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.  Continue reading

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.thirteen

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. Continue reading

Where were you on these consecutive dates?

Like the alignment of planets, there are events that only only occur a few times in a century or millennium. One of such events are the appearance of dates with consecutive numbers, the example of such are the shown below. These dates with  only appear once every century if we consider the last two digits of the year, or every millennium if we consider the last three digits.

We are lucky because we are the only generation in this millennium (or century) who are present these consecutive dates. If you are keeping a daily diary, check out what happened on these dates.

01/02/03

02/03/04

03/04/05

04/05/06

05/06/07

06/07/08

07/08/09

08/09/10

09/10/11

010/11/12

When will this phenomenon happen again? In year 3003, 991 years from now if we consider the last three digits of the year. If we consider only the two digits , it will repeat 91 years from now which is in year 2103.

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