Specular holograms by Matthew Brand currently on display at the new Museum of Mathematics in New York.
See his site for more.
The technique used by Brand to create these pieces is not one of conventional holography. He meticulously controls the unique shape of thousands of tiny optical pieces placed on a surface creating a 3D effect when the light source or viewer moves. This is essentially a mathematical problem in differential geometry and combinatorial optimization. Brand is the first person to correctly describe this technique in 2008 even though it dates back as early as the 1930s (check out his paper for details).
'…Todd, trust math. As in Matics, Math E. First-order predicate logic. Never fail you. Quantities and their relation. Rates of change. The vital statistics of God or equivalent. When all else fails. When the boulder's slid all the way back to the bottom. When the headless are blaming. When you do not know your way about. You can fall back and regroup around math. Whose truth is deductive truth. Independent of sense or emotionality. The syllogism. The identity. Modus Tollens. Transitivity. Heaven's theme song. The nightlight on life's dark wall, late at night. Heaven's recipe book. The hydrogen spiral. The methane, ammonia H20. Nucleic acids. A and G, T and C. The creeping inevitability. Caius is mortal. Math is not mortal. What it is is: listen: it's true.'
“
— | David Foster Wallace, Infinite Jest |
“My body just before I disappeared.”
-Edwin Abbott Abbott, Flatland: A Romance of Many Dimensions, 1884
If you’re sharing a pizza with another person, there’s no need to cut it into precisely equal slices.Make four cuts at equal angles through an arbitrary point and take alternate slices. You’ll both get the same amount of pizza.
Also: If a pizza has thickness a and radius z, then its volume is pi z z a. (via Futility Closet)
Hi-res (700x700):
r = 12.35664 ≤ a ≤ 2.35773
s = 320
Mathematica code:
Manipulate[Graphics[Line[
Table[{-r^n*Sin[n*2*Pi/a], r^n*Cos[n*2*Pi/a]}, {n, 0, s}]],
PlotRange -> 1.3],
{r, .1, 1}, {a, 0.001, 4*Pi, .00005}, {s, 1, 800, 1}]
The knight can visit each square on a chess board exactly once. Sure.
Source: Chess.com