Understanding Pi: its Role in Symmetry and How it Was Found

[Integral]

I disagree with "it originally came about in desire to find the area of a circle". I think there is clear historical evidence that $\pi$ was first used to find the circumference of a circle. Yes, one can easily write that "$c= 2\pi r$" using [it ex]2\pi[/itex], but if you are talking about a pillar or tree trunk, it is far easier to measure the diameter rather than the radius. That's why '$c= \pi d$" is much more natural.

Timber cruisers in the woods of the Pacific Northwest use a tape measure marked in Pi units to measure the diameter of a tree. Just wrap the tape around the tree and read the diameter. At least they were used when there was a active logging industry.

 

[Werg22]

Why on Earth would anyone wish to do such a thing? What possible purpose or reason is there in denying at the outset what pi actually is?

It's simply not correct to come up with a formula or series that gives pi and take that as the definition, and later simply point out that the number also happens to be the ratio of the circumference to the diameter. That would be akin to coming up with a formula or series for Plank's constant or the magnetic permeability of a vacuum and declaring it as the definition for these constants.

Pi is the ratio of the circumference of a circle to its diameter. That's what it is. Millennia from now when no one is doing integration, or series or working in base ten, or using fractions, or just about anything we do now, pi will still be there as the ratio of circumferences to diameters. No number system, no analysis, no axioms, no definitions, nothing.

That's what pi is. How we find, measure or approximate it is entirely up to us, but the definition is quite out of our hands. You may be uncomfortable with this, but the universe does care about any philosophical objections you might have. It just is. Like pi.

The circle is not a physical entity, it's a mathematical one. The circle does not exist in nature for the simple reason that it is not applicable.

 

[Integral]

The circle is not a physical entity, it's a mathematical one. The circle does not exist in nature for the simple reason that it is not applicable.

nonsense, mankind has been making wheels for thousands of years. We have been making "perfect circles" , that is circles within our ability to measure, for thousands of years.

Whether or not a perfect circle exists is irrelevant.

 

[Werg22]

A ten year old might qualify a wheel a circle, I do not.

 

[Integral]

That is your problem not mine.

Thread done.