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A ring defined on a singleton set {*}. The ring operations (multiplication and addition) are defined in the only possible way, *·*=*, (1) and *+*=*. (2) It follows that this ...

A paradox also known as the surprise examination paradox or prediction paradox. A prisoner is told that he will be hanged on some day between Monday and Friday, but that he ...

An improper use of the symbol sqrt(-1) for the imaginary unit leads to the apparent proof of a false statement. sqrt(-1) = sqrt(-1) (1) sqrt((-1)/1) = sqrt(1/(-1)) (2) ...

An Egyptian fraction is a sum of positive (usually) distinct unit fractions. The famous Rhind papyrus, dated to around 1650 BC contains a table of representations of 2/n as ...

Euclidean n-space, sometimes called Cartesian space or simply n-space, is the space of all n-tuples of real numbers, (x_1, x_2, ..., x_n). Such n-tuples are sometimes called ...

The generalized minimal residual (GMRES) method (Saad and Schultz 1986) is an extension of the minimal residual method (MINRES), which is only applicable to symmetric ...

A helix, sometimes also called a coil, is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not ...

In Book IX of The Elements, Euclid gave a method for constructing perfect numbers (Dickson 2005, p. 3), although this method applies only to even perfect numbers. In a 1638 ...

A formal type of proof most frequently encountered in elementary geometry courses in which known or derived statements are written in the left column, and the reason that ...

A fallacy is an incorrect result arrived at by apparently correct, though actually specious reasoning. The great Greek geometer Euclid wrote an entire book on geometric ...