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Re: [Phys-L] quickest route



Suppose one ramp is a straight shot from A to B (where B is lower than
point A but not directly below it). There are other shape ramps from A to B
that will take the same time of descent (ignoring drag). In particular,
suppose we want a smooth ramp. (No cusp such as Donald's two straight ramps
connected together.) Further suppose we require that the ramp can be
described by a function such that point B can be moved around arbitrarily
and still give a tie with the straight ramp.

Hard problem: Find such a ramp shape.

Solution: See the lower right-hand graphic at:
http://en.wikipedia.org/wiki/Gian_Francesco_Malfatti

I have a mathematical proof at:
http://www.usna.edu/Users/physics/mungan/_files/documents/Publications/EJP14.pdf

--
Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/