Saturday, February 2, 2008

Geometry and Roller Coasters

Have you ever thought about geometry when you're riding a roller coaster? Of course you haven't! You will be happy to know, however, that the designer of the roller coaster did. If you've ever ridden an old wooden roller coaster, you probably have seen wooden supports like the ones found in this picture of The Beast at Paramount's Kings Island.

So you're at the very top of the first big drop of a world famous roller coaster. If you're an average person, you're thinking, "OMG, I am really high up."

If you're a nerdy geometry teacher, you're thinking, "OMG, look at all the triangles."

Here I have pointed out three of the literally thousands of triangles found in The Beast. Why so many triangles? The reason lies in a simple property of triangles.

If the lengths of the sides of a triangle are fixed, the angles are fixed, too. In a wooden roller coaster, the sides of the triangles are made of wood. The wood is nailed together and cannot stretch, so the size and shape of each triangle is unchanging. Putting triangles into the structure of the coaster makes it strong and rigid.

This is a property that is unique to triangles. You can find many quadrilaterals with equal length sides but different angles. Pentagons are even worse. Only the triangle has angle measures determined by the length of its sides.

So next time you're speeding down a track at 60+ mph. Take a moment to stop and appreciate the geometry all around you.

Geometric Art

The coolest thing about geometry is that it is such a visual kind of math. Many famous artists use geometry in their work. One very famous mathematical artist was named M.C. Escher. He is famous for his tessellations, where one image was repeated to fill an entire page without gaps.

He is also famous for being able to morph an image into another image. Look how he changes the fish into a flying duck.

Sometimes he would draw things that were physically impossible in real life. In this picture, the stairway always goes up, but you would never get anywhere.

Look how Escher mixes geometry and math with creativity!

For more information and pictures by M.C. Escher, visit his official website at

A blog with a purpose

I think one of the greatest flaws in teaching is when the students do not understand the relevance of what they're learning. Every student at some point or another has said, "When am I ever going to need this?" Through this blog I hope to show students some practical and cool uses of geometry in the world. I will also post any interesting geometry news.