Why are manhole covers round? - Marc Chamberland
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Why are most manhole covers round? Sure it makes
them easy to roll, and slide into place in any alignment. But there’s
another, more compelling reason, involving a peculiar geometric property
of circles and other shapes. Marc Chamberland explains curves of
constant width and Barbier’s theorem.
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The Reuleaux Tetrahedron is actually a surface of almost constant width. Because of the way it is formed, each vertex is the same distance away from points on the opposite face, but opposite edges are a little farther apart from each other. However, if you were to smooth down three of the edges, you can create a true surface of constant width called the Meissner Tetrahedron.
The Reuleaux triangle is named after Franz Reuleaux, a 19^{th}-century German engineer. This shape is the most easily constructed non-circular curve of constant width. There are many other curves of constant, some being infinitely smooth, while others having infinitely many corners. Visit the Museum of Math, Shapes that Roll and Mime-matics, and watch the video on Reuleaux triangles. For more on manhole covers and their shape, visit Releaux Stones.
There are several coins around the world that are curves of constant width. This includes the American Susan B. Anthony silver dollar, the Canadian dollar coin (the “loonie”), and the British 50p coin. Such coins are as not as easy to counterfeit as circular coins yet their constant width makes them a logical choice for vending machines. Why?
You can find other interesting facts and figures about curves of constant width at this site. Interested in how you can drill a square hole? Watch this animation!
Learning more math concepts in a fun and unimaginable way interest you? Visit: Tipping Point Math by Marc Chamberland and learn about math as you have never imagined!
Marc Chamberland is the Myra Steele Professor of Mathematics and Natural Science at Grinnell College. He has published over 40 research articles in diverse areas such as number theory, combinatorics, differential equations, and dynamical systems. Marc is a huge proponent of experimental mathematics, a growing paradigm that uses computers to discover, conjecture and prove mathematical results. He has received support from the National Science Foundation to develop an advanced course in this area. Marc is passionate about communicating the beauty and excitement of mathematics. He has given about 100 talks and has reaches out to a general audience. His book "Single Digits: In Praise of Small Numbers" (Princeton University Press, 2015) describes magical properties of each of the numbers from one to nine. Marc is also the creator of the YouTube channel Tipping Point Math which shows "math as you never imagined."
The Reuleaux triangle is named after Franz Reuleaux, a 19^{th}-century German engineer. This shape is the most easily constructed non-circular curve of constant width. There are many other curves of constant, some being infinitely smooth, while others having infinitely many corners. Visit the Museum of Math, Shapes that Roll and Mime-matics, and watch the video on Reuleaux triangles. For more on manhole covers and their shape, visit Releaux Stones.
There are several coins around the world that are curves of constant width. This includes the American Susan B. Anthony silver dollar, the Canadian dollar coin (the “loonie”), and the British 50p coin. Such coins are as not as easy to counterfeit as circular coins yet their constant width makes them a logical choice for vending machines. Why?
You can find other interesting facts and figures about curves of constant width at this site. Interested in how you can drill a square hole? Watch this animation!
Learning more math concepts in a fun and unimaginable way interest you? Visit: Tipping Point Math by Marc Chamberland and learn about math as you have never imagined!
Marc Chamberland is the Myra Steele Professor of Mathematics and Natural Science at Grinnell College. He has published over 40 research articles in diverse areas such as number theory, combinatorics, differential equations, and dynamical systems. Marc is a huge proponent of experimental mathematics, a growing paradigm that uses computers to discover, conjecture and prove mathematical results. He has received support from the National Science Foundation to develop an advanced course in this area. Marc is passionate about communicating the beauty and excitement of mathematics. He has given about 100 talks and has reaches out to a general audience. His book "Single Digits: In Praise of Small Numbers" (Princeton University Press, 2015) describes magical properties of each of the numbers from one to nine. Marc is also the creator of the YouTube channel Tipping Point Math which shows "math as you never imagined."
Create and share a new lesson based on this one.
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