## Bach’s Music on a Moebius Strip

If you are fond of classical music, then you have probably heard of Johann Sebastian Bach. He was one of the great composers of the Baroque period. His music was known for its intellectual depth, technical command, and artistic beauty (I copied the last sentence from Wikipedia, lol).

But what will surprise you more is how his music is tied to mathematics. Watch the video below of how playing the music backwards and forwards simultaneously can be visualized using a Moebius Strip.

H/T: Open Culture

## Aristotle’s Theory on the Mathematics of Rainbows

Rainbows are one of the most beautiful things that we see in the sky during the day. They are the circular arcs formed by the Sun’s rays and water droplets in the Earth’s atmosphere. For thousands of years, mathematicians and scientists wondered about its mystery. Is there a mathematical explanation why rainbows appear as they do?

The video below shows a  modern analysis of the structure and the mathematics of rainbows. What is surprising is that the modern explanation is very similar to that of Aristotle’s theory who lived about 300 BC. The mathematics involved are parallel lines, circles, and arcs.

## Math Trick 4: A Shortcut on Multiplying Numbers by 13

This is the fourth part of the Math and Multimedia’s Math Tricks and Shortcuts Series. In this post, I am going to discuss a shortcut on multiplying numbers by 13 (my aplogies to all the triskaidekaphobic). Well, I am not really sure if you would like to call it a shortcut since multiplying large numbers by 13 using the conventional method might be faster. Anyway, I am going to show you though that it works with few cases and we will later discuss why it works.

Shortcut on Multiplying Numbers by 13

Append 0 before and after the number you are multiplying by 13.

Starting with the ones digit of the original number, multiply it by 3 and add the product to the next digit on the right.  The result of this calculation is the ones digit of the product of the number and 13.

Do the process again to the tens digit. Multiply it by 3 and add the product to the next digit on the right. The result of the calculation is the tens digit of the product of the number and 13.