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There is a well known pattern that turns up in nature involving the golden ratio $\phi = \frac{\sqrt{5}-1}{2}$.     (source) To get this "sunflower spiral" pattern, put the $k$th node at an angle of …

Consider three circles of radius $1$ in $\mathbb{R}^3$, linked with each other in the same arrangement as three fibers of the Hopf fibration. Now thicken the circles up into non-overlapping standard r …

The result (for 3 dimensions and I think easily generalises to any dimension) follows from Theorem 3 of the Bollobás and Leader paper. The theorem (in 3 dimensions) states that for any subset $A$ of t …

(Too long for a comment.) Following on from Gerhard's parabolic mirrors suggestion: take a parabolic mirror surface, cut off by a plane perpendicular to the axis of symmetry, so that the resulting su …

Talking with Saul Schleimer, we came up with the following: Orthogonally project the great stellated dodecahedron into the $z=0$ plane, choosing a direction that does not result in any zero length edg …

The Cheeger constant of a finite graph measures the "bottleneckedness" of the graph, and is defined as: $$h(G) := \min\Bigg\lbrace\frac{|\partial A|}{|A|} \Bigg| A\subset V, 0<|A|\leq \frac{|V|}{2} \ …