## 11 Proven Proof Techniques Non-Math Majors Should Know

Proofs is the heart of mathematics.  It is what differentiates mathematics from other sciences.  In mathematical proofs, we can show that a statement is true for all possible cases without showing all the cases. We can be certain that the sum of two even numbers is  even without adding all the possible pairs.

For those who are “non-math people,” the proof techniques below will help you, but the “math people” are probably those who are going to enjoy them more.  » Read more

## The Mathematical Reason Why Manholes are Round

Have you ever wondered why manholes are circular?

The answer is simple. Using other shapes, it is possible for manhole covers to fall through the hole. For example, a square cover with side length 1 meter can fall through a square manhole even if the lip (stopper) makes the side length of the manhole  less than that of its cover.

To explain further, suppose a 5-cm lip is placed on each side of the hole, then that leaves a square hole with side length 90 cm.  Using the Pythagorean theorem, that hole has diagonal of more than 1.27 meters, large enough to swallow the cover (see 3rd illustration in the 1st figure) with a burp. On the other hand, the constant diameter of a circular cover ensures that it  does not fall through the circular hole no matter how roughshod (I hope I used the word correctly) it is moved by vehicles.  » Read more

## The Kaleidoscopic Mathematics of Colors

What is amazing about mathematics is that it can be used to represent or approximate reality.  Shapes can be represented by graphs, patterns by equations, and events by mathematical models. In this post, we discuss another type of representation — the mathematics  of colors. Although movies and animations, nowadays, show vibrant and life-like colors, all of the colors we see are just combinations of three primary colors: red, green, and blue. The technology used in many of these movies (both software and hardware) use the red-green-blue or the RGB color model. » Read more

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