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The formula giving the roots of a quadratic equation ax^2+bx+c=0 (1) as x=(-b+/-sqrt(b^2-4ac))/(2a). (2) An alternate form is given by x=(2c)/(-b+/-sqrt(b^2-4ac)). (3)

There exist numbers y_1<y_2<...<y_(n-1), a<y_(n-1), y_(n-1)<b, such that lambda_nu=alpha(y_nu)-alpha(y_(nu-1)), (1) where nu=1, 2, ..., n, y_0=a and y_n=b. Furthermore, the ...

A pair of dice which have the same odds for throwing every number as a normal pair of 6-sided dice. They are the only such alternate arrangement if face values are required ...

The term "transition matrix" is used in a number of different contexts in mathematics. In linear algebra, it is sometimes used to mean a change of coordinates matrix. In the ...

Trigonometry

The Markov numbers m are the union of the solutions (x,y,z) to the Markov equation x^2+y^2+z^2=3xyz, (1) and are related to Lagrange numbers L_n by L_n=sqrt(9-4/(m^2)). (2) ...

The vertex of an isosceles triangle having angle different from the two equal angles is called the apex of the isosceles triangle. The common polygon vertex at the top of a ...

A reflex angle is an angle of more than 180 degrees. A full angle is therefore a reflex angle, while acute, obtuse, right, and straight angles are not.

The angle bisector of an angle in a triangle divides the opposite side in the same ratio as the sides adjacent to the angle.

Given ∠AXB+∠AYB=pi radians in the above figure, then X and Y are said to be antigonal points with respect to A and B.