In algebra, a Pythagorean field is a field in which every sum of two squares is a square: equivalently it has Pythagoras number equal to 1. A Pythagorean extension of a field is an extension obtained by adjoining an element for some in . So a Pythagorean field is one closed under taking Pythagorean extensions. For any field there is a minimal Pythagorean field containing it, unique up to isomorphism, called its Pythagorean closure. The Hilbert field is the minimal ordered Pythagorean field. (Wikipedia).
From playlist Miscellaneous
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
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
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 Trig ID via Areas (2)
Pythagorean Trig Identity via Areas. Made with #GeoGebra: https://www.geogebra.org/m/xmhyyapn
From playlist Trigonometry: Dynamic Interactives!
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
Pythagorean theorem - What is it?
► My Geometry course: https://www.kristakingmath.com/geometry-course Pythagorean theorem is super important in math. You will probably learn about it for the first time in Algebra, but you will literally use it in Algebra, Geometry, Trigonometry, Precalculus, Calculus, and beyond! That’s
From playlist Geometry
Let’s Get To Know The Pythagorean Theorem….Step-by-Step….
TabletClass Math: https://tcmathacademy.com/ Math help with the Pythagorean Theorem. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebra Notes: https://tabletclass
From playlist GED Prep Videos
Ravi Vakil: Algebraic geometry and the ongoing unification of mathematics
Abstract: I will try to share a glimpse of this strange unification of many different ideas. This talk is aimed at a general audience, and no particular background will be assumed. When we look carefully at nature, we can discover surprising coincidences, which suggest deeper underlying s
From playlist Popular presentations
Pythagoras had a problem with beans and irrationality. What really happened? I don't know! The square root of two is irrational, and beans are delicious. My personal website, which you might like: http://vihart.com
From playlist Doodling in Math and more | Math for fun and glory | Khan Academy
[T2 2019] Les mathématiques au fil du temps ; Les points rationnels - Schappacher/Peyre
Norbert Schappacher (Université de Strasbourg) & Emmanuel Peyre (Université Grenoble Alpes) / 09.05.2019 Les mathématiques au fil du temps Les points rationnels : des tablettes babyloniennes jusqu'au XXè siècle La première partie présentera une série d'exemples tirés de l’histoire des m
From playlist 2019 - T2 - Reinventing rational points
True History of "Pythagoras" Theorem
It is common in science to attribute results to people who were not original discoverers. This is likely to be the case with Pythagoras Theorem- the most well- known mathematical fact ! Big thanks to Dr. Daniel Mansfield for kindly consulting me on his research. Please refer to his paper
From playlist Math history and stories
Episode 1 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is an introduction to the course and some history of ideas about the real numbers. Actual course starts at 17:50. Class webpage: http://cstaecker.fa
From playlist Math 3371 (Real analysis) Fall 2020
Relativity 7a - differential geometry I
The mathematical field of Differential Geometry turns out to provide the ideal mathematical framework for General Relativity. Here we look at some of the basic concepts, in particular the idea of a "metric tensor." Note: To keep these videos "bite sized" I stopped this one before the part
From playlist Relativity
You've never seen imaginary numbers like this before
#some2 The material in this video is heavily inspired by Norman Wildberger's Youtube Channel. Go check it out! https://www.youtube.com/c/njwildberger/featured 0:00 Intro 1:23 2D symmetries 3:00 Matrix representation 5:04 Field 6:24 Quadratic Forms 8:34 Dot Product 11:20 Determinant 13:1
From playlist Summer of Math Exposition 2 videos
Net electric field from multiple charges in 2D | Physics | Khan Academy
In this video David solves an example 2D electric field problem to find the net electric field at a point above two charges. Created by David SantoPietro. Watch the next lesson: https://www.khanacademy.org/science/physics/electric-charge-electric-force-and-voltage/electric-field/v/electro
From playlist Electric charge, field, and potential | AP Physics 1 | Khan Academy
Physical Science 2.4b - The Pythagorean Theorem
A simple introduction to the Pythagorean Theorem, along with an example, and some comments on the Pythagoreans.
From playlist Physical Science Chapter 2 (Complete chapter)
Why does the Pythagorean Theorem Work? #SoME1
Some exploration of the Pythagorean Theorem and why it works.
From playlist Summer of Math Exposition Youtube Videos
http://www.teachastronomy.com/ Pythagoras was one of the most influential thinkers in history. This Greek philosopher and mathematician came up with the idea that numbers were the basis of everything. There is no written record, and nothing about Pythagoras survives in writing. He essen
From playlist 02. Ancient Astronomy and Celestial Phenomena