology.com/calendar/9-14.htm
Numerology
http://www...
First Contact Radio 9/17/14 Show #1230 hosted by Joshua Poet
COSMIC WEATHER
Astrology
http://www.mooncatsastrology.com/calendar/9-14.htm
Numerology
http://www.numerology.com/number-6
Highlights of Tarot
http://www.botaineurope.org/index.php?id=17&L;=0
Tree of Life
http://www.bota.org/images/treeclr-7.jpg
Moon Phase
http://www.calculatorcat.com/moon_phases/phasenow.php
This Week’s Sky at a Glance, September 12–20
http://www.skyandtelescope.com/observing/weeks-sky-glance-september-1220/
Mayan Oracle
http://www.starroot.com/cgi/daycalc.pl
Spaceweather.com
http://www.spaceweather.com
Jewish Calendar
http://www.chabad.org/calendar/view/month.htm
UFO NEWS
Fast UFOs filmed over Mexico 11-Sep-2014
http://www.latest-ufo-sightings.net/2014/09/fast-ufos-filmed-mexico-11-sep-2014.html
Multiple Witnesses Film White UFO As It Hovers Over New Mexico
http://www.educatinghumanity.com/2014/09/ufo-reported-filmed-new-mexico.html
Giant UFOs near the Sun on September 16, 2014
http://www.ufosightingsdaily.com/2014/09/giant-ufos-near-sun-on-september-16.html
Witnesses State Low Flying UFO in Florida Caused Power Outage
http://www.educatinghumanity.com/2014/09/ufo-florida-caused-power-outage.html
Triangle UFO Hovers Over Lithuania
http://www.educatinghumanity.com/2014/09/triangle-ufo-video-lithuania.html
President Eisenhower had three secret meetings with Aliens From Venus - 2 Witness Speak Out!
http://www.ufosightingsdaily.com/2012/02/president-eisenhower-had-three-secret.html
A Holy Stranger in the Pentagonal Lodge
http://www.bibliotecapleyades.net/bb/stranges.htm
Daily Stories
Teaching With Documents: Observing Constitution Day
http://www.archives.gov/education/lessons/constitution-day/
Constitution of the United States
http://www.archives.gov/exhibits/charters/constitution_transcript.html
Underwater cemetery looks like the ruins of the lost city of Atlantis
http://io9.com/underwater-cemetery-looks-like-the-ruins-of-the-lost-ci-1505790815
Has the real lost city of Atlantis finally been found... buried under mud flats in Spain?
http://www.dailymail.co.uk/sciencetech/article-1365824/Has-real-lost-city-Atlantis-finally--buried-mud-flats-Spain.html
Lost city of Atlantis, swamped by tsunami, may be found
http://www.reuters.com/article/2011/03/12/us-tsunami-atlantis-idUSTRE72B2JR20110312
Scientists Admit There Is a Second, Secret DNA Code Which Controls Genes
http://www.in5d.com/scientists-2nd-dna-code.html
Daily Affirmations 17 September 2014
http://www.everydayaffirmations.org/2014/09/daily-affirmations-17-september-2014.html
Arcturians The Illuminated Ones September-13-2014
https://www.youtube.com/watch?v=rEEZbe31l8c&index;=11&list;=UUdD1ICsaDIZUA8qK24pxBig
FREE Meditation Music "Reflections"
http://www.youtube.com/watch?v=B1S1nfVu9bs
wn.com/First Contact Radio 9 17 14 Esoteric Science, Ufos, US Constitution, Atlantis, Daily Meditation
First Contact Radio 9/17/14 Show #1230 hosted by Joshua Poet
COSMIC WEATHER
Astrology
http://www.mooncatsastrology.com/calendar/9-14.htm
Numerology
http://www.numerology.com/number-6
Highlights of Tarot
http://www.botaineurope.org/index.php?id=17&L;=0
Tree of Life
http://www.bota.org/images/treeclr-7.jpg
Moon Phase
http://www.calculatorcat.com/moon_phases/phasenow.php
This Week’s Sky at a Glance, September 12–20
http://www.skyandtelescope.com/observing/weeks-sky-glance-september-1220/
Mayan Oracle
http://www.starroot.com/cgi/daycalc.pl
Spaceweather.com
http://www.spaceweather.com
Jewish Calendar
http://www.chabad.org/calendar/view/month.htm
UFO NEWS
Fast UFOs filmed over Mexico 11-Sep-2014
http://www.latest-ufo-sightings.net/2014/09/fast-ufos-filmed-mexico-11-sep-2014.html
Multiple Witnesses Film White UFO As It Hovers Over New Mexico
http://www.educatinghumanity.com/2014/09/ufo-reported-filmed-new-mexico.html
Giant UFOs near the Sun on September 16, 2014
http://www.ufosightingsdaily.com/2014/09/giant-ufos-near-sun-on-september-16.html
Witnesses State Low Flying UFO in Florida Caused Power Outage
http://www.educatinghumanity.com/2014/09/ufo-florida-caused-power-outage.html
Triangle UFO Hovers Over Lithuania
http://www.educatinghumanity.com/2014/09/triangle-ufo-video-lithuania.html
President Eisenhower had three secret meetings with Aliens From Venus - 2 Witness Speak Out!
