## 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 $\sqrt{5}$?

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

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.

## Angles and the Hindu-Arabic Numerals

The image below has been circulating on the internet for quite a while. It shows that the number of angles on the numerals is equal to the value of the number. The number four, for instance, has four angles.

The image was not created without basis. During the infancy of the Hindu-Arabic numeral system, the way of writing numbers  that we use today, a system of counting angles as shown above was adopted. This was shortly after the release of two books namely On the Calculation with Hindu Numerals by al-Kwharizmi (about 825 AD) and On the Use of Indian Numerals by Abu Yusuf Yaqub Ibn Ishdaq al-Kindi (830 AD).  These two books popularized the use of Hindu-Arabic numerals in the Middle East.

As we all know, eventually the Hindu-Arabic way of writing numbers and computations replaced the Roman Numerals.

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Reference: The Story of Mathematics: From Creating the Pyraminds to Exploring Infinity