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A curve of order n is generally determined by n(n+3)/2 points. So a conic section is determined by five points and a cubic curve should require nine. But the Maclaurin-Bézout ...

Consider the length of the diagonal of a unit square as approximated by piecewise linear steps that may only be taken in the right and up directions. Obviously, the length so ...

A paradox or contradiction.

A man of Seville is shaved by the Barber of Seville iff the man does not shave himself. Does the barber shave himself? This pseudoparadox was proposed by Bertrand Russell.

Even though real arithmetic is uncountable, it possesses a countable "model."

Socrates is reported to have stated: "One thing I know is that I know nothing."

Consider a library which compiles a bibliographic catalog of all (and only those) catalogs which do not list themselves. Then does the library's catalog list itself?

In the depiction of a row of identical columns parallel to the plane of a perspective drawing, the outer columns should appear wider even though they are farther away.

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.