Search results
Results from the WOW.Com Content Network
P ' is the inverse of P with respect to the circle. To invert a number in arithmetic usually means to take its reciprocal. A closely related idea in geometry is that of "inverting" a point. In the plane, the inverse of a point P with respect to a reference circle (Ø) with center O and radius r is a point P ', lying on the ray from O through P ...
The inverse of the curve C is then the locus of P as Q runs over C. The point O in this construction is called the center of inversion, the circle the circle of inversion, and k the radius of inversion. An inversion applied twice is the identity transformation, so the inverse of an inverse curve with respect to the same circle is the original ...
In mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, [1] cyclometric, [2] or arcus functions [3]) are the inverse functions of the trigonometric functions, under suitably restricted domains. Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, [4 ...
Two points z 1 and z 2 are conjugate with respect to a generalized circle C, if, given a generalized circle D passing through z 1 and z 2 and cutting C in two points a and b, (z 1, z 2; a, b) are in harmonic cross-ratio (i.e. their cross ratio is −1). This property does not depend on the choice of the circle D.
A function f and its inverse f −1. Because f maps a to 3, the inverse f −1 maps 3 back to a. In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by.
Thales's theorem. Angle formed by a point on a circle and the 2 ends of a diameter is a right angle. Thales’ theorem: if AC is a diameter and B is a point on the diameter's circle, the angle ∠ ABC is a right angle. In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the ...
a value of −1 for two circles that are tangent to each other, one inside of the other, and a value less than −1 when one circle contains the other. (Some authors define the absolute inversive distance as the absolute value of the inversive distance.) Some authors modify this formula by taking the inverse hyperbolic cosine of the value given ...
Specifically, stereographic projection from the north pole (0,1) onto the x-axis gives a one-to-one correspondence between the rational number points (x, y) on the unit circle (with y ≠ 1) and the rational points of the x-axis. If ( m / n , 0) is a rational point on the x-axis, then its inverse stereographic projection is the point