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Soubresaut's avatar

Why isn't pi 6.28?

Asked by Soubresaut (13690points) 1 month ago

If a circle’s shape is defined by its radius—the radius being the distance all points are from the center point—why isn’t pi the relationship between circumference and radius, rather than circumference and diameter?

Is it arbitrary? Is there a historical reason why people first described the relationship in terms of diameter? Is there a mathematical reason that makes circumference-and-diameter the better relationship to describe?

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12 Answers

SavoirFaire's avatar

Because the original problems that motivated people to calculate/estimate the value that we would come to know as π were conceived of and/or solved in terms of the relationship between the circumference and the diameter of circles, and that way of thinking stuck. So it’s both historical and arbitrary.

It’s important to remember that defining a circle’s shape in terms of its circumference, center, and radius is something that developed. We didn’t start with the idea that the radius of a circle was more fundamental than its diameter, and it is not necessary to think of circles in those terms. It is a decision.

There are people who believe that 2π—which they propose to represent with the letter τ (tau)—is superior. There’s a paper about it here and an entire website dedicated to it here if you’re interested. It seems to me that neither π nor τ is likely to be strictly better than the other, but I’ve never been much for absolutes.

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LostInParadise's avatar

Technically speaking, the term circle only refers to the boundary. The inside is called a disc or disk. You can talk about the area enclosed by a circle, but not the area of a circle. Why there are two terms for circles but only one term for polygons, I don’t know. But given the distinction, the center is not part of the circle, so it makes sense to characterize the circle by the diameter, which goes from one part of a circle to another.

LostInParadise's avatar

Of course, you can then ask why the formulas for circumference and area are given in terms of the radius if we consider the diameter as the defining quantity. It does seem inconsistent.

stanleybmanly's avatar

I think the radius is the deciding factor simply because geometry is taught around formulas and definitions. The radius is used because it is the line segment which generates the circle. It’s merely consistent to continue further discussion using the single term when possible.

zenvelo's avatar

It seems silly to try to define it as a relationship that has an integral multiplier in it.

πd is the circumference. No need to multiply by 2.

And, you need π as a singular value for other functions. Having π=6.28 would mean you have to divide when calculating the area. It gets more complicated when calculating the surface area of a sphere or the volume of a sphere.

You would make the job of engineers trying to calculate buckling more difficult

Soubresaut's avatar

Thank you all! I figured there would just be a simple, black-and-white reason that I just didn’t know about, and if that had been the case that would have been fine, but I do find the discussion as-is much more personally satisfying—including the reminder that radius is a concept as much as diameter.

I also had no idea this was something entertained by people who have studied math more and know math better than I do… I’d never heard of tau!

zenvelo's avatar

Also, Pi Day is March 14, which is also Einstein’s birthday, so it is cosmically correct.

June 28, Tau day, is Elon Musk’s birthday, and we all know he is irrational.

Soubresaut's avatar

@zenvelo—hahaha, well that settles it then!

kritiper's avatar

Because you can divide all the numbers by 2.

zenvelo's avatar

Thank you @Call_Me_Jay, that Scientific American article leads me to rethink my position and follow the TauTao

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