Fermat's Last Theorem | Diophantine equations | Theorems in number theory | Arithmetic problems of plane geometry | Squares in number theory
Fermat's right triangle theorem is a non-existence proof in number theory, published in 1670 among the works of Pierre de Fermat, soon after his death. It is the only complete proof given by Fermat. It has several equivalent formulations, one of which was stated (but not proved) in 1225 by Fibonacci. In its geometric forms, it states: * A right triangle in the Euclidean plane for which all three side lengths are rational numbers cannot have an area that is the square of a rational number. The area of a rational-sided right triangle is called a congruent number, so no congruent number can be square. * A right triangle and a square with equal areas cannot have all sides commensurate with each other. * There do not exist two integer-sided right triangles in which the two legs of one triangle are the leg and hypotenuse of the other triangle. More abstractly, as a result about Diophantine equations (integer or rational-number solutions to polynomial equations), it is equivalent to the statements that: * If three square numbers form an arithmetic progression, then the gap between consecutive numbers in the progression (called a congruum) cannot itself be square. * The only rational points on the elliptic curve are the three trivial points with and . * The quartic equation has no nonzero integer solution. An immediate consequence of the last of these formulations is that Fermat's Last Theorem is true in the special case that its exponent is 4. (Wikipedia).
What are the trigonometric definitions of a right triangle
👉 Learn all about the trigonometry of right triangles. A right triangle is a triangle that has 90 degrees as one of its angles. The trigonometric identities of right triangles give us the relationship between the angles of a right triangle and the side lengths of the right triangle. These
From playlist Right Triangle Trigonometry | Learn About
How to apply the pythagorean theorem to a triangle
Learn about the Pythagorean theorem. The Pythagoras theorem is a fundamental relation among the three sides of a right triangle. It is used to determine the missing length of a right triangle. The Pythagoras theorem states that the square of the hypotenuse (the side opposite the right angl
From playlist Geometry - PYTHAGOREAN THEOREM
Learn to write the three trigonometric function ratios from a triangle
👉 Learn all about the trigonometry of right triangles. A right triangle is a triangle that has 90 degrees as one of its angles. The trigonometric identities of right triangles give us the relationship between the angles of a right triangle and the side lengths of the right triangle. These
From playlist Right Triangle Trigonometry | Learn About
How to determine the hypotenuse, opposite, and adjacent legs of a triangle
👉 Learn all about the trigonometry of right triangles. A right triangle is a triangle that has 90 degrees as one of its angles. The trigonometric identities of right triangles give us the relationship between the angles of a right triangle and the side lengths of the right triangle. These
From playlist Right Triangle Trigonometry | Learn About
How can you remember the three trigonometric ratios sohcahtoa
👉 Learn all about the trigonometry of right triangles. A right triangle is a triangle that has 90 degrees as one of its angles. The trigonometric identities of right triangles give us the relationship between the angles of a right triangle and the side lengths of the right triangle. These
From playlist Right Triangle Trigonometry | Learn About
Pythagoras twisted squares: Why did they not teach you any of this in school?
