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...)
Vedic Sutra is one of many ancient Indian sutras which involves a
cross subtraction method. Can you give a good explanation of WHY it
Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.
How do we find the square root of 40 on a calculator that only
does simple '4 rules' arithmetic?
What exactly is the method here?