The conditions of the problem uniquely determine the ratio of side lengths of the rectangle as .512858431636277... If t=tan(theta)^2 then define r = (3-t)/8/(1-t) s = 1-r then rectangle ratio = .25/sqrt(rs) Sent from my iPhone
On Jul 7, 2018, at 6:39 PM, James Propp <jamespropp@gmail.com> wrote:
Dick,
Can you tell us the conjectural aspect ratio of the rectangle? (I’m assuming that it’s unique, or that it takes on only finitely many values, related to the cosines and sines of multiples of 90/7 degrees.)
Jim Propp
On Saturday, July 7, 2018, Richard Hess <rihess@cox.net> wrote:
Imagine a power station with towers of negligible (=0)width built at the four corners of a rectangle on a flat plane. At a certain viewing point, P, on the plane, the bases of the four towers are equally spaced in viewing angle by an angle, theta. P is at a different distance from each corner and the distance from P to the closest tower is equals the length of the long side of the rectangle. For this case theta equals 90/7 degrees to 15 places of accuracy but I’m unable to prove equality.
Any takers in finding a proof?
Dick Hess
Sent from my iPhone
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