- published: 08 Dec 2012
- views: 3307
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Ring Theory: As an application of all previous ideas on rings, we determine the primes in the Euclidean domain of Gaussian integers Z[i]. Not only is the answer somewhat elegant, but it contains a beautiful theorem on prime integers due to Fermat. We finish with examples of factorizations in Z[i].
Each of the 223 frames is a plot of the Gaussian primes within a certain norm. The norm for each frame is determined by the square of prime numbers (in the real integers) in the arithmetic progression 4n+3 starting from n = 0 (p = 3). In other words, the increment is chosen to show the next Gaussian prime on the real/imaginary axis using squares of primes congruent to 3 (mod 4).
The first frame is all the Gaussian primes with norm less than or equal to 3^2. The last frame is all Gaussian primes with norm less than or equal to 3163^2.
The full project report can be found at https://danielhutama.wordpress.com/research/
Created by D. Hutama at McGill University, June 2016
- published: 15 Jun 2016
- views: 461
http://demonstrations.wolfram.com/GaussianPrimeSpirals
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Start a loop with a point having integer coordinates in the complex plane (called a Gaussian integer) and trace a path as follows: ? Move right until a Gaussian prime p is encountered, then turn left 90. ? Continue, always moving straight in the curren...
Contributed by: Joseph O'Rourke and Stan Wagon
Audio created with WolframTones:
http://tones.wolfram.com
- published: 27 Sep 2013
- views: 248
http://demonstrations.wolfram.com/GaussianPrimes/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
The pattern of Gaussian primes in the complex plane.
Contributed by: Stephen Wolfram
- published: 09 Jul 2009
- views: 858
Here I wrap up our thoughts on Chapter 6. We see how Z[i] provides a natural framework to prove Fermat's two square theorem. Most of this is directly from Stillwell, but I tried to add a bit here and there about why Z[i] still supports Division Algorthim, Euclidean Algorithm, Prime Divisor Property and Unique Factorization. To be careful, I would have to write much, much more. But, the point here is not to be super rigorous, the point is to be reasonably rigorous and see how abstraction solves problems.
- published: 02 Mar 2015
- views: 852
Carl Friedrich Gauss one of the greatest mathematicians, is said to have claimed: "Mathematics is the queen of the sciences and number theory is the queen of mathematics." The properties of primes play a crucial part in number theory. An intriguing question is how they are distributed among the other integers. The 19th century saw progress in answering this question with the proof of the Prime Number Theorem although it also saw Bernhard Riemann posing what many think to be the greatest unsolved problem in mathematics - the Rieman Hypothesis.
The transcript and downloadable versions of the lecture are available from the Gresham College website:
http://www.gresham.ac.uk/lectures-and-events/the-queen-of-mathematics
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently nearly 1,500 lectures free to access or download from the website.
Website: http://www.gresham.ac.uk
Twitter: http://twitter.com/GreshamCollege
Facebook: http://www.facebook.com/pages/Gresham-College/14011689941
- published: 31 Jan 2013
- views: 92058
More on the math behind this: http://youtu.be/oYlB5lUGlbw
Professor David Eisenbud - director of MSRI - on the amazing 17-gon and its link to Gauss.
See end of this video for a bit MSRI's address at 17 Gauss Way!
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
Support us on Patreon: http://www.patreon.com/numberphile
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
A run-down of Brady's channels: http://www.bradyharan.com
Sign up for (occasional) emails: http://eepurl.com/YdjL9
Brown papers: http://bit.ly/brownpapers
- published: 13 Feb 2015
- views: 570145
The Great Courses Plus free trial: http://ow.ly/RJw3301cRhU
Cliff Stoll discusses a "Remarkable Theorem", Gaussian curvature and pizza.
Postscript note from Cliff: "Cliff says he forgot to mention that at each point, he calls an outward going curve positive, and an inward going curve negative. He also neglected to say that saddle points have negative Gaussian curvature. Finally, he insists that the frozen pizza shown in this video is inferior to his wife's homemade pizza. But both have zero Gaussian curvature."
Animation by Pete McPartlan.
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
Support us on Patreon: http://www.patreon.com/numberphile
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
- published: 16 Jun 2016
- views: 602412
Gaussian integer
In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as Z[i]. This integral domain is a particular case of a commutative ring of quadratic integers. It does not have a total ordering that respects arithmetic.
Formal definition
Formally, the Gaussian integers are the set
Note that when they are considered within the complex plane the Gaussian integers may be seen to constitute the 2-dimensional integer lattice.
Norm of a Gaussian integer
The (arithmetic or field) norm of a Gaussian integer is the square of its absolute value (Euclidean norm) as a complex number. It is the natural number defined as
where ⋅ (an overline) is complex conjugation.
