- published: 11 May 2016
- views: 254846
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems—and generally accepted statements, such as axioms. A theorem is a logical consequence of the axioms. The proof of a mathematical theorem is a logical argument for the theorem statement given in accord with the rules of a deductive system. The proof of a theorem is often interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally deductive, in contrast to the notion of a scientific law, which is experimental.
Many mathematical theorems are conditional statements. In this case, the proof deduces the conclusion from conditions called hypotheses or premises. In light of the interpretation of proof as justification of truth, the conclusion is often viewed as a necessary consequence of the hypotheses, namely, that the conclusion is true in case the hypotheses are true, without any further assumptions. However, the conditional could be interpreted differently in certain deductive systems, depending on the meanings assigned to the derivation rules and the conditional symbol.
Khan Academy is a non-profit educational organization created in 2006 by educator Salman Khan with the aim of providing a free, world-class education for anyone, anywhere. The organization produces short lectures in the form of YouTube videos. In addition to micro lectures, the organization's website features practice exercises and tools for educators. All resources are available for free to anyone around the world. The main language of the website is English, but the content is also available in other languages.
The founder of the organization, Salman Khan, was born in New Orleans, Louisiana, United States to immigrant parents from Bangladesh and India. After earning three degrees from the Massachusetts Institute of Technology (a BS in mathematics, a BS in electrical engineering and computer science, and an MEng in electrical engineering and computer science), he pursued an MBA from Harvard Business School.
In late 2004, Khan began tutoring his cousin Nadia who needed help with math using Yahoo!'s Doodle notepad.When other relatives and friends sought similar help, he decided that it would be more practical to distribute the tutorials on YouTube. The videos' popularity and the testimonials of appreciative students prompted Khan to quit his job in finance as a hedge fund analyst at Connective Capital Management in 2009, and focus on the tutorials (then released under the moniker "Khan Academy") full-time.
In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation":
where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides.
Although it is often argued that knowledge of the theorem predates him, the theorem is named after the ancient Greek mathematician Pythagoras (c. 570 – c. 495 BC) as it is he who, by tradition, is credited with its first recorded proof.There is some evidence that Babylonian mathematicians understood the formula, although little of it indicates an application within a mathematical framework.Mesopotamian, Indian and Chinese mathematicians all discovered the theorem independently and, in some cases, provided proofs for special cases.
In mathematics, Green's theorem gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C. It is named after George Green and is the two-dimensional special case of the more general Kelvin–Stokes theorem.
Let C be a positively oriented, piecewise smooth, simple closed curve in a plane, and let D be the region bounded by C. If L and M are functions of (x, y) defined on an open region containing D and have continuous partial derivatives there, then
where the path of integration along C is counterclockwise.
In physics, Green's theorem is mostly used to solve two-dimensional flow integrals, stating that the sum of fluid outflows from a volume is equal to the total outflow summed about an enclosing area. In plane geometry, and in particular, area surveying, Green's theorem can be used to determine the area and centroid of plane figures solely by integrating over the perimeter.
"Want To" is a song co-written and recorded by American country music duo Sugarland. It was released in August 2006 as the first single from the album Enjoy the Ride. It was their first single not to feature former member Kristen Hall, although Jennifer Nettles had previously been featured on Bon Jovi's Number One country hit, "Who Says You Can't Go Home", the song was also the first regular Number One hit of Sugarland's career in the U.S., spending two weeks at the top of the Billboard Hot Country Songs charts in late 2006. The duo's members, Jennifer Nettles and Kristian Bush, wrote the song along with Bobby Pinson. The song has sold 856,000 copies in the US as of April 2013.
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Sure, technically it's a Geometry topic, but why not learn about it in Algebra? Don't be lured into a false sense of security, there may be problems on this video that you may not be able to do! Check out my tie. YAY MATH! Visit yaymath.org Videos copyright (c) Yay Math
In this video I do a full breakdown of the Theorem Atomizer. The Wismec Theorem is designed by Jay-Bo & inspired by SMM. Here is where it can be pre-ordered http://wismec.us/products/wismec-theorem-atomizer.html If you own a retail shop, here is where you to go for wholesale. http://www.myvapors.com Please subscribe to SMM for more great content! http://www.youtube.com/subscription_c... Here is our ZB profiles for you guys to check out! Matt's is http://bit.ly/1OlD7S5 Vee's is http://bit.ly/1Huk3jn Once again don’t forget to join http://casaa.org and http://thevapingmilitia.org Please like our Facebook Page! https://www.facebook.com/smmvapereviews Instagram https://www.instagram.com/suckmymod/ Twitter https://twitter.com/suckmymod These videos are my opinions based on the experien...
