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The centroid is center of mass of a two-dimensional planar lamina or a three-dimensional solid. The mass of a lamina with surface density function sigma(x,y) is ...

A parallelian is a line drawn parallel to one side of a triangle. The three lines drawn through a given point are known as the triangle's parallelians. There exists a unique ...

The common incircle of the medial triangle DeltaM_AM_BM_C (left figure) and the congruent triangle DeltaQ_AQ_BQ_C, where Q_i are the midpoints of the line segment joining the ...

The term "arbelos" means shoemaker's knife in Greek, and this term is applied to the shaded area in the above figure which resembles the blade of a knife used by ancient ...

Geometry

The nesting of two or more functions to form a single new function is known as composition. The composition of two functions f and g is denoted f degreesg, where f is a ...

Given relatively prime integers p and q (i.e., (p,q)=1), the Dedekind sum is defined by s(p,q)=sum_(i=1)^q((i/q))(((pi)/q)), (1) where ((x))={x-|_x_|-1/2 x not in Z; 0 x in ...

A mathematical statement of the equivalence of two quantities. The equality "A is equal to B" is written A=B.

The exists quantifier exists .

The hyperbolic sine is defined as sinhz=1/2(e^z-e^(-z)). (1) The notation shz is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). It is implemented in the Wolfram ...