[Geometry] Angle Maximization Problem
By: Tao Steven Zheng
【Problem】
This problem was first posed and solved by a late Medieval German astronomer Johannes Müller von K?nigsberg (1436 – 1476 AD), known more famously as Regiomontanus. The solution presented below uses differentiation. Regiomontanus solved the problem without calculus!
Refer to the above diagram. If the heights and
are given constants, at what horizontal distance
should one stand to maximize the viewing angle
? Solve this problem using calculus.
【Solution】
Consider the angles and
such that
. According to the above diagram,
Thus,
To maximize the angle , derive the above function with respect to
.
Set and solve for
.
The positive square root is the true solution to this problem.
標(biāo)簽：
