Brahmagupta theorem

A New Proof of Bhramagupta’s Formula

For years John Conway searched for an elegant, symmetric, and geometric proof of Brahmagupta’s formula. Here it is, presented by a team of students from Proof School!

From playlist Summer of Math Exposition Youtube Videos

Brahmagupta's formula and the Quadruple Quad Formula (II) | Rational Geometry Math Foundations 126

The classical Brahmaguptas' formula gives the area for a convex cyclic quadrilateral, in terms of the four side lengths. We want to connect this with the purely 1-dimensional result called the Quadruple Quad Formula. First we review the corresponding relation between Heron's formula and th

From playlist Math Foundations

Brahmagupta's formula and the Quadruple Quad Formula (I) | Rational Geometry Math Foundations 125

In this video we introduce Brahmagupta's celebrated formula for the area of a cyclic quadrilateral in terms of the four sides. This is an obvious extension of Heron's formula. We are interested in finding a rational variant of it, that will be independent of a prior theory of `real numbers

From playlist Math Foundations

The Bretschneider von Staudt formula for a quadrilateral | Rational Geometry Math Foundations 132

Brahmagupta's formula gives the area of a cyclic quadrilateral in terms of its four (outside) `lengths', and the CQQ theorem was a logically correct reformulation of that result, using quadrances instead of `distances'. But what about a general quadrilateral? This is a redo of last week's

From playlist Math Foundations

Calculus - The Fundamental Theorem, Part 1

The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.

From playlist Calculus - The Fundamental Theorem of Calculus

Heron’s formula: What is the hidden meaning of 1 + 2 + 3 = 1 x 2 x 3 ?

Today's video is about Heron's famous formula and Brahmagupta's and Bretschneider's extensions of this formula and what these formulas have to do with that curious identity 1+2+3=1x2x3. 00:00 Intro 01:01 1+2+3=1x2x3 in action 02:11 Equilateral triangle 02:30 Golden triangle 03:09 Chapter

From playlist Recent videos

Theory of numbers: Gauss's lemma

This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di

From playlist Theory of numbers

History of Indian Mathematics Part II: Brahmagupta, Algebra, and Zero

Ever wonder how zero evolved from placeholder to integer? Or about how the formula for the area of a cyclic quadrilateral was discovered? Then check out this video! And be sure to check out the rest of the series on the blog: https://centerofmathematics.blogspot.com/2019/11/history-of-indi

From playlist History of Indian Mathematics

Calculus 5.3 The Fundamental Theorem of Calculus

My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart

From playlist Calculus

What Is The Area? Square Between Two Circles

Thanks to Nibedan Mukherjee who sent me the problem and its solution all the way back in October 2018. I was also told this problem appeared in the 2019 Senior Mathematical Challenge by the UKMT. 2019 Senior Mathematical Challenge paper (see question 25) https://www.ukmt.org.uk/sites/defa

From playlist Math Puzzles, Riddles And Brain Teasers

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

The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg

In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t

From playlist Algebraic Calculus One

Who invented zero? | India and The Divinity of Numbers | Math and the Rise of Civilization

Who invented zero in India? In 628 CE, astronomer-mathematician Brahmagupta wrote his text Brahma Sphuta Siddhanta which contained the first mathematical treatment of zero. He defined zero as the result of subtracting a number from itself, postulated negative numbers and discussed their pr

From playlist Civilization

The Cyclic quadrilateral quadrea theorem | Rational Geometry Math Foundations 127a | NJ Wildberger

The Cyclic quadrilateral quadrea (CQQ) theorem is a major re-evaluation of the classical theorem of Brahmagupta on the area of a convex cyclic quadrilateral, which combines it with Robbins much more recent formula for the corresponding area of a non-convex cyclic quadrilateral. We illustr

From playlist Math Foundations

The Cyclic quadrilateral quadrea theorem (cont.) | Rational Geometry Math Foundations 127b

The Cyclic quadrilateral quadrea (CQQ) theorem is a major re-evaluation of the classical theorem of Brahmagupta on the area of a convex cyclic quadrilateral, which combines it with Robbins much more recent formula for the corresponding area of a non-convex cyclic quadrilateral. We exhibit

From playlist Math Foundations

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

What are complex numbers? | Essence of complex analysis #2

A complete guide to the basics of complex numbers. Feel free to pause and catch a breath if you feel like it - it's meant to be a crash course! Complex numbers are useful in basically all sorts of applications, because even in the real world, making things complex sometimes, oxymoronicall

From playlist Essence of complex analysis