Start with any triangle T1 and its inscribed circle. Draw the
triangle T2 which has its vertices at the points of contact between
the triangle T1 and its incircle. Now keep repeating this process
starting with T2 to form a sequence of nested triangles and
circles. What happens to the triangles? You may like to investigate
this interactively on the computer or by drawing with ruler and
compasses. If the angles in the first triangle are a, b and c prove
that the angles in the second triangle are given (in degrees) by
f(x) = (90 - x/2) where x takes the values a, b and c. Choose some
triangles, investigate this iteration numerically and try to give
reasons for what happens. Investigate what happens if you reverse
this process (triangle to circumcircle to triangle...)
A Short introduction to using Logo. This is the first in a twelve part series.
What happens when a procedure calls itself?