Check out our Patreon page: https://www.patreon.com/teded View full lesson: https://ed.ted.com/lessons/how-many-ways-are-there-to-prove-the-pythagorean-theorem-betty-fei What do Euclid, 12-year-old Einstein, and American President James Garfield have in common? They all came up with elegant proofs for the famous Pythagorean theorem, one of the most fundamental rules of geometry and the basis for practical applications like constructing stable buildings and triangulating GPS coordinates. Betty Fei details these three famous proofs. Lesson by Betty Fei, animation by Nick Hilditch. Thank you so much to our patrons for your support! Without you this video would not be possible. Steph, Jack Ta, Jose Fernandez-Calvo, PnDAA , Marcel Trompeter-Petrovic, Radoslava Vasileva, Sandra Tersluisen,...
Let’s learn Pythagoras Theorem visually with the help of a video class. Implementation of the Pythagoras theorem requires a triangle to be right-angled. If the length of any two sides of a triangle are known, you can easily calculate the length of the other side. According to Pythagoras Theorem, In a right angled triangle, the square of the length of hypotenuse is always equal to the sum of the length of squares of the other two sides. The longest side of a right-angled triangle is called the hypotenuse which is always opposite to 90 degree angle. Suppose, one side is AB, other side is BC and the hypotenuse is AC, then according to Pythagoras theorem: (AB)^2 + (BC)^2 = (AC)^2
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Introduction to the central limit theorem and the sampling distribution of the mean Watch the next lesson: https://www.khanacademy.org/math/probability/statistics-inferential/sampling_distribution/v/sampling-distribution-of-the-sample-mean?utm_source=YT&utm;_medium=Desc&utm;_campaign=ProbabilityandStatistics Missed the previous lesson? https://www.khanacademy.org/math/probability/statistics-inferential/normal_distribution/v/ck12-org-more-empirical-rule-and-z-score-practice?utm_source=YT&utm;_medium=Desc&utm;_campaign=ProbabilityandStatistics Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are...
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You will learn about "Pythagorean Theorem" in this video. To implement the Pythagorean Theorem, a triangle has to be a right-angled triangle. The longest side of a right-angled triangle is always opposite to the 90-degree angle. It is called the hypotenuse. The other 2 adjacent sides are called the legs of the triangle. Pythagorean theorem states that the square of the hypotenuse of a right angled triangle is equal to the sum of the squares of the other 2 sides. If one side = AB, other side = BC and the hypotenuse = AC, then according to Pythagorean theorem, AB^2 + BC^2 = AC^2 Let us understand this with the help of an example. Consider this triangle in which the length of AB = 3 m and the length of BC is 4 m. We need to find the length of AC. By Pythagorean theorem, AB^2 + BC^2 = AC^2 ...
This is a graphic, simple and memorable way to remember the difference from a chord or a tangent or a segments and sectors! I made this after struggling to understand it myself, once i got to grips with it i decided to help others who were also stuck.. so this video was created... This video includes Perpendicular bisectors of any chord the angles in a semi-circle, what happens when a tangent and a radius meet, Angles that are in the same segment and how different they are, the circumference subtended by the same arc, the meaning of subtended, lengths of two tangents and finally the angle between a tangent and a chord.. aka Alternate Segment Theorem. I re-uploaded this video because the last one had some glitches so here we are againn.... FOR THE QUESTION IF YOU ARE STUCK okay so ang...
Introduction to the Pythagorean Theorem Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geometry/right_triangles_topic/pyth_theor/e/pythagorean_theorem_1?utm_source=YT&utm;_medium=Desc&utm;_campaign=Geometry Watch the next lesson: https://www.khanacademy.org/math/geometry/right_triangles_topic/pyth_theor/v/pythagorean-theorem-1?utm_source=YT&utm;_medium=Desc&utm;_campaign=Geometry Missed the previous lesson? https://www.khanacademy.org/math/geometry/right_triangles_topic/pyth_theor/v/pythagorean-theorem?utm_source=YT&utm;_medium=Desc&utm;_campaign=Geometry Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we...
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Definition and examples for the four triangle congruence postulates and theorems
Green's Theorem - In this video, I give Green's Theorem and use it to compute the value of a line integral.
Part one on odd polynomials: http://youtu.be/8l-La9HEUIU More links & stuff in full description below ↓↓↓ A nice extra bit about complex numbers: http://youtu.be/-IJuqR6nz_Q Professor David Eisenbud is an algebraic geometer (and director of the Mathematical Sciences Research Institute at Berkeley) Hello Internet: http://www.hellointernet.fm Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/Brady...
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Look at me walking the streets at 3 a.m. and you're saying what a crazy fool I am
But the one I love is out tonight with him somewhere making love at 3 a.m.
I need a drink but all the bars are locked up tight
A lonely man gets mighty thirsty late at night
I won't ever kiss her sweet sweet lips again this old world's an awful place at 3 a.m.
[ steel ]
There's the river here's the bridge it's too late now
I've got nothing left to live for anyhow
In the news they'll say he couldn't even swim and he gave his love for love at 3 a.m.