Why do coins have constant width

Same for the 1p smooth and it's similar size to the 5p groved. And the same for 2p, 10p and 50p, respectively. The designs were to aid the blind who could feel the coin to know what is was as the sizes were too similar to distinguish. Sign up to join this community.

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Create a free Team What is Teams? Learn more. Why are some coins Reuleaux triangles? Ask Question. Asked 3 years, 4 months ago. Active 3 years, 4 months ago. Viewed 6k times. Rodrigo de Azevedo Now draw a circular arc connecting the two other points, as shown in the picture below.

The radius of this arc will be the length of the triangle's sides. Repeat for the other two corners to get a triangle with curved sides. It's hard to believe, but the resulting shape has constant width. If you were to trap the Reuleaux triangle between two rulers, one of the rulers would always touch a corner of the triangle and the other the opposing arc.

The distance between the rulers would then be the radius of the circular arc, which is the same for all three arcs. If you need further convincing, look at the video below, featuring a roller whose wheels, in cross section, are Reuleaux triangles.

The roller itself appears to have a bumpy ride, but the glass plate placed on top glides along smoothly, parallel to the surface below. That's because the width of the wheels, which is the distance between glass plate and surface, remains constant throughout. Image courtesy Dale Hathaway. In the UK there aren't any triangular coins in circulation, but a similar technique as the one that creates the Reuleaux triangle also works for the seven-sided heptagon the 20p and 50p coins are based on — in fact it works for any regular polygon with an odd number of sides.

Prick the needle of a compass into one of the corner points and then draw a circular arc connecting the end points of the opposite edge. The resulting shape has constant width. Therefore, the new sided pound coin will be the first non-constant width British coin since the also sided threepenny bit was phased out in Back in , I wrote to my MP in an attempt to find out why the new coin was not of a constant width.

He forwarded my letter to the Treasury, but I never heard back from them. When cutting a pizza into equal shaped pieces, the usual approach is to cut along a few diameters to make triangles. There are other ways to fairly share pizza, including the following that has appeared here before as an answer to this puzzle :. The slices in this solution are closely related to a triangle of constant width.

And the same for 2p, 10p and 50p, respectively. The designs were to aid the blind who could feel the coin to know what is was as the sizes were too similar to distinguish. Python Javascript Linux Cheat sheet Contact. Why are some coins Reuleaux triangles? The reason to not have a circle is likely purely aesthetic.