THIS IS THE CUTEST THING EVER

they both look a little nervous about what the other one might write

then just the biggest smiles when they are reassured yet again how much they just love each other

Curves of Constant Width and Odd-Sided Reuleaux PolygonsA curve of constant width is a convex, two-dimensional shape that, when rotated inside a square, always makes contact with all four sides.

A circle is the most obvious (but somewhat trivial) example. Some non-trivial examples are the odd-sided Reuleaux polygons — the first four of which are shown above.

Since they don’t have fixed axes of rotation, curves of constant width (except the circle) have few practical applications. One notable use of the Reuleaux triangle, though, is in drilling holes in the shape of a slightly rounded square (watch one of the triangle’s vertices and notice the shape it traces out as it spins).

On a less technical note, all curves of constant width are solutions to the brainteaser, “Other than a circle, what shape can you make a manhole cover such that it can’t fall through the hole it covers?”

Mathematica code posted here.Additional source not linked above.

i have seen a man wanting to weep

but

instead

beat his heart until it was unconscious.

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(via the1paradox) |