Reuleaux Polygons - Blog Posts

Curves of constant width

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The width of a circle is constant: its diameter.

But the circle is not the only shape that holds this pristine title. For instance let’s look at the Reuleaux triangle

Reuleaux triangle

A Reuleaux triangle is a shape formed from the intersection of three circular disks, each having its center on the boundary of the other two.

The Reuleaux triangle is the first of a sequence of Reuleaux polygons, curves of constant width formed from regular polygons with an odd number of sides.

Some of these curves have been used as the shapes of coins

To drill square holes.

They are not entirely square, their edges are fillets i.e the edges are rounded and not sharp.

This animation offers a good insight as to why that is so.

And in china, apparently on bicycles.

The man Guan Baihua shows his self-made multi-angle-wheel bicycle on May 6, 2009 in Qingdao of Shandong Province, China. Guan Baihua spent 18 months to complete this strange bicycle.

Other shapes of constant width

There are other shapes of constant width beside the Reuleaux triangle ( that has been discussed in this post ), a whole bunch of them really. Do take a look at them. ( links below )

I will leave you guys with my favorite one.

More:

If this post fascinated you, i strongly suggest you check these out. They go in-depth with the mathematics that underlies these curves and talk about other cool stuff:

An animation of non-circular rollers

Shapes and Solids of Constant Width - Numberphile  

Shapes of constant width

Reuleaux Polygons,           

Edit:

For those who are wondering if these are something that one would stumble upon on a regular basis. You may not find perfect ones but similiar ones definitely.

I found mine on a really old BMI calculator thingy. ( not sure what you would call it )

Have fun exploring !