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Problem of the Week #6 – Prove That π Must be Less Than 4, and More Than 3

Posted by Jeff Simpson under

All Problems of the Week - And Solutions,

Geometry,

Pi | Tags:

learning math,

math instruction,

math problems,

teaching math |

1 Comment
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.

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March 18, 2010 at 4:47 am

Right on! I love this kind of empirical teaching/learning. I think you reach a much higher percent of kids when you respect their minds like this.

Great post!

Brian