Xah Math Blog Archive 2015-05 to 2015-05

The Stanford Encyclopedia of Philosophy

The Stanford Encyclopedia of Philosophy is a great thing. A different take than Wikipedia.

magic polyhedron

the Rubik cube of today have advanced. Now, there's stickerless versions, and better mechanical design.

Kawai MP9000 piano dodecahedron
magic dodecahedron.

see updated Magic Polyhedrons

ℭ = Cardinality of the continuum.

ℚ = be rational, ℝ = get real.

ℭ = Cardinality of the continuum.

Math Font ℤ ℚ ℝ ℂ ℜ ℑ ℵ

Tiling and Patterns, Classic Text Now in Print Again

tiling and patterns
Tiling and Patterns By Branko Grunbaüm, G C Shaphard. Buy at amazon

just discovered, this classic, definitive, book on tilings and patterns is in print again, now reprinted by Dover.

see also: Reading Notes on Tilings and Patterns

tiling the plane with 5-fold symmetry tiles

John Baez, gave a intro on the problem of tiling the plane with 5-fold symmetry tiles At https://plus.google.com/117663015413546257905/posts/5CHdeLRckRm

see also [• The trouble with five By Craig Kaplan. At https://plus.maths.org/content/trouble-five , Accessed on 2015-05-11 ]

sample of tiling and patterns, see:

See also: Discontinuous Groups of Rotation and Translation in the Plane

Skew But Fair Dice

skew dice

it supposed to be fair dice. Am thinking there's a major difference from the cube. This one, has 2 different sides, like a coin. In a sense, when you throw this dice, it decides which of the side will fall first, then, decide which of the 3 faces will land.

So, one can actually make a 3-sided pyramid, and have 2 of them and glue the bottom together. So, we could make a infinite shape of 6 faced dice that's still fair. Then, if we wiggle the cutting plane like a saw tooth, we could create quite a lot strange looking and still fair 6-faced dice.

comment at https://plus.google.com/+XahLee/posts/L9FP178N6eq

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