Ken's blog

by some estimates, the U.S. directly killed 900,000 Muslims in the War on Islam ("Terror") after 9/11.  (many more if indirect dea...

chess variant removing ranged diagonal movement: replace bishop with fairy ferz, or fairy ferz + fairy dabbaba.  the new piece is colorbou...

various tasks related to constructing a random D-dimensional linear programming problem: we want a convex polyhedron (polytope) specified ...

it seems appropriate to present the unique nontrivial magic hexagon with its numbers expressed in base 6.  final number = 31 (base 6) = 19 (...

first, create a random smooth shape by picking random weights for the first few spherical harmonics and summing them.  reject if the object ...

we rearrange the standard triple-angle trigonometric identity for sine to make it more clear the cubic polynomial that you need to solve for...

inspired by "___: the 3D virtual reality experience"

a cube can be oriented in 24 ways (octahedral group, isometries of a cube) .  vote two letters off the island, then mark a cube with 24 lett...

the following Perl script feeding GP uses Lagrange polynomials to interpolate a polynomial between given points.  input is stdin (or a file ...

fly anywhere, unimpeded by the rods.  you can see quite far because the rods are thin.  slide a cursor that rides on the rods to the exit. ...

consider a horizontal row of dots equally spaced 1 unit apart.  put another such row above it, also with horizontal spacings of 1 unit.  let...

solutions to the Thomson problem up to 12 points (excluding 11) have nice symmetry.  (though I feel that the solution for 1 point also lacks...

create a deck of cards representing the 48 elements of the symmetry group of a cube (isometries of a cube) (automorphism group of a cube).  ...

what rectangle aspect ratios permit finite tessellations of regular hexagons to be neatly inscribed within them? assuming one edge of hexa...

the point at coordinates (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24) in 24-dimensional space is ...

consider a brick in N dimensions composed of unit hypercubes.  for example, let N=3.  each unit cube is labeled 0 or 1, subject to the follo...

consider the axis-aligned square between (0,0) and (4,4).  we will draw a binary tree inside this box. the root node is centered on the top ...

a square (or rectangle) fundamental polygon is good for 2D games. previously on the various spaces (manifolds) that a fundamental polygon c...

"Convex Regular Faced" is usually applied to polytopes in 4D and above, but it is a useful term for 3D as well, subsuming the Plat...

both people lying on their side, next to each other.  4 possibilities: big spoon, little spoon, face to face, back to back.  we do not count...