Squares in number theory

The Book of Squares

The Book of Squares, (Liber Quadratorum in the original Latin) is a book on algebra by Leonardo Fibonacci, published in 1225. It was dedicated to Frederick II, Holy Roman Emperor. After being brought to Pisa by Master Dominick to the feet of your celestial majesty, most glorious prince, Lord F., — Leonardo Fibonacci, Liber quadratorum, epistle (translated by L. E. Sigler) The Liber quadratorum has been passed down by a single 15th-century manuscript, the so-called ms. E 75 Sup. of the Biblioteca Ambrosiana (Milan, Italy), ff. 19r-39v. During the 19th century, the work has been published for the first time in a printed edition by Baldassarre Boncompagni Ludovisi, prince of Piombino. Appearing in the book is Fibonacci's identity, establishing that the set of all sums of two squares is closed under multiplication. The book anticipated the works of later mathematicians such as Fermat and Euler. The book examines several topics in number theory, among them an inductive method for finding Pythagorean triples based on the sequence of odd integers, the fact that the sum of the first odd integers is , and the solution to the congruum problem. (Wikipedia).

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Chapter 3 - Perfect Squares - IB Math Studies (Math SL)

Hello and welcome to What The Math. This is a Chapter 3 video about perfect squares expansion and a few common misconceptions about it. This is a part of Chapter 3 from Harris Publication version of IB math book by Haese.

From playlist IB Math Studies Chapter 3

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Magic Squares part 3: The magic in the mirror.

Time to start to learn how to build even-order magic squares! Playlist:https://youtube.com/playlist?list=PLV_8Ld73yCWEJlCA4LQrioGYgMCn4gN7x Part 1: https://youtu.be/dvkREHaqQWM Part 2: https://youtu.be/-r2VPdxjCqE Part 3: https://youtu.be/seCFxxnid_0 Part 4: https://youtu.be/2h3DHubiROo

From playlist Magic Squares

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Difference of squares formula

Visual explanation of the difference of squares formula from math class. #shorts #math #maths #mathematics The Difference - The Wallflowers https://youtu.be/5qSAMtomFvk

From playlist Math Shorts

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Square Root of 2

In this video, I have fun composing the digits of the square root of 2 into a song

From playlist Math Play

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What’s the difference of two squares?

This is a short animation showing one way to think of the difference of squares formula (at least when the two numbers involved are positive). #manim #math #proofwithoutwords #visualproof

From playlist Algebra

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Introduction to Square Roots

This video introduces perfect squares and square roots. http://mathispower4u.yolasite.com/

From playlist Radicals

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Dimensions Chapter 6

Chapter 6 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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Dimensions Chapter 1

Chapter 1 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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Complete the Square Without Fractions

In this video I will show you a new way to complete the square when solving quadratic equations. I have never seen this method before in any book. I did not come up with this method but I did find it in a really old book written in the 1800's. The good thing about this method is that you c

From playlist Learn Math From Books

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The Calculus Problem Nobody Could Solve

In this video I go over a book and then do a harder calculus problem. The book is called Essential Calculus with Applications and it was written by Richard Silverman. The calculus problem is one which I put on various exams every semester as extra credit. Nobody was ever able to get it com

From playlist Book Reviews

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Math Everyone Should Know

In this video I go over a book on Algebra and Trigonometry. I talk a little bit about the book and then go on to do a problem from the book. The problem involves a quadratic equation and it's kind of cool I think. The book is called Algebra and Trigonometry and it was written by Edward Cam

From playlist Book Reviews

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Learn Math Proofs with this FREE Book

In this video I go over a book that you can use to teach yourself how to write mathematical proofs. Several people have left very positive comments about this book and I agree with them, it's a great book! This book is available for FREE in pdf version. You can also purchase softcover and

From playlist Book Reviews

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A Powerful Elementary Integral [ (Almost) Impossible Integrals #1 ]

Support Cornel! =) Springer: http://www.dpbolvw.net/click-9116313-13350268?url=https%3A%2F%2Fwww.springer.com%2Fde%2Fbook%2F9783030024611%3Futm_medium%3Daffiliate%26utm_source%3Dcommission_junction%26utm_campaign%3D3_nsn6445_product_PID%25zp%26utm_content%3Dde_05032018%23otherversion%3D97

From playlist Integrals

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Integral of (2x - 1)/sqrt(4x^2 + 4x + 2)

In this problem I evaluate the indefinite integral of (2x - 1)/sqrt(4x^2 + 4x + 2). This problem is from a book called Integral Calculus written by H.B. Phillips. This book was published in 1917. The book on amazon: https://amzn.to/3y4f71y The pencils I used in this video: https://amzn.to

From playlist Solutions to Integral Calculus by H.B. Phillips 1917

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Quadratic Equations - Short Revision || CBSE Class 10 Math || Infinity Learn Class 9&10

Don’t Memorise brings learning to life through its captivating educational videos. To Know More, visit https://infinitylearn.com/ ✅ Please Join Our Telegram Channel ►https://t.me/InfinityLearn9_10 ✅Watch Board Brahmastra for Complete CBSE Class 10 Revision👉 https://www.youtube.com/watch?

From playlist Short Revision || Mathematics || Infinity Learn Class 9&10

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Magic Squares part 4: The most magical of them all

This is the last part. Enjoy my very special magic square! Playlist:https://youtube.com/playlist?list=PLV_8Ld73yCWEJlCA4LQrioGYgMCn4gN7x Part 1: https://youtu.be/dvkREHaqQWM Part 2: https://youtu.be/-r2VPdxjCqE Part 3: https://youtu.be/seCFxxnid_0 Part 4: https://youtu.be/2h3DHubiROo 00

From playlist Magic Squares

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Visualising Pythagoras: ultimate proofs and crazy contortions

NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Finally, a Mathologer video about Pythagoras. Featuring some of the most beautiful and simplest proofs o

From playlist Recent videos

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NUMBERS: Pi (π) - Number of the Sky | Five numbers that changed the world | Cool Math

NUMBERS - secrets of Math. Mathematics is shrouded behind a veil and does not easily reveal itself. Students resort to rote memorization of math formulas to solve problems in a boring exercise of the mind that is also repetitive. However, if you knew the history of mathematics, the way the

From playlist Civilization

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Chapter 3 - Differences of Squares - IB Math Studies (Math SL)

Hello and welcome to What The Math. This is a Chapter 3 video about differences of squares and a Minecraft like game to help you visualize it. This is a part of Chapter 3 from Harris Publication version of IB math book by Haese.

From playlist IB Math Studies Chapter 3

Related pages

Integer | Congruum | Pierre de Fermat | Pythagorean triple | Brahmagupta–Fibonacci identity | Algebra | Leonhard Euler | Square (algebra) | Mathematical induction | Number theory