http://www.ufosightingsdaily.com/2012/02/president-eisenhower-had-three-secret.html
A Holy Stranger in the Pentagonal Lodge
http://www.bibliotecapleyades.net/bb/stranges.htm
Daily Stories
Teaching With Documents: Observing Constitution Day
http://www.archives.gov/education/lessons/constitution-day/
Constitution of the United States
http://www.archives.gov/exhibits/charters/constitution_transcript.html
Underwater cemetery looks like the ruins of the lost city of Atlantis
http://io9.com/underwater-cemetery-looks-like-the-ruins-of-the-lost-ci-1505790815
Has the real lost city of Atlantis finally been found... buried under mud flats in Spain?
http://www.dailymail.co.uk/sciencetech/article-1365824/Has-real-lost-city-Atlantis-finally--buried-mud-flats-Spain.html
Lost city of Atlantis, swamped by tsunami, may be found
http://www.reuters.com/article/2011/03/12/us-tsunami-atlantis-idUSTRE72B2JR20110312
Scientists Admit There Is a Second, Secret DNA Code Which Controls Genes
http://www.in5d.com/scientists-2nd-dna-code.html
Daily Affirmations 17 September 2014
http://www.everydayaffirmations.org/2014/09/daily-affirmations-17-september-2014.html
Arcturians The Illuminated Ones September-13-2014
https://www.youtube.com/watch?v=rEEZbe31l8c&index;=11&list;=UUdD1ICsaDIZUA8qK24pxBig
FREE Meditation Music "Reflections"
http://www.youtube.com/watch?v=B1S1nfVu9bs
- published: 17 Sep 2014
- views: 131
LSU Number Theory Lecture 20 primitive roots
- Order: Reorder
- Duration: 59:23
- Updated: 21 Apr 2016
- views: 120
- published: 21 Apr 2016
- views: 120
Ep. 173 - Rent a Gaijin
- Order: Reorder
- Duration: 35:37
- Updated: 03 Feb 2014
- views: 328
http://badcommunicationjapan.com - Coming up on this week's show we talk about an exam taking robot, the new rent a 'gaijin' service, cats and sightseeing, the ...
http://badcommunicationjapan.com - Coming up on this week's show we talk about an exam taking robot, the new rent a 'gaijin' service, cats and sightseeing, the resignation of Osaka Mayor Hashimoto, a record high number of foreign employees and pentagonal oranges that will help you pass your next exam! All that and more on this week's Bad Communication!
Exam Taking Robot [Telegraph]
http://www.telegraph.co.uk/news/worldnews/asia/japan/10474490/Japanese-researchers-develop-exam-taking-robot.html
Rent a Gaijin [Tofugu]
http://www.tofugu.com/2014/01/24/rent-a-gaijin-for-all-your-temporary-gaijin-needs/
Cats are the Cutest Guides to Japan [Kotaku]
http://kotaku.com/cats-are-the-cutest-guides-to-japan-1510546846
Osaka Mayor Hashimoto to Resign [News on Japan]
http://newsonjapan.com/html/newsdesk/article/106463.php
Japan Employs Record-high 718,000 Foreigners in 2013 [Asahi]
http://ajw.asahi.com/article/economy/business/AJ201402010030
Pentagonal Oranges [Rocketnews24]
http://en.rocketnews24.com/2014/02/02/ensure-your-fruit-never-rolls-away-with-pentagon-oranges/
***Show Notes***
Our full episodes go live every Tuesday and can be found on our blog and on YouTube. Our show is also filmed live every Sunday night at 8:00pm EST, 5:00pm PST and Monday morning at 10:00am here in Japan. Watch us live on YouTube and say hello in chat!
