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A sextic surface given by the implicit equation 4(x^2+y^2+z^2-13)^3+27(3x^2+y^2-4z^2-12)^2=0.

Three impossible ways to combine four bars.

An impossible figure that locally (but only locally!) looks like a torus.

An irreducible fraction is a fraction p/q for which GCD(p,q)=1, i.e., p and q are relatively prime. For example, in the complex plane, (4+7i)/(2+i)=3+2i is reducible, while ...

An optical illusion, illustrated above, in which the eye perceives a white upright equilateral triangle where none is actually drawn.

Approximations to Khinchin's constant include K = -(ln85181832)/(tan8) (1) = 1/(29)sqrt(6065) (2) = 6-sqrt(ln59055) (3) = 18^(27/79), (4) which are correct to 9, 7, 6, and 5 ...

Every Möbius strip dissection of unequal squares can be glued along its edge to produce a dissection of the Klein bottle. There are no other ways to tile a Klein bottle with ...

A method for constructing magic squares of singly even order n>=6.

A roll of 4 on a pair of six-sided dice in the game of craps (Gardner 1978, p. 256). The probability of rolling "a little Joe" is 1/12, or 8.333...%. A roll of "4 the hard ...

A method for constructing magic squares of odd order.