Consider the two numbers a and b, where the values of each are given by the following formulae:
a = n x sin(180/n) and b = n x tan(180/n)
Disregard the values given when n is 1 or 2, but consider the values of a and b when n is an integer value greater than 2:
When n=3, a=2.598 and b=5.196
When n=4, a=2.828 and b=4.000
When n=5, a=2.939 and b=3.633
When n=6, a=3.000 and b=3.464
As can be seen, the value of a increases as n increases, whereas, the value of b decreases.
Question: what happens to a and b as n gets very much larger, and why?
(Problem mulled over and solved whilst on the way home in the car from Brighton this evening, inspired by a couple of pictures in the book that I finished on the train earlier in the day.)