wn.com/Ep. 173 Rent A Gaijin
http://badcommunicationjapan.com - Coming up on this week's show we talk about an exam taking robot, the new rent a 'gaijin' service, cats and sightseeing, the resignation of Osaka Mayor Hashimoto, a record high number of foreign employees and pentagonal oranges that will help you pass your next exam! All that and more on this week's Bad Communication!
Exam Taking Robot [Telegraph]
http://www.telegraph.co.uk/news/worldnews/asia/japan/10474490/Japanese-researchers-develop-exam-taking-robot.html
Rent a Gaijin [Tofugu]
http://www.tofugu.com/2014/01/24/rent-a-gaijin-for-all-your-temporary-gaijin-needs/
Cats are the Cutest Guides to Japan [Kotaku]
http://kotaku.com/cats-are-the-cutest-guides-to-japan-1510546846
Osaka Mayor Hashimoto to Resign [News on Japan]
http://newsonjapan.com/html/newsdesk/article/106463.php
Japan Employs Record-high 718,000 Foreigners in 2013 [Asahi]
http://ajw.asahi.com/article/economy/business/AJ201402010030
Pentagonal Oranges [Rocketnews24]
http://en.rocketnews24.com/2014/02/02/ensure-your-fruit-never-rolls-away-with-pentagon-oranges/
***Show Notes***
Our full episodes go live every Tuesday and can be found on our blog and on YouTube. Our show is also filmed live every Sunday night at 8:00pm EST, 5:00pm PST and Monday morning at 10:00am here in Japan. Watch us live on YouTube and say hello in chat!
- published: 03 Feb 2014
- views: 328
Quadratic residues: The Legendre symbol
- Order: Reorder
- Duration: 46:26
- Updated: 15 Feb 2016
- views: 368
- published: 15 Feb 2016
- views: 368
William and Mary Math-Physics Seminar 8.1.07
- Order: Reorder
- Duration: 69:16
- Updated: 23 Apr 2011
- views: 281
This week Professor Zobin discusses the relationship between the mixed volume of the Newton polyhedra and the number of nonzero solutions of a system of polynom...
This week Professor Zobin discusses the relationship between the mixed volume of the Newton polyhedra and the number of nonzero solutions of a system of polynomial equations.
Speaker: Nahum Zobin
wn.com/William And Mary Math Physics Seminar 8.1.07
A Case Study In Early 21st-Century Mathematical Narrow-Mindedness Part 1
- Order: Reorder
- Duration: 30:19
- Updated: 23 Feb 2012
- views: 2105
Date: February 23, 2012
Speaker: Doron Zeilberger, Rutgers University
Title: A Case Study In Early 21st-Century Mathematical Narrow-Mindedness: How a "Non-Rigor...
Date: February 23, 2012
Speaker: Doron Zeilberger, Rutgers University
Title: A Case Study In Early 21st-Century Mathematical Narrow-Mindedness: How a "Non-Rigorous", but ABSOLUTELY CERTAIN Disproof of a 45-Year Old Conjecture Made by One of the Greatest Number Theorists of the 20th Century Got Rejected By Three Journals
Abstract:
I will tell the sad (but funny!) story how the beautiful refutation by Drew Sills and myself, of a long-standing conjecture by Hans Rademacher, got rejected by three journals. First we (naively!) submitted it to George Andrews, Rademacher's "Benjamin" (see the bottom of this page) for the Proceedings of the National Academy of Science, who rejected it because it was "only experimental". Then we submitted it to Mathematics of Computation (see its editorial board), who rejected it because, while "interesting", it "does not meet the `high' standards of the journal, since it is 'only computational'". Finally we submitted it to the journal Experimental Mathematics (see its editorial board), that when it was founded, was a breath of fresh air, but in recent times, under the current editor-in-chief, has deterioated into "J. of Algorithmic Algebraic Geometry", who once again rejected our masterpiece, ostensibly because it "does not ring with enduring significance" (whatever that means), but most probably because it was "only experimental".
