The sum of the first n odd integers is a square. This is a theorem and can easily be proven if you have already learned proof by mathematical induction. Even though it sounds like a boring theorem, it is actually very interesting if represented visually. Consider the following diagrams and their numerical representations. Can […]

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# Posts tagged with 'proof without words'

## Representing the Sum and Difference of Two Squares

One of the most beautiful characteristics of mathematics is you can create multiple representations of a single concept. Functions for example can represented in words, equations, graphs, or tables. In this post, we represent geometrically an algebraic concept namely the sum and difference of two squares. The difference of two squares states you can factor […]

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## A Geometric Proof of an Infinite Series

In the previous post, we have seen how easy it is to prove a problem in Geometry using Algebra. The problem could also be proven geometrically, but the proof is longer. In this post, we will learn how to use Geometry to prove a problem on infinite series. That is, we have to show geometrically, […]

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