Readers Respond: Kite Math

For the Museum of Mathematics

Math Mondays has been accumulating a lot of mail from all you fellow makers out there with a mathematical bent so today’s installment marks the beginning of a series (the length of which depends on how much more mail you all send) based on readers’ responses to earlier columns. We’re going to start with photos sent by Terry Thillman in response to Geometry Takes Flight; Terry built all of the kites pictured below. Although the word “kite” when used as a mathematical term for a particular sort of shape means “a quadrilateral with two pairs of adjacent equal edges,” Terry wanted to re-emphasize the fact that a kite does not have to be a kite, so to speak. The first example is a kite called “Oops” which is made from six scalene triangles, no two sides the same length:

  

The second design, entitled “Mr. X,” simply shows an unusual and striking three-dimensional geometry:

And the final photo “Crazy Eddy” actually shows a very large geometric structure constructed out of 208 kite-shaped kites interconnected by string:

This photo begs our final question of the day: suppose you had a single long (idealized weightless) string with many kites attached at equal intervals along the string. And suppose further that every kite experienced the same force from the wind, and that both ends of the string were attached to the ground. What shape would the resulting kite arch take on? Answers to mondays@momath.org — I’ll give a shout out to the first correct one received.