wn.com/A Case Study In Early 21St Century Mathematical Narrow Mindedness Part 1
Date: February 23, 2012
Speaker: Doron Zeilberger, Rutgers University
Title: A Case Study In Early 21st-Century Mathematical Narrow-Mindedness: How a "Non-Rigorous", but ABSOLUTELY CERTAIN Disproof of a 45-Year Old Conjecture Made by One of the Greatest Number Theorists of the 20th Century Got Rejected By Three Journals
Abstract:
I will tell the sad (but funny!) story how the beautiful refutation by Drew Sills and myself, of a long-standing conjecture by Hans Rademacher, got rejected by three journals. First we (naively!) submitted it to George Andrews, Rademacher's "Benjamin" (see the bottom of this page) for the Proceedings of the National Academy of Science, who rejected it because it was "only experimental". Then we submitted it to Mathematics of Computation (see its editorial board), who rejected it because, while "interesting", it "does not meet the `high' standards of the journal, since it is 'only computational'". Finally we submitted it to the journal Experimental Mathematics (see its editorial board), that when it was founded, was a breath of fresh air, but in recent times, under the current editor-in-chief, has deterioated into "J. of Algorithmic Algebraic Geometry", who once again rejected our masterpiece, ostensibly because it "does not ring with enduring significance" (whatever that means), but most probably because it was "only experimental".
- published: 23 Feb 2012
- views: 2105
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12:15
Pentagonal numbers
math 211 HW 1.2
published: 15 Oct 2014
Pentagonal numbers
6:18
Pentagonal Numbers
Try this on your own....
The figures above show the first four pentagonal numbers. What is...
published: 02 Sep 2012
Pentagonal Numbers
Pentagonal Numbers
- Report rights infringement
- published: 02 Sep 2012
- views: 3694
10:05
MathFoundations52: Leonhard Euler and Pentagonal numbers
Leonhard Euler was the greatest mathematician of modern times. His work on pentagonal numb...
published: 27 Apr 2010
MathFoundations52: Leonhard Euler and Pentagonal numbers
MathFoundations52: Leonhard Euler and Pentagonal numbers
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- published: 27 Apr 2010
- views: 5700
9:54
MathFoundations51: More patterns with algebra
The patterns formed by triangular numbers and square numbers have generalizations in diffe...
published: 26 Apr 2010
MathFoundations51: More patterns with algebra
MathFoundations51: More patterns with algebra
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- published: 26 Apr 2010
- views: 5445
4:30
Java 6.01 Pentagonal Numbers
Introduction to Java Comprehensive 10th Edition
Chapter 6 Methods
Programming Exercise 6.0...
published: 16 Feb 2016
Java 6.01 Pentagonal Numbers
Java 6.01 Pentagonal Numbers
- Report rights infringement
- published: 16 Feb 2016
- views: 50
6:30
Pentagonal number
Pentagonal number
A pentagonal number is a figurate number that extends the concept of ...
published: 22 Jan 2016
Pentagonal number
Pentagonal number
- Report rights infringement
- published: 22 Jan 2016
- views: 43
6:02
Some new companions to Euler's pentagonal numbers theorem part1
Date: September 23, 2010
Speaker: Krishnaswami Alladi, Univeristy of Florida
Title: Some...
published: 13 Oct 2010
Some new companions to Euler's pentagonal numbers theorem part1
Some new companions to Euler's pentagonal numbers theorem part1
- Report rights infringement
- published: 13 Oct 2010
- views: 658
6:02
Some new companions to Euler's pentagonal numbers theorem part2
Date: September 23, 2010
Speaker: Krishnaswami Alladi, Univeristy of Florida
Title: Some n...
published: 13 Oct 2010
Some new companions to Euler's pentagonal numbers theorem part2
Some new companions to Euler's pentagonal numbers theorem part2
- Report rights infringement
- published: 13 Oct 2010
- views: 253
6:01
Some new companions to Euler's pentagonal numbers theorem part3
Date: September 23, 2010
Speaker: Krishnaswami Alladi, Univeristy of Florida
Title: Some n...
published: 14 Oct 2010
Some new companions to Euler's pentagonal numbers theorem part3
Some new companions to Euler's pentagonal numbers theorem part3
- Report rights infringement
- published: 14 Oct 2010
- views: 172
4:58
Pentagon with Oranges | Kannada | Fun with Maths
We arranged these oranges in triangles and squares, can we go to higher orders.
