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Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
This group has six mirror planes, each containing two edges of the cube or one edge of the tetrahedron, a single S 4 axis, and two C 3 axes. T d is isomorphic to S 4, the symmetric group on 4 letters, because there is a 1-to-1 correspondence between the elements of T d and the 24 permutations of the four 3-fold axes.
In a Cartesian plane, one can define canonical representatives of certain geometric figures, such as the unit circle (with radius equal to the length unit, and center at the origin), the unit square (whose diagonal has endpoints at (0, 0) and (1, 1)), the unit hyperbola, and so on. The two axes divide the plane into four right angles, called ...
Two distinct planes are either parallel or they intersect in a line. A line is either parallel to a plane, intersects it at a single point, or is contained in the plane. Two distinct lines perpendicular to the same plane must be parallel to each other. Two distinct planes perpendicular to the same line must be parallel to each other.
The Poincaré half-plane model takes one-half of the Euclidean plane, bounded by a line B of the plane, to be a model of the hyperbolic plane. The line B is not included in the model. The Euclidean plane may be taken to be a plane with the Cartesian coordinate system and the x-axis is taken as line B and the half plane is the upper half ( y > 0 ...
The circle is obtained when the cutting plane is parallel to the plane of the generating circle of the cone; for a right cone, this means the cutting plane is perpendicular to the axis. If the cutting plane is parallel to exactly one generating line of the cone, then the conic is unbounded and is called a parabola.
The Euclidean plane corresponds to the case ε 2 = −1, an imaginary unit. Since the modulus of z is given by = (+) = +, this quantity is the square of the Euclidean distance between z and the origin. For instance, {z | z z* = 1} is the unit circle.
When, in the model, these lines are considered to be the points and the planes the lines of the projective plane PG(2, R), this association becomes a correlation (actually a polarity) of the projective plane. The sphere model is obtained by intersecting the lines and planes through the origin with a unit sphere centered at the origin.