Dodgem Cars: A Pretty Interesting Abstract Game

It’s a rainy holiday morning where I am and while browsing at a math forum, I came across with a pretty clever game called Dodgem. The game is really simple, but it has some interesting properties. After a couple internet search, I found out that the game was credited to Colin Vout and described the book in Winning Ways by Berlekamp, Conway and Guy. The book according to a discussion thread is the manual of the game and contains mathematical analysis about it.  Here is how the game works.

Two players are seated crosswise and play on a 3 x 3 grid.  Each player has two cars. The objective of each player is to move all the cars off the far end of the board while blocking the opponent’s cars.  The cars may only be moved forward and sideward (in respect to the player) and not backward. The cars may also not be moved to occupied grids. They may leave the board with only a forward move. The winner is the player who first has no legal move on his turn because either all his cars are off the board or blocked by the opponent’s cars. » Read more

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.  » Read more

Mathematics and Multimedia Blog Carnival 23

Welcome to the 23rd edition of the Mathematics and Multimedia Blog Carnival. This is a repost from Mathematical Palette, a blog which I no longer maintain.

In this edition, we have a miscellany of mathematics and mathematics teaching articles.

John Cook presents a proof technique that seems to give you something for nothing, an interesting Binomial coefficient trick, posted at the Endeavor.

Shaun Klassen has a clear explanation about the basic concept of limits in Using Limits to Find Tangents posted at Mathematics Concepts Explained. » Read more

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