colonel@gloria.UUCP (Col. G. L. Sicherman) (03/14/85)
> In response to the question, "Why are manhole covers round?" : I learned > that it was because the circle is the only two-dimensional shape that has > the same diameter no matter how you turn it. Mathematicians know better. They call such curves "curves of constant breadth," and there are an infinity of them. Martin Gardner did a column on them once. The simplest example (besides a circle) is constructed thus: let ABC be an equilateral triangle. Draw arcs AB with C as center, AC with B as center, BC with A as center. The three arcs form a curve of constant breadth. -- Col. G. L. Sicherman ...{rocksvax|decvax}!sunybcs!colonel
wws@whuxlm.UUCP (Stoll W William) (03/17/85)
> > Mathematicians know better. They call such curves "curves of constant > breadth," and there are an infinity of them. Martin Gardner did a column > on them once. > > The simplest example (besides a circle) is constructed thus: let ABC be > an equilateral triangle. Draw arcs AB with C as center, AC with B as center, > BC with A as center. The three arcs form a curve of constant breadth. > -- > Col. G. L. Sicherman > ...{rocksvax|decvax}!sunybcs!colonel Now I understand. Triangular manhole covers are not really triangular. They have three vertices, but the sides are arcs, not straight lines. Is this figure called "triangular curve of constant breadth" or is there a shorter name? An odd number of vertices is required when this trick is used (e.g., doesn't work for squares), and the polygon must be equilateral. Arcs must be drawn using all vertices as centers. When choosing the endpoints of the arc, always choose the two endpoints farthest from the current center. Bill Stoll, ..!whuxlm!wws