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A parallelohedron is a space-filling polyhedron that fills space using an infinite number of similarly situated copies (Tutton 1964, pp. 567 and 723; Coxeter 1973, pp. ...

The equation of a line ax+by+c=0 in slope-intercept form is given by y=-a/bx-c/b, (1) so the line has slope -a/b. Now consider the distance from a point (x_0,y_0) to the ...

Let C be a curve and let O be a fixed point. Let P be on C and let Q be the curvature center at P. Let P_1 be the point with P_1O a line segment parallel and of equal length ...

A configuration of 12 planes and 12 points such that six points lie in every plane and six planes pass through every point. Alternatively, the configuration consists of 16 ...

A rhombus is a quadrilateral with both pairs of opposite sides parallel and all sides the same length, i.e., an equilateral parallelogram. The word rhomb is sometimes used ...

The study of figures on the surface of a sphere (such as the spherical triangle and spherical polygon), as opposed to the type of geometry studied in plane geometry or solid ...

A number of the form Tt_n=((n+2; 2); 2)=1/8n(n+1)(n+2)(n+3) (Comtet 1974, Stanley 1999), where (n; k) is a binomial coefficient. The first few values are 3, 15, 45, 105, 210, ...

Begin with the Yff central triangle and then parallel-displace the isoscelizers in such a way as to reduce the central triangle to a point while keeping the other three ...

The 10_3 configuration of ten lines intersecting three at a time in 10 points which arises in Desargues' theorem. Its Levi graph is the Desargues graph.

The Diophantine equation x^n+y^n=z^n. The assertion that this equation has no nontrivial solutions for n>2 has a long and fascinating history and is known as Fermat's last ...