piefoot
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9 years ago
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on: University of Tokyo Graduate School Entrance Exam – Mathematics (2016) [pdf]
The solution to the Euler equation gives the minimal surface with is obtained when y(x) is a catenoid, y=c cosh(x/c) here c satisfies 2=c cosh(1/c). The Euler equation gives the minimal distance when the function F is the length of the arc.
piefoot
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9 years ago
|
on: University of Tokyo Graduate School Entrance Exam – Mathematics (2016) [pdf]
Solving 3.1 I think the solution is binomial(n1+r-1,r-1) where n1=n-r, but I obtained that formula by calculating the formula for r=1, then r=2, and the relation f(r,n) = sum(f(r-1,n-i),i,0,n) and using maxima with simpsum and factor to obtain a simplified expression whose form suggest the general rule, but I don't see a simpler way.
