Tag: Math

glenn-griffon:

[Thread removed.]

(I know I’m two weeks late on this one, but whatever.)

Why is pi so special? Oh, right, it’s derived from a circle and is one of the first irrational numbers people encounter when learning mathematics (or is it?). This basically applies to any random sequence: Any truly random sequence will eventually yield certain data.

A real number with random digits is known as a normal number. These numbers are “normal” in the sense that they vastly outnumber “abnormal” numbers. Pi is usually considered “normal,” but this has not been proven. The same goes for e (anyone remember this one?) and the humble square root of 2.

TL;DR: Pi is not special. The OP applies to many other numbers.

dialbm:

juicyjacqulyn:

entropiaorganizada:

hookteeth:

hethatcures:

This legitimately upsets me.

… Y’see, now, y’see, I’m looking at this, thinking, squares fit together better than circles, so, say, if you wanted a box of donuts, a full box, you could probably fit more square donuts in than circle donuts if the circumference of the circle touched the each of the corners of the square donut.

So you might end up with more donuts.

But then I also think… Does the square or round donut have a greater donut volume? Is the number of donuts better than the entire donut mass as a whole?

Hrm.

HRM.

A round donut with radius R₁ occupies the same space as a square donut with side 2R₁. If the center circle of a round donut has a radius R₂ and the hole of a square donut has a side 2R₂, then the area of a round donut is πR₁² - πr₂². The area of a square donut would be then 4R₁² - 4R₂². This doesn’t say much, but in general and  throwing numbers, a full box of square donuts has more donut per donut than a full box of round donuts.

The interesting thing is knowing exactly how much more donut per donut we have. Assuming first a small center hole (R₂ = R₁/4) and replacing in the proper expressions, we have a 27,6% more donut in the square one (Round: 15πR₁²/16 ≃ 2,94R₁², square: 15R₁²/4 = 3,75R₁²). Now, assuming a large center hole (R₂ = 3R₁/4) we have a 27,7% more donut in the square one (Round: 7πR₁²/16 ≃ 1,37R₁², square: 7R₁²/4 = 1,75R₁²). This tells us that, approximately, we’ll have a 27% bigger donut if it’s square than if it’s round.

tl;dr: Square donuts have a 27% more donut per donut in the same space as a round one.

god i love this site

I’m reblogging this again just for these comments

It doesn’t matter what the radius of the small hole is relative to the large hole. The formulae are already given: πR² - πr² for a circle and 4R² - 4r² for a square. It’s easy to see that the square is 4/π times larger than the circle. 4/π is about 1.273, so the square is actually 27.3% times larger.

TL;DR: Squares will always be larger than circles, and there was a little rounding error in the original calculation.