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The equation defining Killing vectors. L_Xg_(ab)=X_(a;b)+X_(b;a)=2X_((a;b))=0, where L is the Lie derivative and X_(b;a) is a covariant derivative.

A leg of a triangle is one of its sides. For a right triangle, the term "leg" generally refers to a side other than the one opposite the right angle (which is termed the ...

Lemoine-Brocard geometry is that part of triangle geometry concerned with the Brocard points, Brocard triangles, etc. and with symmedians and symmedian points.

In space, the only conformal mappings are inversions, similarity transformations, and congruence transformations. Or, restated, every angle-preserving transformation is a ...

For a logarithmic spiral with parametric equations x = e^(bt)cost (1) y = e^(bt)sint, (2) the involute is given by x = (e^(bt)sint)/b (3) y = -(e^(bt)cost)/b, (4) which is ...

The winding number W(theta) of a map f(theta) with initial value theta is defined by W(theta)=lim_(n->infty)(f^n(theta)-theta)/n, which represents the average increase in the ...

Every point which can be constructed with a straightedge and compass, and no other points, can be constructed using identical matchsticks (i.e., identical movable line ...

The triangle DeltaM_AM_BM_C formed by joining the midpoints of the sides of a triangle DeltaABC. The medial triangle is sometimes also called the auxiliary triangle (Dixon ...

A graph with minimum vertex degree at least 5 is a line graph iff it does not contain any of the above six graphs, known in this work as Metelsky graphs, as an induced ...

A phenomenon in which a system being forced at an irrational period undergoes rational, periodic motion which persists for a finite range of forcing values. It may occur for ...