Discrete geometry | Mathematical problems | Geometric dissection | Recreational mathematics | Tessellation

Squaring the square

Squaring the square is the problem of tiling an integral square using only other integral squares. (An integral square is a square whose sides have integer length.) The name was coined in a humorous analogy with squaring the circle. Squaring the square is an easy task unless additional conditions are set. The most studied restriction is that the squaring be perfect, meaning the sizes of the smaller squares are all different. A related problem is squaring the plane, which can be done even with the restriction that each natural number occurs exactly once as a size of a square in the tiling. The order of a squared square is its number of constituent squares. (Wikipedia).

Squaring the square
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Squaring Square Roots

In this video, we look at a very useful pattern found in squaring square roots

From playlist Middle School - Worked Examples

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Squaring the circle illusion #shorts

How to make a shape that looks like a square from one direction and a circle from another. Buy from Shapeways: http://shpws.me/Te9N Download to print yourself: https://www.printables.com/model/270848-squaring-the-circle-illusion

From playlist 3D printing

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Squaring Numbers with Digits of 1

#shorts This video shows a pattern when squaring number with digits of 1.

From playlist Math Shorts

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Squaring the Circle by Rolling (animated visual proof)

This is a short, animated visual proof that we can square the circle IF we allow the circle to roll. Unfortunately, this is not a solution to the squaring the circle problem from antiquity because that requires it to be done with only a straightedge and compass. #mathshorts​ #mathvideo​ #m

From playlist Pi

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Solving an equation by taking the square root of a fraction

👉Learn how to solve quadratic equations using the square root method. It is important to understand that not all quadratics have to be solved using factoring or quadratic formula. When we only have one variable but it is squared we can just use inverse operations to isolate the variable.

From playlist Solve Quadratic Equations by Factoring

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Solving using the square root method with fractions

👉Learn how to solve quadratic equations using the square root method. It is important to understand that not all quadratics have to be solved using factoring or quadratic formula. When we only have one variable but it is squared we can just use inverse operations to isolate the variable.

From playlist Solve Quadratic Equations by Factoring

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Solving a quadratic equation using inverse operations

👉Learn how to solve quadratic equations using the square root method. It is important to understand that not all quadratics have to be solved using factoring or quadratic formula. When we only have one variable but it is squared we can just use inverse operations to isolate the variable.

From playlist Solve Quadratic Equations by Factoring

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Solving an equation by using the square root property - Math help

👉Learn how to solve quadratic equations using the square root method. It is important to understand that not all quadratics have to be solved using factoring or quadratic formula. When we only have one variable but it is squared we can just use inverse operations to isolate the variable.

From playlist Solve Quadratic Equations by Factoring

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AP Calculus BC: Lesson 2.4 Trigonometric Substitution

AP Calculus BC Unit 2: Advanced Integration Lesson 4: Trigonometric Substitution

From playlist AP Calculus BC

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Calculus 7.3 Trigonometric Substitution

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

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How To Factor Difference of Squares - Algebra

This algebra video tutorial explains how to factor difference of squares. It contains examples with parentheses and multiple variables.

From playlist New Algebra Playlist

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AP Calculus BC Homework 2.4 Trigonometric Substitution

================================= AP Calculus BC / IB Math HL Unit 2: Advanced Integration Lesson 4: Trigonometric Substitution =================================

From playlist AP Calculus BC

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Simplifying Numerical Square Roots 8 Examples

I introduce Simplifying Numerical Square Roots and then work through 8 Examples Square root of a perfect square 7:21 Simplifying a non perfect square 8:06 Simplifying a fraction 9:36 Square root of the sum of two numbers 11:20 Square root of a fraction. Denominator not a perfect square. 1

From playlist PreCalculus (New)

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Circumference of an Ellipse

This calculus 2 video tutorial explains how to calculate the circumference of an ellipse using integration and the arc length formula and it explains how to estimate the circumference of an ellipse using a simple formula. Subscribe: https://www.youtube.com/channel/UCEWpbFLzoYGPfuWUMFPSaoA

From playlist New Calculus Video Playlist

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Pythagoras' Theorem: Introduction

An introduction to Pythagoras' Theorem with interactive examples and illustrations. Introduction: 0:00 Discover Pythagoras Yourself (Graph Paper Needed!): 0:43 Visual Demonstration (Water Wheel):

From playlist GCSE Topic Tutorials

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Integration into Inverse trigonometric functions using Substitution

This calculus video tutorial focuses on integration of inverse trigonometric functions using formulas and equations. Examples include techniques such as integrating by substitution, u-substitution, splitting fractions and completing the square. This video contains plenty of practice pro

From playlist New Calculus Video Playlist

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Introduction to number theory lecture 40. Examples of positive definite forms

This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We study some examples of positive defiite forms of small discriminant, and work out which

From playlist Introduction to number theory (Berkeley Math 115)

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Maximize the area of one ellipse!

We look at a nice geometry problem involving ellipses inscribed in a circle. Sacred Mathematics: Japanese Temple Geometry: https://amzn.to/2ZIadH9 Playlist: https://youtube.com/playlist?list=PL22w63XsKjqyZZAicSHbpVhJzLPfPMJf6 Please Subscribe: https://www.youtube.com/michaelpennmath?sub

From playlist Geometry

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How to solve a quadratic when there are no solutions

👉Learn how to solve quadratic equations using the square root method. It is important to understand that not all quadratics have to be solved using factoring or quadratic formula. When we only have one variable but it is squared we can just use inverse operations to isolate the variable.

From playlist Solve Quadratic Equations by Factoring

Related pages

Kirchhoff's circuit laws | Greatest common divisor | List of Martin Gardner Mathematical Games columns | Journal of Combinatorial Theory | Tessellation | Square packing in a square | Branko Grünbaum | Integer | Cube | Martin Gardner | R. Leonard Brooks | Squaring the circle | Exponential growth | Cuboid | W. T. Tutte | Hypercube