The norm is multiplicative, since the absolute value of complex numbers is multiplicative, i.e., one has
The latter can also be verified by a straightforward check. The units of Z[i] are precisely those elements with norm 1, i.e. the set {±1, ±i}.
This page contains text from Wikipedia, the Free Encyclopedia -
https://wn.com/Gaussian_integer
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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22:31RNT2.4. Gaussian Primes
RNT2.4. Gaussian PrimesRNT2.4. Gaussian Primes
Ring Theory: As an application of all previous ideas on rings, we determine the primes in the Euclidean domain of Gaussian integers Z[i]. Not only is the answer somewhat elegant, but it contains a beautiful theorem on prime integers due to Fermat. We finish with examples of factorizations in Z[i]. -
0:28Gaussian Prime Number Plot
Gaussian Prime Number PlotGaussian Prime Number Plot
Each of the 223 frames is a plot of the Gaussian primes within a certain norm. The norm for each frame is determined by the square of prime numbers (in the real integers) in the arithmetic progression 4n+3 starting from n = 0 (p = 3). In other words, the increment is chosen to show the next Gaussian prime on the real/imaginary axis using squares of primes congruent to 3 (mod 4). The first frame is all the Gaussian primes with norm less than or equal to 3^2. The last frame is all Gaussian primes with norm less than or equal to 3163^2. The full project report can be found at https://danielhutama.wordpress.com/research/ Created by D. Hutama at McGill University, June 2016 -
0:13Gaussian Prime Spirals
Gaussian Prime SpiralsGaussian Prime Spirals
http://demonstrations.wolfram.com/GaussianPrimeSpirals The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. Start a loop with a point having integer coordinates in the complex plane (called a Gaussian integer) and trace a path as follows: ? Move right until a Gaussian prime p is encountered, then turn left 90. ? Continue, always moving straight in the curren... Contributed by: Joseph O'Rourke and Stan Wagon Audio created with WolframTones: http://tones.wolfram.com -
0:21Gaussian Primes
Gaussian PrimesGaussian Primes
http://demonstrations.wolfram.com/GaussianPrimes/ The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. The pattern of Gaussian primes in the complex plane. Contributed by: Stephen Wolfram -
51:16Number Theory: Lecture 11, Gaussian Integers Applied
Number Theory: Lecture 11, Gaussian Integers AppliedNumber Theory: Lecture 11, Gaussian Integers Applied
Here I wrap up our thoughts on Chapter 6. We see how Z[i] provides a natural framework to prove Fermat's two square theorem. Most of this is directly from Stillwell, but I tried to add a bit here and there about why Z[i] still supports Division Algorthim, Euclidean Algorithm, Prime Divisor Property and Unique Factorization. To be careful, I would have to write much, much more. But, the point here is not to be super rigorous, the point is to be reasonably rigorous and see how abstraction solves problems. -
1:00:20The Queen of Mathematics - Professor Raymond Flood
The Queen of Mathematics - Professor Raymond FloodThe Queen of Mathematics - Professor Raymond Flood
Carl Friedrich Gauss one of the greatest mathematicians, is said to have claimed: "Mathematics is the queen of the sciences and number theory is the queen of mathematics." The properties of primes play a crucial part in number theory. An intriguing question is how they are distributed among the other integers. The 19th century saw progress in answering this question with the proof of the Prime Number Theorem although it also saw Bernhard Riemann posing what many think to be the greatest unsolved problem in mathematics - the Rieman Hypothesis. The transcript and downloadable versions of the lecture are available from the Gresham College website: http://www.gresham.ac.uk/lectures-and-events/the-queen-of-mathematics Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently nearly 1,500 lectures free to access or download from the website. Website: http://www.gresham.ac.uk Twitter: http://twitter.com/GreshamCollege Facebook: http://www.facebook.com/pages/Gresham-College/14011689941 -
8:10Gauss Prime: A Weapon At Its PRIME
Gauss Prime: A Weapon At Its PRIMEGauss Prime: A Weapon At Its PRIME
-
8:01Every Time I Get a Good Killstreak Going - Gauss Prime
Every Time I Get a Good Killstreak Going - Gauss PrimeEvery Time I Get a Good Killstreak Going - Gauss Prime
MAX units ruin everything. -
13:40The Amazing Heptadecagon (17-gon) - Numberphile
The Amazing Heptadecagon (17-gon) - NumberphileThe Amazing Heptadecagon (17-gon) - Numberphile
More on the math behind this: http://youtu.be/oYlB5lUGlbw Professor David Eisenbud - director of MSRI - on the amazing 17-gon and its link to Gauss. See end of this video for a bit MSRI's address at 17 Gauss Way! NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Support us on Patreon: http://www.patreon.com/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ A run-down of Brady's channels: http://www.bradyharan.com Sign up for (occasional) emails: http://eepurl.com/YdjL9 Brown papers: http://bit.ly/brownpapers -
7:42The Remarkable Way We Eat Pizza - Numberphile
The Remarkable Way We Eat Pizza - NumberphileThe Remarkable Way We Eat Pizza - Numberphile
The Great Courses Plus free trial: http://ow.ly/RJw3301cRhU Cliff Stoll discusses a "Remarkable Theorem", Gaussian curvature and pizza. Postscript note from Cliff: "Cliff says he forgot to mention that at each point, he calls an outward going curve positive, and an inward going curve negative. He also neglected to say that saddle points have negative Gaussian curvature. Finally, he insists that the frozen pizza shown in this video is inferior to his wife's homemade pizza. But both have zero Gaussian curvature." Animation by Pete McPartlan. NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Support us on Patreon: http://www.patreon.com/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9
-
RNT2.4. Gaussian Primes
Ring Theory: As an application of all previous ideas on rings, we determine the primes in the Euclidean domain of Gaussian integers Z[i]. Not only is the answer somewhat elegant, but it contains a beautiful theorem on prime integers due to Fermat. We finish with examples of factorizations in Z[i].
