Theorems about quadrilaterals and circles | Area
In Euclidean geometry, Brahmagupta's formula is used to find the area of any cyclic quadrilateral (one that can be inscribed in a circle) given the lengths of the sides; its generalized version (Bretschneider's formula) can be used with non-cyclic quadrilateral. Heron's formula can be thought as a sub-case of the Brahmagupta's formula. (Wikipedia).
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
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
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
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
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
Given a point and vertex find the formula of the parabola
👉 Learn how to write the equation of a parabola given three points. The equation of a parabola is of the form f(x) = ax^2 + bx + c, where a, b and c are constants. Since, the equation of a parabola has 3 constants, three equations and hence three points are needed to solve/obtain the equat
From playlist Write the Equation of a Quadratic Given Vertex and a Point
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
Some students in Finland missed out on 1000 euros because they missed this problem! Sources for problem https://old.reddit.com/r/math/comments/cy7u04/a_very_simple_but_tricky_question_from_finnish/ @rizka commented with a link to the 2014 exam (in Finnish). It is question 4: https://yle.f
From playlist Math Puzzles, Riddles And Brain Teasers
Euler's formulas, Rodrigues' formula
In this video I proof various generalizations of Euler's formula, including Rodrigues' formula and explain their 3 dimensional readings. Here's the text used in this video: https://gist.github.com/Nikolaj-K/eaaa80861d902a0bbdd7827036c48af5
From playlist Algebra
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
Describe and solve for the zeros using quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | x^2+bx+c
This is a visual way to understand Brahmagupta's quadratic formula. #Shorts Song Credits Song: Kajra Re Singers: Alisha Chinai, Shankar Mahadevan, Javed Ali Music: Shankar-Ehsaan-Loy Lyrics: Gulzar https://youtu.be/4dsFQFCvVGU Lucas Vieira animation https://1ucasvb.tumblr.com/post/427390
From playlist Math Shorts
Some Snapshots of India's Mathematical Past by S. G. Dani
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022