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"Tell the chef, the beer is on me."

Me:can u give me x²+4y+ of tomatoes & 2(x²+8xy^3) of potatoes please

Seller:I dont understand

Me:well i dont give a fuck i didnt study in vainthose are polynomials you asked for a neverending curve of tomatoes

Maybe I WANT an never ending curve of tomatoes.

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 R

_{1}occupies the same space as a square donut with side 2R_{1}. If the center circle of a round donut has a radius R_{2}and the hole of a square donut has a side 2R_{2}, then the area of a round donut is πR_{1}^{2}- πr_{2}^{2}. The area of a square donut would be then 4R_{1}^{2}- 4R_{2}^{2}. 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 (R_{2}= R_{1}/4) and replacing in the proper expressions, we have a 27,6% more donut in the square one (Round: 15πR_{1}^{2}/16 ≃ 2,94R_{1}^{2}, square: 15R_{1}^{2}/4 = 3,75R_{1}^{2}). Now, assuming a large center hole (R_{2}= 3R_{1}/4) we have a 27,7% more donut in the square one (Round: 7πR_{1}^{2}/16 ≃ 1,37R_{1}^{2}, square: 7R_{1}^{2}/4 = 1,75R_{1}^{2}). 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

can’t argue with science. Heretofore, I want my donuts square.

more donut per donut

Radians: the natural way of measuring anglesThis is the third animation I posted today: here’s the first and the second. Be sure to check the other two if you missed them!

Another one for Wikipedia. Tumblr forced me to cut the amount of frames in half. Here it is in its full, smooth glory.

There’s a multitude of ways you can specify an angle, from the familiar degrees to the obscure—and altogether alternative—provided by "spreads".

However, only one of these angle units earns a special place in mathematics: the

.radianThis animation illustrates what the radian is:

it’s the angle associated with a section of a circle that has the same length as the circle’s own radius.For a unit circle, with radius 1, the radian angle is the same value as the length of the arc around the circle that is associated with the angle.

In the animation, the radius line segment

r(in red) is used to generate a circle. The same radius is then “bent”—without changing its length—around the circle it just generated. The angle (in yellow) that’s associated with this bent arc of lengthris exactly 1 radian.Making 3 copies of this arc gets you 3 radians, just a bit under half of a circle. This is because half of a circle is π radians. So that missing piece accounts for π - 3 ≈ 0.14159265… radians.

Our π radians arc is then copied once again, revealing the full circle, with 2π radians all around.

There are several great reasonsto use radians instead of degrees in mathematics and physics. Everything seems to suggest this is the most natural system of measuring angles.Radians look complicated to most people due to their reliance on the irrational number π to express relations to circle, and the fact the full circle contains 2π radians, which may seem arbitrary.

In order to simplify things, some people have been proposing a new constant τ (tau), with τ = 2π. When using τ with radians, fractions of τ correspond to the same fractions of a circle: a fourth of a tau is a fourth of a circle, and so on.

Tau does seem to make more sense than pi when dealing with radians, but pi shows up elsewhere too, with plenty of merits of its own.

I, for one, do enjoy the idea of tau being used,

exclusively, as an angle constant, so that it immediately implies the use of radians. If such were the case, a student seeing Euler’s identity for the first time, but in terms of tau, would be immediately compelled to think in terms of rotations:e^{τi}= 1 would instantly convey the idea of a full rotation, bringing you back where you started. That seems like a good thing.

EDIT: here’s a long post where I detail my thoughts on the pi vs. tau discussion.So

happy Pi day!(or half-tau day, if you prefer!)

Is Tau Better Than Pi? - DNews

ugh summer

look at my awful tan line

stop the maths jokes guys, cos they’re not funny

oh yeah i secant that

There must be a limit to these terrible puns.

"that's a sine you should just stop right there" - katie

Maybe Soup is currently being updated? I'll try again automatically in a few seconds...

You've reached the end.

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