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The butterfly curve can be defined by parametric equations of x and y.. In mathematics, a parametric equation expresses several quantities, such as the coordinates of a point, as functions of one or several variables called parameters.
The Earth-centered, Earth-fixed coordinate system (acronym ECEF), also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth (including its surface, interior, atmosphere, and surrounding outer space) as X, Y, and Z measurements from its center of mass.
For example, the sine of angle θ is defined as being the length of the opposite side divided by the length of the hypotenuse. The six trigonometric functions are defined for every real number , except, for some of them, for angles that differ from 0 by a multiple of the right angle (90°).
For the simplest version of Theta*, the main loop is much the same as that of A*. The only difference is the update _ vertex ( ) {\displaystyle {\text{update}}\_{\text{vertex}}()} function. Compared to A*, the parent of a node in Theta* does not have to be a neighbor of the node as long as there is a line-of-sight between the two nodes.
In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle .
In computational geometry, the Theta graph, or -graph, is a type of geometric spanner similar to a Yao graph. The basic method of construction involves partitioning the space around each vertex into a set of cones , which themselves partition the remaining vertices of the graph.
In mathematics, a theta characteristic of a non-singular algebraic curve C is a divisor class Θ such that 2Θ is the canonical class. In terms of holomorphic line bundles L on a connected compact Riemann surface , it is therefore L such that L 2 is the canonical bundle , here also equivalently the holomorphic cotangent bundle .
When B > 0, the solvent is "good," and when B < 0, the solvent is "poor". For a theta solvent, the second virial coefficient is zero because the excess chemical potential is zero; otherwise it would fall outside the definition of a theta solvent. A solvent at its theta temperature is, in this way, analogous to a real gas at its Boyle temperature.