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/sci/ - Science & Math

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File: 762 KB, 1152x1082, 20180301_124541-1-1.jpg [View same] [iqdb] [saucenao] [google]
9553903 No.9553903 [Reply] [Original]

Prove that the circumfrence of a circle with diameter 1 isn't 4.

Protip, you cant.

A square with diameter 1 and perimeter 4 needs 4 rotations to end flat on the face it started rotating from, for a total of 360° rotation. With its original position + 4 rotations, it covers a distance of 5

A circle with diameter 1 can also rotate 4 times in 90 degree increments for a total of 360° of rotation, but where the square needed to count its full coverage from its two bottom most corners forming a face, the circle has innumerable faces and only need worry about the vertex directly beneath the center on the edge. From this format, a 360° rotation with diameter 1 circle will cover a distance of 4, given the same starting positions between the circle and the square and the same 360° rotational roll forward.
As the circle starts its roll on the vertex beneath the center but the square starts its roll with a corner that is 0.5 distance adjusted from the center, after a complete rotation the square would have covered an initial 0.5 extra followed by another 0.5 extra after the full 360, for a total of 1 more distance than the circle with a diameter of 1.

>> No.9553930
File: 44 KB, 500x500, 1513584407617.jpg [View same] [iqdb] [saucenao] [google]
9553930

>0.999 =/= 1
>pi exists for no reason
>manmade climate change isn't real
I can't take it /sci/ i'm at my limit everything is a lie

>> No.9553971

>>9553903
Picture is misleading. putting circles side by side is different then measuring the complete distance around a circle. The arc traveled is greater than the radius.

>> No.9554040

>>9553971
A quarter arc rotates by 90° and covers a distance of 1.

>> No.9554057

>>9554040
>and covers a distance of 1

look at this guy

>> No.9554078

>>9554040
It travels a distance of [math]\frac\pi2[/math]. Look at the path the origin of the circle traces and then look at the path the center of the square traces as it rotates. With a curved surface it's actually possible to have a square wheel.

>> No.9554106

>>9554040
Well I'll be damned, give this man a fields medal.

The length traveled by the arc is somewhere between the square root of one-half and half the perimeter of the radius squared.
>A quarter arc rotates by 90° and covers a distance of 1.
The point you mistakenly called a vertex had only traveled the length of half it's diameter. Stop discombobulating the matter.

>> No.9554124

>>9553903

but the circle travels half a pi, not 1, for a 90 degree rotation

ergo the circumference of a circle is 2 pi, not 4.

>> No.9554219

>>9553903
>Protip, you cant.
Sure I can.
Just draw a circle with a 1" diameter and then cut a 4" piece of string.
Lay the string around the circumference of the circle, then lie on the ground and cry.
Then cry some more.

>> No.9555042

Circle

D × 4 - [math]\frac{5}{6} [/math]D = C

>> No.9556426

>>9554124
It's true for π=4

>> No.9556428

>>9556426
π=2, my bad

>> No.9557428

>>9553903
now do it with a triangle and three rotations of 120°.

Wow, 3 = 4 = 5 = 6...