The value 4.47204 from Geometers' Sketchpad
could be R*2*sqrt(5)
. (That identification of the number 4.47204 comes from A Dictionary of Real Numbers, by Jonathan Borwein and Peter Borwein, Wadsworth and Brooks/Cole Advanced Books and Software, Pacific Grove, California, 1990.)
Via calculus we want to maximize 2*sin(x) + 4*cos(x), leaving R constant of course:
Its derivative is 2*cos(x) - 4*sin(x)
Equate this to zero so that
That value squared = 20, whose square root is indeed 2*sqrt(5).
So the maximum perimeter is in fact R*2*sqrt(5).
Posted by Charlie
on 2017-11-07 10:07:58