Search Results for ""

A quadrilateral whose consecutive sides have the lengths a_1b_3, a_3b_2, a_2b_3, a_3b_1, where a_1^2+a_2^2=a_3^2 (1) and b_1^2+b_2^2=b_3^2. (2) Brahmagupta's trapezium is a ...

There are at least two meanings on the word congruent in mathematics. Two geometric figures are said to be congruent if one can be transformed into the other by an isometry ...

A coordinate system composed of intersecting surfaces. If the intersections are all at right angles, then the curvilinear coordinates are said to form an orthogonal ...

The Pythagoras tree is a fractal constructed iteratively from a right triangle with squares erected on each of the sides. Subsequent iterations add additional similar right ...

A rounded rectangle is the shape obtained by taking the convex hull of four equal circles of radius r and placing their centers at the four corners of a rectangle with side ...

Trigonometry

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 ...

An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length b and the remaining side has length a. This property ...

If x takes only nonnegative values, then P(x>=a)<=(<x>)/a. (1) To prove the theorem, write <x> = int_0^inftyxP(x)dx (2) = int_0^axP(x)dx+int_a^inftyxP(x)dx. (3) Since P(x) is ...

The Riemann-Lebesgue Lemma, sometimes also called Mercer's theorem, states that lim_(n->infty)int_a^bK(lambda,z)Csin(nz)dz=0 (1) for arbitrarily large C and "nice" ...