A Beautiful Proof of Ptolemy's Theorem.
Ptolemy's Theorem seems more esoteric than the Pythagorean Theorem, but it's just as cool. In fact, the Pythagorean Theorem follows directly from it. Ptolemy used this theorem in his astronomical work. Google for the historical details. Thanks to this video for the idea of this visual
From playlist Mathy Videos
Pythagorean Theorem VII (visual proof)
This is a short, animated visual proof of an extended version of the Pythagorean theorem (the right triangle theorem) that implies the Pythagorean theorem. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths, and
From playlist Proof Writing
This one is famous! And super ancient. We aren't sure if old Pythag was the first to come up with it, but if not, he arrived at it independently of anyone prior, and his name is associated with it. It's quite nifty when you really think about it. Take a look! Watch the whole Mathematics p
From playlist Geometry
The Pythagorean Theorem I: Two Proofs and a Corollary
Are you interested in math or physics tutoring for you or someone you know? Please check out my website for more details of my registered business, or give me a call or email anytime! https://www.whatthehectogon.com/ +1 (973) 597-8775 sam@whatthehectogon.com In this video lesson, I intr
From playlist Geometry
Proving the Pythagorean Theorem
We learned about the Pythagorean Theorem, but where did it come from? How do we know it's definitely true? What if old Pythag just made it up off the top of his mystical skull? Lucky for us, in math we can proof that things are definitely true, and there are tons of ways to prove that the
From playlist Geometry
Pythagorean Theorem VIII (Bhāskara's visual proof)
This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) following essentially Bhāskara's proof (Behold!). This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. #math #manim #
From playlist Pythagorean Theorem
This geometry video tutorial provides a basic introduction into the pythagorean theorem. It explains how to use it to find missing sides and solve for x. In addition, it provides examples of solving word problems using pythagorean theorem for shapes such as right triangles, squares, rhom
From playlist Geometry Video Playlist
Pythagorean Theorem V (visual proof; Leonardo da Vinci)
This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using the a diagram that is now attributed to Leonardo da Vinci. The proof uses reflection and rotation symmetry arguments. This theorem states the square of the hypotenuse of a right triangle is
From playlist Pythagorean Theorem
How Coloring Triangles Revolutionized Mathematics [Schur's Theorem]
#some2 An explanation of Schur's Theorem and New Perspectives. This video was a submission to the Second Summer of Math Exposition. Also, apologies for the bad audio quality. SOURCES: MIT OCW 18.217: https://ocw.mit.edu/courses/18-217-graph-theory-and-additive-combinatorics-fall-2019/
From playlist Summer of Math Exposition 2 videos
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
Hermann Weyl Lectures Topic: The PCP theorem Speaker: Irit Dinur Affiliation: Weizmann Institute of Science; Visiting Professor, School of Mathematics Date: November 18, 2019 For more video please visit http://video.ias.edu
From playlist Hermann Weyl Lectures
High dimensional expansion and agreement testing - Irit Dinur
Computer Science/Discrete Mathematics Seminar II Topic: High dimensional expansion and agreement testing Speaker: Irit Dinur Affiliation: Weizmann Institute of Science; Visiting Professor, School of Mathematics Date: March 31, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
The Five Color Theorem (without Kempe chains)
Submission for the #SoME2 competition. Most animations were done in manim (https://www.manim.community/), and the 3d images were rendered using svg3d (https://github.com/prideout/svg3d). Proofs: The degree of a vertex or a face is the number of edge incidences (edges that meet a vertex o
From playlist Summer of Math Exposition 2 videos
AlgTop10: More on graphs and Euler's formula
We discuss applications of Euler's formula to various planar situations, in particular to planar graphs, including complete and complete bipartite graphs, the Five neighbours theorem, the Six colouring theorem, and to Pick's formula, which lets us compute the area of an integral polygonal
From playlist Algebraic Topology: a beginner's course - N J Wildberger
The Four-Color Theorem and an Instanton Invariant for Spatial Graphs I - Peter Kronheimer
Peter Kronheimer Harvard University October 13, 2015 http://www.math.ias.edu/seminars/abstract?event=83214 Given a trivalent graph embedded in 3-space, we associate to it an instanton homology group, which is a finite-dimensional Z/2 vector space. The main result about the instanton hom
From playlist Geometric Structures on 3-manifolds
Fermat's Last Theorem implies Euclids Theorem #SoME2
This video is based on the following article: Christian Elsholtz (2021) Fermat’s Last Theorem Implies Euclid’s Infinitude of Primes, The American Mathematical Monthly, 128:3, 250-257, DOI: 10.1080/00029890.2021.1856544 Here is an open accessible link to the article for you to check out:
From playlist Summer of Math Exposition 2 videos
Knots, three-manifolds and instantons – Peter Kronheimer & Tomasz Mrowka – ICM2018
Plenary Lecture 11 Knots, three-manifolds and instantons Peter Kronheimer & Tomasz Mrowka Abstract: Over the past four decades, input from geometry and analysis has been central to progress in the field of low-dimensional topology. This talk will focus on one aspect of these developments
From playlist Plenary Lectures
Ahlfors-Bers 2014 "Surface Subgroups, Cube Complexes, and the Virtual Haken Theorem"
Jeremy Kahn (CUNY Graduate Center): In a largely expository talk, I will summarize the results leading up to the Virtual Haken and Virtual Fibered Theorem for three manifolds, including 1. The Geometrization Theorem of Thurston and Perelman 2. The Surface Subgroup Theorem of the speaker an
From playlist The Ahlfors-Bers Colloquium 2014 at Yale
Converse Pythagorean Theorem & Pythagorean Triples
I explain the Converse Pythagorean Theorem and what Pythagorean Triples are. Find free review test, useful notes and more at http://www.mathplane.com If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage www.YouTube.com/Profro
From playlist Geometry