published: 08 Dec 2012 -
Gaussian Prime Number Plot
Each of the 223 frames is a plot of the Gaussian primes within a certain norm. The norm for each frame is determined by the square of prime numbers (in the real integers) in the arithmetic progression 4n+3 starting from n = 0 (p = 3). In other words, the increment is chosen to show the next Gaussian prime on the real/imaginary axis using squares of primes congruent to 3 (mod 4). The first frame is all the Gaussian primes with norm less than or equal to 3^2. The last frame is all Gaussian primes with norm less than or equal to 3163^2. The full project report can be found at https://danielhutama.wordpress.com/research/ Created by D. Hutama at McGill University, June 2016
published: 15 Jun 2016 -
Gaussian Prime Spirals
http://demonstrations.wolfram.com/GaussianPrimeSpirals The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. Start a loop with a point having integer coordinates in the complex plane (called a Gaussian integer) and trace a path as follows: ? Move right until a Gaussian prime p is encountered, then turn left 90. ? Continue, always moving straight in the curren... Contributed by: Joseph O'Rourke and Stan Wagon Audio created with WolframTones: http://tones.wolfram.com
published: 27 Sep 2013 -
Gaussian Primes
http://demonstrations.wolfram.com/GaussianPrimes/ The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. The pattern of Gaussian primes in the complex plane. Contributed by: Stephen Wolfram
published: 09 Jul 2009 -
Number Theory: Lecture 11, Gaussian Integers Applied
Here I wrap up our thoughts on Chapter 6. We see how Z[i] provides a natural framework to prove Fermat's two square theorem. Most of this is directly from Stillwell, but I tried to add a bit here and there about why Z[i] still supports Division Algorthim, Euclidean Algorithm, Prime Divisor Property and Unique Factorization. To be careful, I would have to write much, much more. But, the point here is not to be super rigorous, the point is to be reasonably rigorous and see how abstraction solves problems.
published: 02 Mar 2015 -
The Queen of Mathematics - Professor Raymond Flood
Carl Friedrich Gauss one of the greatest mathematicians, is said to have claimed: "Mathematics is the queen of the sciences and number theory is the queen of mathematics." The properties of primes play a crucial part in number theory. An intriguing question is how they are distributed among the other integers. The 19th century saw progress in answering this question with the proof of the Prime Number Theorem although it also saw Bernhard Riemann posing what many think to be the greatest unsolved problem in mathematics - the Rieman Hypothesis. The transcript and downloadable versions of the lecture are available from the Gresham College website: http://www.gresham.ac.uk/lectures-and-events/the-queen-of-mathematics Gresham College has been giving free public lectures since 1597. This tra...
published: 31 Jan 2013 -
Gauss Prime: A Weapon At Its PRIME
published: 25 Mar 2017 -
Every Time I Get a Good Killstreak Going - Gauss Prime
MAX units ruin everything.
