One Math Problem for Pi when a Square Becomes a Circle

Do you love Internet trolls? I mean the ones who pose tricky problems, not those who simply post something outrageous to watch people get angry?

Recently one puzzle was posted that “proved” that pi, usually shown as π, =4 rather than 3.14159276…

At first it seemed like an easy math problem for pi…then I realized it was trickier.

How to Fold a Square into a Circle

"The Square Collapses Again" : image by Mike DeHaan
“The Square Collapses Again” : image by Mike DeHaan

So I wrote “The Circled Square Math Problem Claims Pi Equals Four” for Decoded Science, based on the research I did to demonstrate that “π=4” is false.

I also had to draw some diagrams to explain the “circled square” problem.

This is one of the final pictures, showing how the dark brown square around the yellow circle can be folded closer and closer to that circle.

The diameter of the circle equas the length of one side of the original square, and we arbitrarily say that the diameter is one unit of length. So the perimeter of the square is four units long.

The length of the perimeter of the newly-folded figure is always four units also, and that figure becomes closer and closer to a circle. So that must mean that the length of the circumference of a circle is the same value, four, right?

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Buy Reference Supplements or a Math Textbook Online for Mathematics Programs

Students and teachers can shop online for bargain textbooks, teaching supplements or reference materials.

For example, “Intermediate Algebra” in the Bittinger Worktext Series starts with a review of basic algebra. It goes on to algebraic expressions with real numbers; how to solve linear equations; graphs and their applications; etc. I’ll let you read the table of contents on the University Books Online page.

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As a public service announcement, check the links to Canadian universities offering studies in maths at “Canada Mathematics and Mathematical Science University Programs“.

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Thank you for reading about the math problem for pi in a circled square.