Re: [math-fun] How many spokes does a bicycle need?
Good point, Allan. So: What is the answer to that math problem: --------------------------------------------------------------------------- Given rigid cylinders C_r and C_R in R^3 of equal heights, and radii r < R, what's the smallest number of constraints (*_j) of the form (*_j) ||x_j - y_j|| <= K_j for some x_j in C_r, and some y_j in C_r, and for some constant K_j, such that the (*_j)'s fix C_r in a unique position concentric with, and having the same bounding planes as, C_R. --------------------------------------------------------------------------- And: If <= is replaced by =, what is the answer in that case? --Dan Allan wrote: << It is possible that spokes are intended to be only tensile, in which case the equality in the constraint should be replaced by "less than or equal", and the answer is almost certainly different.
(*&^$#@ earthlink sent my previous post prematurely, sorry): I wrote: << In the biography of H.S.M. Coxeter "King of Infinite Space", one section describes his interaction with Buckminster Fuller. It states that Fuller erroneously claimed that a bicycle wheel needs 12 spokes "to hold it rigid", whereas the correct number is 7. This seems to be stated as a fact of geometry, rather than one of structural engineering. Anybody have any insight into this claim?
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Dan Asimov