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The maximal number of regions into which n lines divide a plane are N(n)=1/2(n^2+n+2) which, for n=1, 2, ... gives 2, 4, 7, 11, 16, 22, ... (OEIS A000124), the same maximal ...

A polygonal number is a type of figurate number that is a generalization of triangular, square, etc., to an n-gon for n an arbitrary positive integer. The above diagrams ...

Virtually nothing is known about dissection of a projective plane using unequal squares.

A diagonal of a square matrix which is traversed in the "northeast" direction. "The" skew diagonal (or "secondary diagonal") of an n×n square matrix is the skew diagonal from ...

An (n,k)-talisman hexagon is an arrangement of nested hexagons containing the integers 1, 2, ..., H_n=3n(n-1)+1, where H_n is the nth hex number, such that the difference ...

A set of n cells in an n×n square such that no two come from the same row and no two come from the same column. The number of transversals of an n×n square is n! (n ...

A compact set W_infty with area mu(W_infty)=8/9(24)/(25)(48)/(49)...=pi/4 created by punching a square hole of length 1/3 in the center of a square. In each of the eight ...

Find a square number x^2 such that, when a given integer h is added or subtracted, new square numbers are obtained so that x^2+h=a^2 (1) and x^2-h=b^2. (2) This problem was ...

Fermat's 4n+1 theorem, sometimes called Fermat's two-square theorem or simply "Fermat's theorem," states that a prime number p can be represented in an essentially unique ...

A closed planar quadrilateral with opposite sides of equal lengths a and b, and with four right angles. A square is a degenerate rectangle with a=b. The area of the rectangle ...