ejnorman@uwmacc.UUCP (Eric Norman) (11/19/85)
In article <325@ihnet.UUCP> eklhad@ihnet.UUCP (K. A. Dahlke) wonders: > It may not be graduate math, but it is interesting (to me) nonetheless. Methinks it might be close; you won't be able to hack it if you barely made it through two semesters of calculus. This is my rationalization for posting to math instead of puzzle. > Construct a topography, such that a bicycle equipped with square > wheels has a smooth ride when traveling over this terrain. > One possibility is "level" ride. That is, the rider This is what was intended. Also, wheels may not slip. > Does this problem have a more general solution, > say for bicycles with N-sided wheels? You'll be able to answer this. -- Eric Norman UUCP: ...{allegra,ihnp4,seismo}!uwvax!uwmacc!ejnorman Pony Express: 1210 West Dayton Street, Madison, WI 53706 Life: Detroit!Alexandria!Omaha!Indianapolis!Madison!Hyde "To err is human; to moo bovine." -- grafitti
ghgonnet@watdaisy.UUCP (Gaston H Gonnet) (11/22/85)
There was a land where they designed the roads in a very bumpy way, so bumpy as to make life miserable to everybody. This was the consequence of a new minister of transportation, who (as opposed to most in the trade) knew something. He once heard about the sqrt(2) not being a rational and that the functions sinh(x) and cosh(x) were not the result of someone lisping sin(x) and cos(x). To apply his knowledge he designed roads which had a cross section given by y(x) = sinh(x) + sqrt(2)*(1-cosh(x)), but since this would give problems for large values of x, he just restricted it to 0 <= x <= ln(sqrt(2)+1). To make long distances he just mirrored the pattern and repeated it. Needles to say that motorists were not very happy, neither cyclists, until they discovered that the town blockhead (who used to ride his "bi-square-cle" (bicycle with square wheels)) was riding at perfect level. (His wheels had internal radius of 1 unit (or side=2)). Of course the idea spread rapidly, and once the smoothness problem was solved, they found that to maintain constant speed their pedalling was uneven, and if they were pedalling evenly then their speed was uneven. Surprisingly this was solved accidentally by Mr Meathead (bi-square-cle repairman) when he "fixed" the gears of Mr Blockhead. What shape of gears did Mr. Meathead designed that will maintain constant speed at level ride (angular speed of the wheels themselves is of no importance) for a constant pedalling speed?