Why not? W...
published: 21 Feb 2015
Pentagon with Oranges | Kannada | Fun with Maths
Pentagon with Oranges | Kannada | Fun with Maths
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- published: 21 Feb 2015
- views: 114
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76:01
Lecture 9 . Enumerative Combinatorics (Federico Ardila)
We prove several partition identities, including Euler's pentagonal number theorem.
Lect...
published: 03 Oct 2013
Lecture 9 . Enumerative Combinatorics (Federico Ardila)
Lecture 9 . Enumerative Combinatorics (Federico Ardila)
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- published: 03 Oct 2013
- views: 901
63:57
John Baez on the number 5
This ain't Sesame Street.
The Rankin Lectures 2008, My Favorite Numbers, were given by Jo...
published: 16 May 2012
John Baez on the number 5
John Baez on the number 5
- Report rights infringement
- published: 16 May 2012
- views: 18996
27:25
How to solve a megaminx
This a tutorial on how to solve a Megaminx, which is a 12 sided rubix puzzle.
Most of th...
published: 26 Dec 2010
How to solve a megaminx
How to solve a megaminx
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- published: 26 Dec 2010
- views: 87275
41:01
MathHistory29: Combinatorics
We give a brief historical introduction to the vibrant modern theory of combinatorics, con...
published: 03 Jun 2015
MathHistory29: Combinatorics
MathHistory29: Combinatorics
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- published: 03 Jun 2015
- views: 19370
63:27
First Contact Radio 9/17/14 - Esoteric Science, UFOs, US Constitution, Atlantis, Daily Meditation
First Contact Radio 9/17/14 Show #1230 hosted by Joshua Poet
COSMIC WEATHER
Astrology
htt...
published: 17 Sep 2014
First Contact Radio 9/17/14 - Esoteric Science, UFOs, US Constitution, Atlantis, Daily Meditation
First Contact Radio 9/17/14 - Esoteric Science, UFOs, US Constitution, Atlantis, Daily Meditation
- Report rights infringement
- published: 17 Sep 2014
- views: 131
59:23
LSU Number Theory Lecture 20 primitive roots
published: 21 Apr 2016
LSU Number Theory Lecture 20 primitive roots
LSU Number Theory Lecture 20 primitive roots
- Report rights infringement
- published: 21 Apr 2016
- views: 120
35:37
Ep. 173 - Rent a Gaijin
http://badcommunicationjapan.com - Coming up on this week's show we talk about an exam tak...
published: 03 Feb 2014
Ep. 173 - Rent a Gaijin
Ep. 173 - Rent a Gaijin
- Report rights infringement
- published: 03 Feb 2014
- views: 328
46:26
Quadratic residues: The Legendre symbol
published: 15 Feb 2016
Quadratic residues: The Legendre symbol
Quadratic residues: The Legendre symbol
- Report rights infringement
- published: 15 Feb 2016
- views: 368
69:16
William and Mary Math-Physics Seminar 8.1.07
This week Professor Zobin discusses the relationship between the mixed volume of the Newto...
published: 23 Apr 2011
William and Mary Math-Physics Seminar 8.1.07
William and Mary Math-Physics Seminar 8.1.07
- Report rights infringement
- published: 23 Apr 2011
- views: 281
30:19
A Case Study In Early 21st-Century Mathematical Narrow-Mindedness Part 1
Date: February 23, 2012
Speaker: Doron Zeilberger, Rutgers University
Title: A Case Study ...
published: 23 Feb 2012
A Case Study In Early 21st-Century Mathematical Narrow-Mindedness Part 1
A Case Study In Early 21st-Century Mathematical Narrow-Mindedness Part 1
- Report rights infringement
- published: 23 Feb 2012
- views: 2105
Lecture 9 . Enumerative Combinatorics (Federico A...
John Baez on the number 5...
How to solve a megaminx...
MathHistory29: Combinatorics...
First Contact Radio 9/17/14 - Esoteric Science, UF...