published: 10 Jun 2015 -
The Amazing Heptadecagon (17-gon) - Numberphile
More on the math behind this: http://youtu.be/oYlB5lUGlbw Professor David Eisenbud - director of MSRI - on the amazing 17-gon and its link to Gauss. See end of this video for a bit MSRI's address at 17 Gauss Way! NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Support us on Patreon: http://www.patreon.com/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ A run-down of Brady's channels: http://www.bradyharan.com Sign up for (occasional) emails: http://eepurl.com/YdjL9 Brown papers: http://bit.ly/brownpapers
published: 13 Feb 2015 -
The Remarkable Way We Eat Pizza - Numberphile
The Great Courses Plus free trial: http://ow.ly/RJw3301cRhU Cliff Stoll discusses a "Remarkable Theorem", Gaussian curvature and pizza. Postscript note from Cliff: "Cliff says he forgot to mention that at each point, he calls an outward going curve positive, and an inward going curve negative. He also neglected to say that saddle points have negative Gaussian curvature. Finally, he insists that the frozen pizza shown in this video is inferior to his wife's homemade pizza. But both have zero Gaussian curvature." Animation by Pete McPartlan. NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http...
published: 16 Jun 2016
RNT2.4. Gaussian Primes
- Order: Reorder
- Duration: 22:31
- Updated: 08 Dec 2012
- views: 3307
Ring Theory: As an application of all previous ideas on rings, we determine the primes in the Euclidean domain of Gaussian integers Z[i]. Not only is the answe...
Ring Theory: As an application of all previous ideas on rings, we determine the primes in the Euclidean domain of Gaussian integers Z[i]. Not only is the answer somewhat elegant, but it contains a beautiful theorem on prime integers due to Fermat. We finish with examples of factorizations in Z[i].
https://wn.com/Rnt2.4._Gaussian_Primes
Ring Theory: As an application of all previous ideas on rings, we determine the primes in the Euclidean domain of Gaussian integers Z[i]. Not only is the answer somewhat elegant, but it contains a beautiful theorem on prime integers due to Fermat. We finish with examples of factorizations in Z[i].
- published: 08 Dec 2012
- views: 3307
Gaussian Prime Number Plot
- Order: Reorder
- Duration: 0:28
- Updated: 15 Jun 2016
- views: 461
Each of the 223 frames is a plot of the Gaussian primes within a certain norm. The norm for each frame is determined by the square of prime numbers (in the real...
Each of the 223 frames is a plot of the Gaussian primes within a certain norm. The norm for each frame is determined by the square of prime numbers (in the real integers) in the arithmetic progression 4n+3 starting from n = 0 (p = 3). In other words, the increment is chosen to show the next Gaussian prime on the real/imaginary axis using squares of primes congruent to 3 (mod 4).
The first frame is all the Gaussian primes with norm less than or equal to 3^2. The last frame is all Gaussian primes with norm less than or equal to 3163^2.
The full project report can be found at https://danielhutama.wordpress.com/research/
Created by D. Hutama at McGill University, June 2016
https://wn.com/Gaussian_Prime_Number_Plot
Each of the 223 frames is a plot of the Gaussian primes within a certain norm. The norm for each frame is determined by the square of prime numbers (in the real integers) in the arithmetic progression 4n+3 starting from n = 0 (p = 3). In other words, the increment is chosen to show the next Gaussian prime on the real/imaginary axis using squares of primes congruent to 3 (mod 4).
The first frame is all the Gaussian primes with norm less than or equal to 3^2. The last frame is all Gaussian primes with norm less than or equal to 3163^2.
The full project report can be found at https://danielhutama.wordpress.com/research/
Created by D. Hutama at McGill University, June 2016
- published: 15 Jun 2016
- views: 461
Gaussian Prime Spirals
- Order: Reorder
- Duration: 0:13
- Updated: 27 Sep 2013
- views: 248
http://demonstrations.wolfram.com/GaussianPrimeSpirals
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entri...
http://demonstrations.wolfram.com/GaussianPrimeSpirals
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Start a loop with a point having integer coordinates in the complex plane (called a Gaussian integer) and trace a path as follows: ? Move right until a Gaussian prime p is encountered, then turn left 90. ? Continue, always moving straight in the curren...
Contributed by: Joseph O'Rourke and Stan Wagon
Audio created with WolframTones:
http://tones.wolfram.com
https://wn.com/Gaussian_Prime_Spirals
http://demonstrations.wolfram.com/GaussianPrimeSpirals
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Start a loop with a point having integer coordinates in the complex plane (called a Gaussian integer) and trace a path as follows: ? Move right until a Gaussian prime p is encountered, then turn left 90. ? Continue, always moving straight in the curren...
Contributed by: Joseph O'Rourke and Stan Wagon
Audio created with WolframTones:
http://tones.wolfram.com
- published: 27 Sep 2013
- views: 248
Gaussian Primes
- Order: Reorder
- Duration: 0:21
- Updated: 09 Jul 2009
- views: 858
http://demonstrations.wolfram.com/GaussianPrimes/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries ...
http://demonstrations.wolfram.com/GaussianPrimes/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
The pattern of Gaussian primes in the complex plane.
