Irrational Lengths and The Root Spiral

When calculators were not yet invented, it was hard for mathematicians to approximate irrational numbers. The irrational numbers was the offshoot of the discovery that the side length of the diagonal of a square with side length 1 is irrational. But how do mathematicians of the ancient time approximate a segment with length, say, \sqrt{5}? Can they draw a segment whose length is exactly \sqrt{5}?

root spiral

With the knowledge of the Pythagorean theorem, it is possible to create a right triangle with side 1 unit making the diagonal \sqrt{2}. The diagonal can then be used as the side of another right triangle whose shorter side length is 1. This process can go on producing the figure above. » Read more

Paul Erdos: The Wandering Mathematician

One of the notable mathematicians who have dedicated his life (literally) to mathematics was Paul Erdos. Erdos, a Hungarian mathematician, was one of the most prolific mathematicians. He has published more research papers than any mathematician in history, 1500 research papers in his lifetime.

paul erdos

Paul Erdos

Starting at age 25, Erdos started traveling from one university to another, and collaborating with numerous mathematicians. Later in his life, he lived almost as a vagabond; he gave up most of his belongings leaving only what is needed for travel. He would use his earnings to help mathematics students. He would offer prizes to solutions to unresolved mathematical problems ranging from $25 to several thousands. The most famous of these problems is the Erdos Conjecture on arithmetic progressions which has a prize of $5000.

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Similarity and Architecture

We often compare and contrast things around us.  Brand X is better than Brand Y, Actress 1 is more beautiful than Actress 2, Usain Bolt is a faster runner compared to most athletes.

We are also fond of people or things with similarities. We are keen in observing people who look alike, we have a habit of collecting similar things of different colors (or sizes), and we even collect gadgets from a single manufacturer.

celebrity-look-alikes1

Similar things are everywhere. There are cartoon characters that are similar in some ways.  Those who do not recognize them would mistake them as family despite their different origins.  Buu and Patrick, for example, are like “uncles”, yet Buu was a violent alien, while Patrick has always been an amiable and friendly Starfish.
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