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There is only one point in front of a perspective drawing where its three mutually perpendicular vanishing points appear in mutually perpendicular directions, but such a ...

Suppose the harmonic series converges to h: sum_(k=1)^infty1/k=h. Then rearranging the terms in the sum gives h-1=h, which is a contradiction.

For n>=3, there exist no additive finite and invariant measures for the group of displacements in R^n.

A fact noticed by physicist G. Gamow when he had an office on the second floor and physicist M. Stern had an office on the sixth floor of a seven-story building (Gamow and ...

A purple cow is a confirming instance of the hypothesis that all crows are black.

Let A be some attribute (e.g., possible, present, perfect, etc.). If all is A, then the non-A must also be A. For example, "All is possible, the impossible too," and "Nothing ...

The set of all sets is its own power set. Therefore, the cardinal number of the set of all sets must be bigger than itself.

Determining the length of a country's coastline is not as simple as it first appears, as first considered by L. F. Richardson (1881-1953) and sometimes known as the ...

After a half rotation of the coin on the left around the central coin (of the same radius), the coin undergoes a complete rotation. In other words, a coin makes two complete ...

If a fixed fraction x of a given amount of money P is lost, and then the same fraction x of the remaining amount is gained, the result is less than the original and equal to ...