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Shapes of constant width
Shapes of constant width
3D Shapes
This shape is based off the triangle but is almost a rounded pyramid except 3 edges are pointed and the other 3 are rounded. You can put something on top of them and roll around with them under just as if they were spheres.
Constant Width on a Bike
A Fifty Pence Coin
Someone used this on a bike and it was a smooth ride even though it had 2 different wheels. This worked because the bike was resting on top of the wheels instead of on an axle.
A fifty pence coin has constant width because of it's rounded edges. Any coin has to be of constant width for a vending machine to be able to tell what kind of a coin is in it.
A Circle
Reuleaux Triangles
A circle is of constant width because it is completely even.
This is a triangle that acts like a circle
A Reuleaux triangle rolls evenly without moving the center of the chassis on top of it but the center of the triangle does move.
Bibliography
- Wikipedia. "Reuleaux Triangle." Wikipedia. Wikimedia Foundation, 24 Nov. 2013. Web. 05 Dec. 2013. -about the Realeaux Triangle
- "A Rolling Reuleaux Triangle." YouTube. YouTube, 03 July 2009. Web. 09 Dec. 2013.
- "Shapes and Solids of Constant Width - Numberphile." YouTube. YouTube, 11 Nov. 2013. Web. 09 Dec. 2013.
- http://web.mat.bham.ac.uk/C.J.Sangwin/howroundcom/roundness/pics/3dgroup_book2.jpg - measurement of roundness photo
- http://www.coins-of-the-uk.co.uk/pics/dec/50/50_97.jpg - Fifty pence coins
- Bike picture-http://britton.disted.camosun.bc.ca/reuleaux_bike/photo.jpg
- http://upload.wikimedia.org/wikipedia/commons/thumb/d/d2/ReuleauxTriangle.svg/200px-ReuleauxTriangle.svg.png triangle picture