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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Proof Without Words
The General Formula of Polygonal Numbers
When objects are arranged in certain ways, they form a pattern. For example, square numbers can be obtained by forming objects in square arrangements. As shown below, the first four square numbers are 1, 4, 9, 16 and 25. Clearly, the number of dots in the 100th square number is . In general, the formula […]
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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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