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Stereographic projection of the unit sphere from the north pole onto the plane z = 0, shown here in cross section. The unit sphere S 2 in three-dimensional space R 3 is the set of points (x, y, z) such that x 2 + y 2 + z 2 = 1. Let N = (0, 0, 1) be the "north pole", and let M be the rest of the sphere.
This shows that a great circle is, with respect to distance measurement on the surface of the sphere, a circle: the locus of points all at a specific distance from a center. Each point is associated with a unique great circle, called the polar circle of the point, which is the great circle on the plane through the centre of the sphere and ...
A circle with non-zero geodesic curvature is called a small circle, and is analogous to a circle in the plane. A small circle separates the sphere into two spherical disks or spherical caps, each with the circle as its boundary. For any triple of distinct non-antipodal points a unique small circle passes through all three.
Projects the globe onto an octahedron with symmetrical components and contiguous landmasses that may be displayed in various arrangements. 1975 Cahill–Keyes projection: Polyhedral Compromise Gene Keyes: Projects the globe onto a truncated octahedron with symmetrical components and contiguous land masses that may be displayed in various ...
2-sphere wireframe as an orthogonal projection Just as a stereographic projection can project a sphere's surface to a plane, it can also project a 3-sphere into 3-space. This image shows three coordinate directions projected to 3-space: parallels (red), meridians (blue), and hypermeridians (green).
The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap.
The circles of Apollonius are any of several sets of circles associated with Apollonius of Perga, a renowned Greek geometer.Most of these circles are found in planar Euclidean geometry, but analogs have been defined on other surfaces; for example, counterparts on the surface of a sphere can be defined through stereographic projection.
Example of a projected area from a hardness indentation. Projected area is the two dimensional area measurement of a three-dimensional object by projecting its shape on to an arbitrary plane. This is often used in mechanical engineering and architectural engineering related fields, especially for hardness testing, axial stress , wind pressures ...