Mathematical Proofs Without Words: What are they?

In  Proof of the Sum of Square Numbers, I have mentioned about proof without words. Some of you are probably wondering what they are, so I will discuss in detail. Proof without words are diagrams or pictures that help readers see why a particular statement is true even without accompanying explanations.  One example is a […]
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A Simple Proof of the Arithmetic Mean Geometric Mean Inequality

Last February, we have used area to prove the Arithmetic Mean – Geometric Mean Inequality (AM-GM Inequality). In this post, we show a simpler proof.   Recall that the AM-GM Inequality states that given two numbers, their geometric mean is always less than or equal to their arithmetic mean.  That is given two numbers and , […]
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Another Proof of the Sum of the First n Positive Integers

We have discussed how Gauss was able to devise  a clever way to add the first positive integers at a very young age in a few minutes. We generalized his method and have also seen the link between the sum and the area of a triangle. In both discussions, we have shown that the sum of the […]
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