Contributed by: Stephen Wolfram
https://wn.com/Gaussian_Primes
http://demonstrations.wolfram.com/GaussianPrimes/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
The pattern of Gaussian primes in the complex plane.
Contributed by: Stephen Wolfram
- published: 09 Jul 2009
- views: 858
Number Theory: Lecture 11, Gaussian Integers Applied
- Order: Reorder
- Duration: 51:16
- Updated: 02 Mar 2015
- views: 852
Here I wrap up our thoughts on Chapter 6. We see how Z[i] provides a natural framework to prove Fermat's two square theorem. Most of this is directly from Still...
Here I wrap up our thoughts on Chapter 6. We see how Z[i] provides a natural framework to prove Fermat's two square theorem. Most of this is directly from Stillwell, but I tried to add a bit here and there about why Z[i] still supports Division Algorthim, Euclidean Algorithm, Prime Divisor Property and Unique Factorization. To be careful, I would have to write much, much more. But, the point here is not to be super rigorous, the point is to be reasonably rigorous and see how abstraction solves problems.
https://wn.com/Number_Theory_Lecture_11,_Gaussian_Integers_Applied
Here I wrap up our thoughts on Chapter 6. We see how Z[i] provides a natural framework to prove Fermat's two square theorem. Most of this is directly from Stillwell, but I tried to add a bit here and there about why Z[i] still supports Division Algorthim, Euclidean Algorithm, Prime Divisor Property and Unique Factorization. To be careful, I would have to write much, much more. But, the point here is not to be super rigorous, the point is to be reasonably rigorous and see how abstraction solves problems.
- published: 02 Mar 2015
- views: 852
The Queen of Mathematics - Professor Raymond Flood
- Order: Reorder
- Duration: 1:00:20
- Updated: 31 Jan 2013
- views: 92058
Carl Friedrich Gauss one of the greatest mathematicians, is said to have claimed: "Mathematics is the queen of the sciences and number theory is the queen of ma...
Carl Friedrich Gauss one of the greatest mathematicians, is said to have claimed: "Mathematics is the queen of the sciences and number theory is the queen of mathematics." The properties of primes play a crucial part in number theory. An intriguing question is how they are distributed among the other integers. The 19th century saw progress in answering this question with the proof of the Prime Number Theorem although it also saw Bernhard Riemann posing what many think to be the greatest unsolved problem in mathematics - the Rieman Hypothesis.
The transcript and downloadable versions of the lecture are available from the Gresham College website:
http://www.gresham.ac.uk/lectures-and-events/the-queen-of-mathematics
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently nearly 1,500 lectures free to access or download from the website.
Website: http://www.gresham.ac.uk
Twitter: http://twitter.com/GreshamCollege
Facebook: http://www.facebook.com/pages/Gresham-College/14011689941
https://wn.com/The_Queen_Of_Mathematics_Professor_Raymond_Flood
Carl Friedrich Gauss one of the greatest mathematicians, is said to have claimed: "Mathematics is the queen of the sciences and number theory is the queen of mathematics." The properties of primes play a crucial part in number theory. An intriguing question is how they are distributed among the other integers. The 19th century saw progress in answering this question with the proof of the Prime Number Theorem although it also saw Bernhard Riemann posing what many think to be the greatest unsolved problem in mathematics - the Rieman Hypothesis.
The transcript and downloadable versions of the lecture are available from the Gresham College website:
http://www.gresham.ac.uk/lectures-and-events/the-queen-of-mathematics
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently nearly 1,500 lectures free to access or download from the website.
Website: http://www.gresham.ac.uk
Twitter: http://twitter.com/GreshamCollege
Facebook: http://www.facebook.com/pages/Gresham-College/14011689941
- published: 31 Jan 2013
- views: 92058
Gauss Prime: A Weapon At Its PRIME
- Order: Reorder
- Duration: 8:10
- Updated: 25 Mar 2017
- views: 117
- published: 25 Mar 2017
- views: 117
Every Time I Get a Good Killstreak Going - Gauss Prime
- Order: Reorder
- Duration: 8:01
- Updated: 10 Jun 2015
- views: 390
MAX units ruin everything.
MAX units ruin everything.
https://wn.com/Every_Time_I_Get_A_Good_Killstreak_Going_Gauss_Prime
The Amazing Heptadecagon (17-gon) - Numberphile
- Order: Reorder
- Duration: 13:40
- Updated: 13 Feb 2015
- views: 570145
More on the math behind this: http://youtu.be/oYlB5lUGlbw
Professor David Eisenbud - director of MSRI - on the amazing 17-gon and its link to Gauss.
See end of ...
