Today is 3.14 so we have a pi problem of the week. has been worshipped and maligned for at least 4000 years. And luminaries like Archimedes (3rd century BC – there on the left), Newton, Leibnitz, and Euler (18th century) all attempted their own precise approximations.  How about that for a number?!  is the (constant) ratio of the circumference “C” to the diameter “d” in any circle.  A ratio is a comparison of two amounts, which can be expressed as a quotient = C/d .

But this explanation can sound like Greek to many students! – who are also told and need to memorize that pi ≈ 3.14. Instead we offer this problem to guide students (with simple geometry and good questions) to reason for themselves why pi must be less than 4 and more than 3 – good mathematical thinking from the ground up.

Imagine that you were never told that ≈ 3.14. Use the figures below to prove that the value of must be less than 4 and greater than 3. We will post the solution next week.