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The MacBeath triangle DeltaX_AX_BX_C (a term coined here for the first time), is the triangle whose vertices are the contact points of the MacBeath inconic with the reference ...

The second Yff triangle is the Cevian triangle DeltaA^'B^'C^' of the second Yff point. The area of the second Yff triangle is Delta=(u^3)/(2R), where R is the circumradius of ...

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. ...

A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center (i.e., the polygon is both equiangular ...

A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the center. ...

1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line ...

The difference between the sum of the angles A, B, and C of a spherical triangle and pi radians (180 degrees), E=A+B+C-pi. The notation Delta is sometimes used for spherical ...

A tetrahedron having a trihedron all of the face angles of which are right angles. The face opposite the vertex of the right angles is called the base. If the edge lengths ...

The cosine function cosx is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent). Let theta be an ...

Two angles alpha and beta are said to be complementary if alpha+beta=pi/2. In other words, alpha and beta are complementary angles if they produce a right angle when combined.