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The Games graph is a strongly regular graph on 729 vertices with parameters (nu,k,lambda,mu)=(729,112,1,20). It is distance-regular but not distance-transitive with ...

All the propositions in projective geometry occur in dual pairs which have the property that, starting from either proposition of a pair, the other can be immediately ...

A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. ...

Given a reference triangle DeltaABC, the trilinear coordinates of a point P with respect to DeltaABC are an ordered triple of numbers, each of which is proportional to the ...

A path composed of connected horizontal and vertical line segments, each passing between adjacent lattice points. A lattice path is therefore a sequence of points P_0, P_1, ...

The dual of Pascal's theorem (Casey 1888, p. 146). It states that, given a hexagon circumscribed on a conic section, the lines joining opposite polygon vertices (polygon ...

The Steiner deltoid is the envelope of the Simson lines of a triangle. Its circumcircle is the Steiner circle, and its incircle is the nine-point circle. The triangle formed ...

Let points A^', B^', and C^' be marked off some fixed distance x along each of the sides BC, CA, and AB. Then the lines AA^', BB^', and CC^' concur in a point U known as the ...

Lagrange multipliers, also called Lagrangian multipliers (e.g., Arfken 1985, p. 945), can be used to find the extrema of a multivariate function f(x_1,x_2,...,x_n) subject to ...

If P be a point in the plane of an equilateral triangle DeltaABC, then the lengths of line segments AP, BP, and CP correspond the sides of a triangle, which is degenerate ...