LSU Number Theory Lecture 20 primitive roots...
Ep. 173 - Rent a Gaijin...
Quadratic residues: The Legendre symbol...
William and Mary Math-Physics Seminar 8.1.07...
A Case Study In Early 21st-Century Mathematical Na...
photo: AP / M. Jameel
Honor Killing: Pakistani Social Media Star Strangled to Death by brother
Edit Voa News 16 Jul 2016
Hundreds of women are murdered in Pakistan for honor every year. On Friday, Pakistani model and social media celebrity Qandeel Balock was killed by one of her brothers, police said. Balock was spending the Ed holiday with her family and had travelled from Karachi to Muzaffarabad village in central Punjab province. She was asleep, police said, when one of her six brothers strangled Baloch to death in the family’s home ... ....
photo: AP / Selahattin Sevi, File
Who is Fethullah Gulen, the man blamed for coup attempt in Turkey?
Edit CNN 16 Jul 2016
(CNN)Was a plan to overthrow Turkey's government really hatched behind a gated compound in a small, leafy Pennsylvania town, or is that merely a smoke screen?. In the throes of a military coup attempt, Turkey's embattled president, Recep Tayyip Erdogan, pointed the finger of blame squarely at his bitter rival. Fethullah Gulen ... It's this division that's destabilizing one of America's most important allies in the Middle East ... Read More ... ....
photo: AP / Ismail Coskun/IHA via AP
What happened in Turkey? Everything we know about military coup attempt to overthrow Erdogan
Edit The Independent 16 Jul 2016
At least 190 people have been killed and more than 1,000 have been wounded in an attempted military coup in Turkey. After a night of chaotic and confusing developments, with tanks appearing on the streets and warplanes circling above the capital Ankara, it appears that President Recep Tayyip Erdogan has regained control – but the situation remains confused and uncertain. Here is what we know so far.. ... ... ... ... ... ... ... ... ... ... ... ... ... .....
photo: AP Photo/Christian Alminana
Nice Terrorist Attack: At Least 77 Dead, Police Kill Suspect
Edit WorldNews.com 15 Jul 2016
... the horror of bodies strewn about the beach that minutes previously had a happy crowd.Nice Matin journalist Damien Allemand was at the fireworks display, explaining how the crowd was just getting up to leave when the chaos began, "An enormous white truck came along at a crazy speed, turning the wheel to mow down the maximum number of people....
photo: AP / Murat Cetinmuhurdar
Turkish coup attempt largely over, says government
Edit The Irish Times 16 Jul 2016
Turkey’s leaders said they have largely quelled an attempted military coup, after army officers claimed to have seized power in the country on Friday night. The coup appeared to crumble in the early hours of Saturday after crowds answered president Tayyip Erdogan’s earlier call to take to the streets to support him ... Soldiers took control of the airport soon after Mr Erdogan had landed ... VIDEO from #Ankara ... Lawmakers in hiding ... Agencies ... ....
« back to news headlines
Obama urges rule of law in Turkey, US warns of damage to relations
Edit Indian Express 17 Jul 2016
US officials were working with Turkish officials to resume air operations quickly, the Pentagon said ... The Incirlik air base near Adana in the southeast of the country was running on internal power sources after a loss of commercial power to the base, the Pentagon said. “US officials are working with the Turks to resume air operations there as soon as possible,” said Pentagon spokesman Peter Cook....
The Pentagon is developing cyber warfare tools to fight ISIS
Edit Engadget 17 Jul 2016
US Cyber Command chief Adm. Michael S. Rogers has created a dedicated unit tasked with developing a suite of malware and digital weapons that can be used to wage (a digital) war against ISIS. The Pentagon originally gave Cyber Command the daunting ta... ....
US support of Afghans could be game-changer: Commander
Edit Indian Express 17 Jul 2016
3 }); }); ... “Perceptions of security remain near all-time lows,” a Pentagon report said ... He was referring to suspicions that a significant number of soldiers and police officers who are listed on the rolls are actually phantoms; they are kept on the rolls so their salaries can be collected by corrupt commanders. A Pentagon report to Congress in June said opinion surveys show Afghans feel less secure than at any recent time ... ....