More on the math behind this: http://youtu.be/oYlB5lUGlbw
Professor David Eisenbud - director of MSRI - on the amazing 17-gon and its link to Gauss.
See end of this video for a bit MSRI's address at 17 Gauss Way!
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
Support us on Patreon: http://www.patreon.com/numberphile
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
A run-down of Brady's channels: http://www.bradyharan.com
Sign up for (occasional) emails: http://eepurl.com/YdjL9
Brown papers: http://bit.ly/brownpapers
https://wn.com/The_Amazing_Heptadecagon_(17_Gon)_Numberphile
More on the math behind this: http://youtu.be/oYlB5lUGlbw
Professor David Eisenbud - director of MSRI - on the amazing 17-gon and its link to Gauss.
See end of this video for a bit MSRI's address at 17 Gauss Way!
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
Support us on Patreon: http://www.patreon.com/numberphile
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
A run-down of Brady's channels: http://www.bradyharan.com
Sign up for (occasional) emails: http://eepurl.com/YdjL9
Brown papers: http://bit.ly/brownpapers
- published: 13 Feb 2015
- views: 570145
The Remarkable Way We Eat Pizza - Numberphile
- Order: Reorder
- Duration: 7:42
- Updated: 16 Jun 2016
- views: 602412
The Great Courses Plus free trial: http://ow.ly/RJw3301cRhU
Cliff Stoll discusses a "Remarkable Theorem", Gaussian curvature and pizza.
Postscript note from Cl...
The Great Courses Plus free trial: http://ow.ly/RJw3301cRhU
Cliff Stoll discusses a "Remarkable Theorem", Gaussian curvature and pizza.
Postscript note from Cliff: "Cliff says he forgot to mention that at each point, he calls an outward going curve positive, and an inward going curve negative. He also neglected to say that saddle points have negative Gaussian curvature. Finally, he insists that the frozen pizza shown in this video is inferior to his wife's homemade pizza. But both have zero Gaussian curvature."
Animation by Pete McPartlan.
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The Great Courses Plus free trial: http://ow.ly/RJw3301cRhU
Cliff Stoll discusses a "Remarkable Theorem", Gaussian curvature and pizza.
Postscript note from Cliff: "Cliff says he forgot to mention that at each point, he calls an outward going curve positive, and an inward going curve negative. He also neglected to say that saddle points have negative Gaussian curvature. Finally, he insists that the frozen pizza shown in this video is inferior to his wife's homemade pizza. But both have zero Gaussian curvature."
Animation by Pete McPartlan.
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
Support us on Patreon: http://www.patreon.com/numberphile
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
- published: 16 Jun 2016
- views: 602412
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22:31
RNT2.4. Gaussian Primes
Ring Theory: As an application of all previous ideas on rings, we determine the primes in...
published: 08 Dec 2012
RNT2.4. Gaussian Primes
RNT2.4. Gaussian Primes
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- published: 08 Dec 2012
- views: 3307
0:28
Gaussian Prime Number Plot
Each of the 223 frames is a plot of the Gaussian primes within a certain norm. The norm fo...
published: 15 Jun 2016
Gaussian Prime Number Plot
Gaussian Prime Number Plot
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- published: 15 Jun 2016
- views: 461
0:13
Gaussian Prime Spirals
http://demonstrations.wolfram.com/GaussianPrimeSpirals
The Wolfram Demonstrations Project...
published: 27 Sep 2013
Gaussian Prime Spirals
Gaussian Prime Spirals
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- published: 27 Sep 2013
- views: 248
0:21
Gaussian Primes
http://demonstrations.wolfram.com/GaussianPrimes/
The Wolfram Demonstrations Project co...
published: 09 Jul 2009
Gaussian Primes
Gaussian Primes
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- published: 09 Jul 2009
- views: 858
51:16
Number Theory: Lecture 11, Gaussian Integers Applied
Here I wrap up our thoughts on Chapter 6. We see how Z[i] provides a natural framework to ...
published: 02 Mar 2015
Number Theory: Lecture 11, Gaussian Integers Applied
Number Theory: Lecture 11, Gaussian Integers Applied
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- published: 02 Mar 2015
- views: 852
1:00:20
The Queen of Mathematics - Professor Raymond Flood
Carl Friedrich Gauss one of the greatest mathematicians, is said to have claimed: "Mathema...
published: 31 Jan 2013
The Queen of Mathematics - Professor Raymond Flood
The Queen of Mathematics - Professor Raymond Flood
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- published: 31 Jan 2013
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8:10
Gauss Prime: A Weapon At Its PRIME
published: 25 Mar 2017
Gauss Prime: A Weapon At Its PRIME
Gauss Prime: A Weapon At Its PRIME
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- published: 25 Mar 2017
- views: 117
8:01
Every Time I Get a Good Killstreak Going - Gauss Prime
MAX units ruin everything.
