Optimization - Best Spot to View a Painting
Author: Jamie Mulholland

A painting in an art gallery has height 3 m and is hung so that its lower edge is about 1 m above the eye of an observer. How far from the wall should the observer stand to get the best view? (i.e. the observer wants to maximize the angel θ subtended at the eye by the painting.)

painting

drag point under observer to move

E = (0, -1.4)
floor = OrthogonalLine(E, yAxis)
observer = Point(floor)
A = Point(yAxis)
B = Point(yAxis)
C: (x(observer), 0.0)
painting = Segment(B, A)
b = Segment(C, B)
c = Segment(C, A)
θ = Angle(A, C, B)
wall = Ray(E, B)
a = Segment(observer, E)
d = Segment(C, (0.0, 0.0))
e = Segment((1.0, 0.0), (1.0, 1.0))
f = Segment((1.5, 1.0), (1.5, 4.0))
text2: "θ = " + θ