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Euler conjectured that at least n nth powers are required for n>2 to provide a sum that is itself an nth power. The conjecture was disproved by Lander and Parkin (1967) with ...

The Gosset graph is a 27-regular graph on 56 vertices which is the skeleton of the Gosset polytope 3_(21). It is a distance-regular graph with intersection array ...

In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 ...

The Menger sponge is a fractal which is the three-dimensional analog of the Sierpiński carpet. The nth iteration of the Menger sponge is implemented in the Wolfram Language ...

Ono (1914) conjectured that the inequality 27(b^2+c^2-a^2)^2(a^2+c^2-b^2)^2(a^2+b^2-c^2)^2<=(4K)^6 holds true for all triangles, where a, b, and c are the lengths of the ...

The catacaustic of a parabola (t,t^2) opening upward is complicated for a general radiant point (x,y). However, the equations simplify substantially in the case x=infty ...

Given a parabola with parametric equations x = at^2 (1) y = at, (2) the evolute is given by x_e = 1/2a(1+6t^2) (3) y_e = -4at^3. (4) Eliminating x and y gives the implicit ...

Also called "Ethiopian multiplication." To multiply two numbers a and b, write a_0=a and b_0=b in two columns. Under a_0, write |_a_0/2_|, where |_x_| is the floor function, ...

The triangular orthobicupola is Johnson solid J_(27), consisting of eight equilateral triangles and six squares. If a triangular orthobicupola is oriented with triangles on ...

Let L denote the n×n triangular lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L ...