Diophantine equations

Brahmagupta's problem

This problem was given in India by the mathematician Brahmagupta in 628 AD in his treatise Brahma Sputa Siddhanta: Solve the Pell's equation for integers . Brahmagupta gave the smallest solution as . (Wikipedia).

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B25 Example problem solving for a Bernoulli equation

See how to solve a Bernoulli equation.

From playlist Differential Equations

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B06 Example problem with separable variables

Solving a differential equation by separating the variables.

From playlist Differential Equations

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Separation of variables and the Schrodinger equation

A brief explanation of separation of variables, application to the time-dependent Schrodinger equation, and the solution to the time part. (This lecture is part of a series for a course based on Griffiths' Introduction to Quantum Mechanics. The Full playlist is at http://www.youtube.com/

From playlist Mathematical Physics II - Youtube

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B04 Example problem with separable variables

Solving a differential equation by separating the variables.

From playlist Differential Equations

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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

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10% Students Solve This Trig Equation Wrong (Including me!)

Once you have a solid idea for how to solve trigonometric equations it is time for a challenge. A problem that will test you knowledge and ability to apply algebraic concepts to trigonometric equations. This problem does exactly that. ✅ Know when to use identities https://youtu.be/UArTc

From playlist Challenged and Confused Videos

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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

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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

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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

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Solve the general solution for differentiable equation with trig

Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give

From playlist Differential Equations

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B07 Example problem with separable variables

Solving a differential equation by separating the variables.

From playlist Differential Equations

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1000 Euro Question!

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

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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

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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

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Solve a Bernoulli Differential Equation Initial Value Problem

This video provides an example of how to solve an Bernoulli Differential Equations Initial Value Problem. The solution is verified graphically. Library: http://mathispower4u.com

From playlist Bernoulli Differential Equations

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SM64 Pendulum Math [EP1]: 6,248,970 and 507,780 (#MegaFavNumbers)

Pannenkoek2012's Pendulum Video: https://www.youtube.com/watch?v=f35hBQ0zfO0 Pell's equation: https://en.wikipedia.org/wiki/Pell%27s_equation Brahmagupta's identity: https://en.wikipedia.org/wiki/Brahmagupta%27s_identity Pendulum Amplitude Equation: https://www.desmos.com/calculator/qimiwh

From playlist MegaFavNumbers

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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

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AWESOME Brachistochrone problem

In this video, i set up and solve the brachistochrone problem, which involves determining the path of shortest travel in the presence of a downward gravitational field. This is done using the techniques of calculus of variations, and it will turn out that the brachistochrone can be represe

From playlist MECHANICS

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2023 Number Challenge: Pell's Equation with d=2023

Check out other 2023 Number Challenges from this list. Share with your friends!! https://www.youtube.com/playlist?list=PLXpXgWDr4HM7KKeX7CaQIu4tfPRJ2HiUM Please subscribe to the channel. In this video, we study Pell's equation when d=2023. We use two methods: 1. With continue continu

From playlist Math Problems with Number 2023

Related pages

Pell's equation | Indeterminate equation | Diophantine equation | Integer