fucking circles man, how do they work

>>8746993
Well, the circle in your picture is black and therefore does not work.

>>8747008
dude all circles are the same

>>8747028
Nah, yellow circles work much more than black or brown circles.

every day I wake up, take out my compass and straightedge and I produce trigonometric identities

They are so simple and so beautiful, perhaps too simple and too beautiful. I do not believe they could possibly be true.

How could a number like pi exist? How can e exist? Why are there so many different formulae for pi? How much information am I missing because my brain doesn't automatically think in terms of 2pi or tau?

And then I go to sleep thinking that there has to be a better way to do trigonometry. But I'm reminded that Wildberger doesn't know how to inscribe a circle in a triangle because he can't do angle bisectors. This reminds me that angles are very real and very fundamental, and I have tortured dreams.

And then I wake up again and reach for the compass

i wish i had never tried conics

>>8746993
Because they're hypothetical. A perfect math answer would be impractical, so it's all "sort of" right.
Or which of you has seen a [perfect] circle in Reality.

>>8747040
yeah but black is worth 7pts, yellows only worth 2 so ha

From the perspective of /sci/, why is Pi so important? Why is it “a thing”? I never understood the importance of Pi in math class.

>>8746993
They roll,dude!

>>8747904
1. It is the ratio [math]\frac{C}{D}[/math] for any circle.
2. Plugging it into our weird exponential power series like [math]cos(\theta)[/math] and [math]exp(i\theta)[/math] give us interesting results.
3. Due to the above 2 properties it gives us a link between anything that rotates and anything that creates rotations.
Other than that it is a bit of a boring one, e is a much more interesting number

>>8747028
>>8747008
The thing that matters is what's on the inside , anyways.

>>8749150
You mean that it's a low iq circle?

>>8746993
There is only one circle. What pi represents is the division of a diameter into a circumference that must be considered a unitary, indivisible length - which in and of itself necessitates the paradox of dividing a singularity that triggers irrationality.

Same goes for a right triangle with equal legs and a hypotenuse of length 1. if a squared + b squared = c squared, then the only values for a and be would have to be the sum of the squares of one-half. This would only be possible with lengths of 1/square-root 2, which, again, would be irrational precisely because it is trying to divide a unitary and indivisible length.

So circles are representations of the limits of the rational universe, basically.

>>8747008
You're forgetting that the circle has red, white and blue inside of it, so it's native American, white, has water, and is in the USA

Circles are nice. Circles are one of the few funny things in geometry.