# Child lamp problem

A street lamp is 12 feet above the ground. A child 3 feet in height amuses itself by walking in such a way that the shadow of its head moves along lines chalked on the ground. (1) How would the child walk if the chalked line is (a) straight, (b) a circle, (c) a square? (2) What difference would it make if the light came from the sun instead of a lamp? Example:

The problem is from Sawyer's "Mathematician's Delight".

Note: Since this is my first post here, I would like to note that this is not homework. I am just trying to improve my math/problem solving skills.

-

Similar triangles show that from each point on the line you draw a line to the base of the lamp. When the child's head makes a shadow at a given point it is $\frac 14$ of the way along the line from the point to the lamp. So the child walks in the same shape: line, circle, or square, with size $\frac 34$ of the figure.