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A cyclocycloid is a roulette traced by a point attached to a circle of radius r rolling around, a fixed circle of radius R, where the point is at a distance d from the center of the exterior circle. The red curve is a cyclocycloid (in this case an hypocycloid ) drawn as the smaller black circle rolls around inside the larger blue circle ...
The fundamental method to create a buffer around a geographic feature stored in a vector data model, with a given radius r is as follows: [4] Single point: Create a circle around the point with radius r. Polyline, which consists of an ordered list of points (vertices) connected by straight lines. This is also used for the boundary of a polygon.
The red curve is an epicycloid traced as the small circle (radius r = 1) rolls around the outside of the large circle (radius R = 3).. In geometry, an epicycloid (also called hypercycloid) [1] is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle.
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown.. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them.
Gauss's circle problem asks how many points there are inside this circle of the form (,) where and are both integers. Since the equation of this circle is given in Cartesian coordinates by x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} , the question is equivalently asking how many pairs of integers m and n there are such that
If =, the region is known as the punctured disk (a disk with a point hole in the center) of radius R around the point a. As a subset of the complex plane, an annulus can be considered as a Riemann surface. The complex structure of an annulus depends only on the ratio r / R .
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The algorithm selects one point p randomly and uniformly from P, and recursively finds the minimal circle containing P – {p}, i.e. all of the other points in P except p. If the returned circle also encloses p, it is the minimal circle for the whole of P and is returned. Otherwise, point p must lie on the