published: 10 Jun 2015
Every Time I Get a Good Killstreak Going - Gauss Prime
Every Time I Get a Good Killstreak Going - Gauss Prime
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- published: 10 Jun 2015
- views: 390
13:40
The Amazing Heptadecagon (17-gon) - Numberphile
More on the math behind this: http://youtu.be/oYlB5lUGlbw
Professor David Eisenbud - direc...
published: 13 Feb 2015
The Amazing Heptadecagon (17-gon) - Numberphile
The Amazing Heptadecagon (17-gon) - Numberphile
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- published: 13 Feb 2015
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7:42
The Remarkable Way We Eat Pizza - Numberphile
The Great Courses Plus free trial: http://ow.ly/RJw3301cRhU
Cliff Stoll discusses a "Remar...
published: 16 Jun 2016
The Remarkable Way We Eat Pizza - Numberphile
The Remarkable Way We Eat Pizza - Numberphile
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- published: 16 Jun 2016
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RNT2.4. Gaussian Primes...
Gaussian Prime Number Plot...
Gaussian Prime Spirals...
Gaussian Primes...
Number Theory: Lecture 11, Gaussian Integers Appli...
The Queen of Mathematics - Professor Raymond Flood...
Gauss Prime: A Weapon At Its PRIME...
Every Time I Get a Good Killstreak Going - Gauss P...
The Amazing Heptadecagon (17-gon) - Numberphile...
The Remarkable Way We Eat Pizza - Numberphile...
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G7 Ends with Trump Pitted Against the Leaders of Europe on a Number of Key Issues
Edit Newsweek 27 May 2017
Under pressure from allies, U.S. President Donald Trump backed a pledge to fight protectionism on Saturday, but refused to endorse a global climate change accord, saying he needed more time to decide ... Trump, who has previously called global warming a hoax, tweeted that he would make a decision next week on whether to back the 2015 Paris Agreement on curbing carbon emissions following lengthy discussions with G7 partners ... The U.S ... U.S ... ....
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Philippines President Rodrigo Duterte jokes that soldiers can rape women under his martial law
Edit The Independent 27 May 2017
Philippines President Rodrigo Duterte has sought to reassure soldiers who might be accused of committing abuses under martial law and jokingly said that if any of them were to rape three women, he would personally claim responsibility for it ... He has, however, said he would not tolerate abuses. "If you go down, I go down....
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Jupiter surprises in first trove of data from NASA’s Juno mission
Edit Astronomy/Spaceflight Now 27 May 2017
This image shows Jupiter’s south pole, as seen by NASA’s Juno spacecraft from an altitude of 32,000 miles (52,000 kilometres). Image credit. NASA/JPL-Caltech/SwRI/MSSS/Betsy Asher Hall/Gervasio Robles ... “The general theme of our discoveries is really how different Jupiter looks from what we expected,” said Scott Bolton, Juno’s principal investigator at the Southwest Research Institute in San Antonio ... Credit ... ....
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Revealed: Jared Kushner 'wanted secret back channel' with Russia
Edit Irish Independent 27 May 2017
US President Donald Trump’s son-in-law and close adviser, Jared Kushner, had at least three previously undisclosed contacts with the Russian ambassador to the United States during and after the 2016 presidential campaign, seven current and former U.S. officials told Reuters. Those contacts included two phone calls between April and November last year, two of the sources said ... The White House did not respond to a request for comment ... ... ....
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Former U.S. national security adviser Brzezinski dies at 89
Edit Yahoo Daily News 27 May 2017
By Bill Trott. REUTERS - Former U.S. national security adviser Zbigniew Brzezinski, who established himself in the Carter administration as a hardliner on foreign policy, died on Friday, his family said. He was 89. Brzezinski's daughter Mika, a host on MSNBC's "Morning Joe" show, said on social media that her father died peacefully. She did not give the cause of his death ... That placed him at odds with two of Carter's closest advisers ... Bush....
Exclusive: Behind Fluent Design, Microsoft’s Vision For The Future Of Interfaces
Edit Fast Company 11 May 2017
Bojana Ostojic was working on Microsoft’s experimental mixed reality headset, HoloLens, when she realized that she was seeing the future of design at the company. advertisement ... [Image ... Again. Holographs ... [Screenshot ... creatives ... [Screenshot ... Microsoft]Acrylic, the first standardized design material the company is publishing under the system, is a glassy layering of materials that are rendering as a thin pane of gaussian-blurred glass....
