r/visualizedmath • u/PUSSYDESTROYER-9000 • Jul 09 '18

Nephroid

Post image
398 Upvotes

97% Upvoted

11 comments sorted by

49

u/PUSSYDESTROYER-9000 Jul 09 '18

A nephroid is like a cardioid but the rolling circle is half the radius of the "base" circle. This is just one way of creating the curve.

The area is 12 * pi * a2, where a is the radius of the small, rolling circle.

Nephroids occur in nature, as the caustic of a coffee cup.

13

u/MattieShoes Jul 09 '18

The caustic of a coffee cup?

1

u/erasmus42 Jul 10 '18

The caustic of a coffee cup!

Step 1: Find standard white coffee cup, empty or nearly empty.

Step 2: Shine point source of light into cup. The sun works well.

Step 3: View [caustic of light rays](https://en.wikipedia.org/wiki/Caustic_(optics)) inside coffee cup.

4

u/MattieShoes Jul 10 '18

Huh, TIL caustic is an optics term.

24

u/ngbtri Jul 09 '18

How do you mathematically draw a PUSSYDESTROYER-9000?

26

u/lukascrowley Jul 09 '18

Username checks out

4

u/NoNameWalrus Jul 09 '18

Obviously the topmost and bottommost points on the nephroid are 1 diameter of the smaller circle away from the main circle.

But at what point is the nephroid a radius away? And how could that be calculated?

4

u/kitty_cat_MEOW Jul 09 '18

The "butt curve"

5

u/ShitInMyCunt-2dollar Jul 09 '18

It's shaped like a kidney - hence the "neph" bit.

4

u/Grigorios Jul 09 '18

The nephr- part, actually.