A video on the iconic twisted squares diagram that just about anybody who knows anything about mathematics has been familiar with since primary school. Surprisingly, there is a LOT more to this diagram than even expert mathematicians are aware of. And lots of this LOT is really really beau
From playlist Recent videos
Right triangle trigonometry evaluate trig functions of a triangle
👉 Learn how to evaluate the six trigonometric functions given a right triangle. A right triangle is a triangle with 90 degrees as one of its angles. A right triangle is made up of two legs, which formed the sides of the 90 degrees angle and the hypothenuse. When the side lengths of a righ
From playlist Evaluate the Trigonometric Functions With Triangles
Fermat's Last Theorem - The Theorem and Its Proof: An Exploration of Issues and Ideas [1993]
supplement to the video: http://www.msri.org/realvideo/ln/msri/1993/outreach/fermat/1/banner/01.html Date: July 28, 1993 (08:00 AM PDT - 09:00 AM PDT) Fermat's Last Theorem July 28, 1993, Robert Osserman, Lenore Blum, Karl Rubin, Ken Ribet, John Conway, and Lee Dembart. Musical interlude
From playlist Number Theory
The Bridges to Fermat's Last Theorem - Numberphile
Ken Ribet - a key player in the solution to Fermat's Last Theorem - gives a taste of how real mathematics is done... piece by piece and by human beings. More links & stuff in full description below ↓↓↓ More Fermat (with Simon Singh): http://youtu.be/qiNcEguuFSA Even more Fermat (with Simo
From playlist Fermat's Last Theorem on Numberphile
1. A bridge between graph theory and additive combinatorics
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX In an unsuccessful attempt to prove Fermat's last theorem
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
The Shortest Ever Papers - Numberphile
Audible 30-day free trial: http://www.audible.com/numberphile (sponsor) Tony Padilla discusses some of the shortest math papers to be published. From Conway to Nash. More links & stuff in full description below ↓↓↓ Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Web
From playlist Tony Padilla on Numberphile
What is the formula for the pythagorean theorem
Learn about the Pythagorean theorem. The Pythagoras theorem is a fundamental relation among the three sides of a right triangle. It is used to determine the missing length of a right triangle. The Pythagoras theorem states that the square of the hypotenuse (the side opposite the right angl
From playlist Geometry - PYTHAGOREAN THEOREM
Quantum Mechanics and the Principle of Least Time
In this short video I would like to tell you about the pioneering work of Pierre de Fermat, who discovered that light is the laziest object in the universe, always preferring to take the path that minimises the amount of time spent travelling between two points. But perhaps what is even mo
From playlist General Physics
How to write the three trigonometric ratios for a triangle
👉 Learn all about the trigonometry of right triangles. A right triangle is a triangle that has 90 degrees as one of its angles. The trigonometric identities of right triangles give us the relationship between the angles of a right triangle and the side lengths of the right triangle. These
From playlist Right Triangle Trigonometry | Learn About
Alex Bellos on Andrew Wiles and Fermat's last theorem
Popular presentation by Alex Bellos on Sir Andrew Wiles and on Fermat's last theorem. This clip is a part of the Abel Prize Announcement 2016. You can view Alex Bellos own YouTube channel here: https://www.youtube.com/user/AlexInNumberland
From playlist Popular presentations
Andrew Wiles talks to Hannah Fry
Oxford Mathematics London Public Lecture: Andrew Wiles in Conversation with Hannah Fry In the first Oxford Mathematics London Public Lecture, in partnership with the Science Museum, world-renowned mathematician Andrew Wiles lectured on his current work around Elliptic Curves followed by c
From playlist Oxford Mathematics Public Lectures
Example: Determine if a Triangle is a Right Triangle Given the Length of 3 Sides
This video uses the Pythagorean Theorem to determine if a triangle is a right triangle given the length of the three sides. Complete Video Lists at www.mathispower4u.yolasite.com or www.mathispower4u.wordpress.com
From playlist Using the Pythagorean Theorem
Sophie Germain - Mathematics for the Modern Age #SoME2
Sophie Germain (1776-1831) was a French mathematician who made huge contributions to physics with her foundational work on elasticity theory, revolutionised mathematics with her work on calculus and… gave Schrödinger the tools he needed to formulate his wave equation for quantum mechanics!
From playlist Summer of Math Exposition 2 videos
How to determine the three trigonometric ratios for a triangle
👉 Learn all about the trigonometry of right triangles. A right triangle is a triangle that has 90 degrees as one of its angles. The trigonometric identities of right triangles give us the relationship between the angles of a right triangle and the side lengths of the right triangle. These
From playlist Right Triangle Trigonometry | Learn About
The Abel Prize announcement 2016 - Andrew Wiles
0:44 The Abel Prize announced by Ole M. Sejersted, President of The Norwegian Academy of Science and Letters 2:07 Citation by Hans Munthe-Kaas, Chair of the Abel committee 8:01 Popular presentation of the prize winners work by Alex Bellos, British writer, and science communicator 21:43 Pho
From playlist The Abel Prize announcements