Turkish prez eyes exile in failed coup
Edit Boston Herald 17 Jul 2016
In a televised speech last night, Erdogan called on the U.S ... The Pentagon said it was trying to get permission to resume air operations from the Incirlik air base in southern Turkey, while adjusting mission operations in the meantime ... “The military had been purged a number of times over the past several years,” said Ali Banuazizi, director of Boston College’s Islamic Civilization and Societies Program ... ... ....
US warns citizens of ‘increased threats’ of terrorism in Turkey
Edit Press TV 17 Jul 2016
The US State Department has cautioned American citizens against travel to Turkey in the wake of a coup attempt that left at least 265 dead ... Travel restrictions have also been imposed on US government personnel in southeastern Turkey, it added ... The Pentagon said US officials were working with Turkish authorities to resume air operations out of the base as soon as possible....
14 ‘Pokemon GO’ Memes That Explain the Ongoing Team Feud (Photos)
Edit The Wrap 17 Jul 2016
If you’re finally entering the world of “Pokemon Go” as it enters its second week of pop culture domination, be warned. there’s a war going on, and you will be asked to take a side ... Team Valor, Team Mystic, or Team Instinct ... Each of the three teams uses a color and insignia based on one of the three legendary birds ... Valor’s conquests include the Empire State Building, Disneyland, and the Pentagon ... ....
Drink driving cases rising by the day in Cyberabad
Edit The Times of India 17 Jul 2016
The number of people booked for the offence has not dipped below 1,518 for any month this year. In fact, the total number of drivers who hit the roads after one too many pegs has only been mounting. If the number of drink driving cases in April stood at 1,593 in the Cyberabad belt, it jumped to 1,800 in May and 1,826 in June ... The number of retail outlets in the same area has also increased by 25....
US-Turkish tensions rise after failed coup attempt
Edit Atlanta Journal 17 Jul 2016
U.S.-Turkish tensions escalated Saturday after a quashed coup in Turkey, as the country's leader bluntly demanded the extradition of a U.S.-based cleric he accused of orchestrating the violence. Another senior official directly blamed the United States ... extradition request for "terrorists." ... The Pentagon said it was trying to get permission to resume air operations from the base, while adjusting mission operations in the meantime ... ___ ... ....
Faculty/Staff—Help Us Update the LAVC Directory! (Los Angeles Valley College)
Edit Public Technologies 17 Jul 2016
(Source. Los Angeles Valley College) ... LAVC has an online LAVC Phone/Email Directory that is used by students, faculty, staff and administrators to reach employees at their office phone number and/or email address ... (1) employee's full name,. (2) nickname (if applicable), ... (5) building location with room number. (6) LAVC phone number or voice mail extension,. (7) fax number, ... (9) secondary phone number or email address (if applicable) ... (noodl....
Winning numbers drawn in 'Daily 3 Evening' game
Edit San Francisco Chronicle 17 Jul 2016
SACRAMENTO (AP) _ The winning numbers in Saturday evening's drawing of the California Lottery's "Daily 3 Evening" game were. 6-0-7 (six, zero, seven) ¶ Ticket-holders with all three winning numbers in the order given win the top prize. Lesser amounts are also awarded to ticket-holders with other varying combinations of the winning numbers ... ....
ANNOUNCEMENT (Ministry of Foreign Affairs of the Republic of Macedonia)
Edit Public Technologies 17 Jul 2016
(Source. Ministry of Foreign Affairs of the Republic of Macedonia) Details Published. 16 July 2016. Late last night the Deputy Prime Minister of the Republic of Macedonia and the Minister of Foreign Affairs, Nikola Poposki, spoke on the phone with his Turkish counterpart Mevlüt Çavuşoğlu ... Mobile phone numbers. +905383130343; +905385466691. Landline numbers ... E-mail ... Mobile phone number ... Landline numbers. T ... Mobile phone numbers ... Landline numbers....
Has streaming broken the UK singles chart?
Edit BBC News 17 Jul 2016
On Friday, the star's single notched up a 14th week at number one - meaning he could soon break the Bryan Adams barrier, and become the UK's longest-running chart topper ... It's only the inclusion of streaming data (where 100 plays count as one sale) that has given him a lock on the number one spot ... It would be, I think, unprecedented to take the number one record off the Radio 1 playlist ... "To some extent, the numbers bear that out....
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