Sony FE 100mm F2.8 STF Gallery and 1st Impressions
Edit Digital Photography Review 09 May 2017
This lens approaches a very Gaussian blur wide open, rendering out-of-focus highlights more of a blur than defined circles ... Photo ... Photo ... By the time you stop down to get any circular, defined character to your highlights (as opposed to almost too buttery-smooth Gaussian bokeh), you suddenly find yourself at T8.0 or worse ... the former, almost too Gaussian, blur wide open leads to a character not immediately appreciated by all ... Take-home....
CIE colour sensor chip is calibrated
Edit Eweekly 09 May 2017
It is part of a family of similar chips – scroll to the end for the other two. Integrated silicon Gaussian interference filters are used, providing direct XYZ coordinates consistent with the CIE 1931 2° standard observer, in the case of the AS7261 ... A Near-IR channel and LED drivers with programmable currents increase application flexibility, including support for electronic shutter applications ... A 16-bit ADC measures them ... ....
Paradox Resolved: Why Risk Decreases Expected Log Return But Not Expected Wealth
Edit Seeking Alpha 04 May 2017
I have been troubled by the following paradox in the past few years. If a stock's log returns (i.e. change in log price per unit time) follow a Gaussian distribution, and if its net returns (i.e. percent change in price per unit time) have mean m and standard distribution s, then many finance students know that the mean log returns is m-s2 /2. That is, the compound growth rate of the stock is m-s2 /2 ... What gives? ... Paradox resolved! ... Expand....
Why the next evolution of AI will be a seamless methodology
Edit Venture Beat 02 May 2017
Many more schools of thought exist, from fuzzy systems to evolutionary computation, chaos theory, Gaussian processes, computational creativity, and more — all with their own supporters and detractors ... Unless your goal is to build a company that utilizes fuzzy systems or Gaussian processes, there’s little way your specific website or application can create a viable input-output contribution to the discipline ... ....
Timing The Market Versus Time In The Market
Edit Yahoo Daily News 02 May 2017
Equity returns come in clusters. Indeed, these clusters, both on the upside and the downside, are hard to foretell. Most people use a combination of fundamental and technical analyses, and mostly intuition, to figure this out. However, we cannot wish away the vagaries of stock returns ... This happens because returns from stocks are not distributed in a Gaussian or bell curve fashion as is assumed in almost all finance theory ... ....
In A Moment Of Clarity While Brushing His Teeth, A Retiree Solves A Decades-Old Math Problem
Edit Good 07 Apr 2017
The Gaussian Correlation Inequality is a very easy concept to imagine and understand but has been notoriously hard for mathematicians to prove....
Retired Man Solves Decades-Old Maths Problems While Brushing His Teeth
Edit IFL Science 05 Apr 2017
Quanta Magazine recently reported the story of an unassuming retired German statistician called Thomas Royen, who came up with a mathematical proof for the Gaussian correlation inequality (GCI) during a brief flash of inspiration while brushing his teeth in July 2014 ... The paper is called “A simple proof of the Gaussian correlation conjecture."...
A retiree solved a math problem that people have been working on for decades — and no one noticed
Edit Business Insider 04 Apr 2017
It's a problem that the world's most experienced mathematicians have spent decades trying to solve, and the solution had eluded them at every turn — the infamous Gaussian correlation inequality (GCI) ... You throw a bunch of darts at the target, and you'll soon discover that a bell curve — or 'Gaussian distribution' — of positions has formed around the centre, with vast majority of the darts sitting in the overlap....
Retired German man solves one of world's most complex maths problem with 'simple proof'
Edit The Independent 03 Apr 2017
... for a pharmaceutical company, from Schwalbach am Taunus, a town on the edge of Frankfurt, found the solution to the conjecture, known as the Gaussian correlation inequality (GCI)....
Game-Changer: Slate Has Obtained Footage of Stephen Colbert Making Fun of Rachel Maddow
Edit Slate 16 Mar 2017
Tonight, Slate is thrilled to announce we’ve obtained video footage of late night host Stephen Colbert spoofing Rachel Maddow’s cynical, reputation-scarring “scoop” from Tuesday night , which we’ll share with you in this very post. But first, a little context ... But first, it’s worth asking ... To avoid spoiling anything before we give you the opportunity to watch the complete footage, we’ve applied a 5.1 pixel Gaussian blur ... Wow....
Bengaluru struggles to remain in top 20 startup ecosystems
Edit The Times of India 15 Mar 2017
India's startup capital did well in the category of `startup value' with a rank of 10 ... A lot of times we have seen Indian companies make projections similar to their Silicon Valley peers without actually having the penchant to create global brands like the Sili on Valley companies do," said Kanwalijit Singh, founder and CEO of gaming company, Gaussian Networks, in the report ... Stay updated on the go with Times of India News App ... RELATED....
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