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passing through the sphere's center, so its extrinsic radius is smaller than that of the sphere and its extrinsic center is an arbitrary point in the interior of the sphere. Parallel planes cut the sphere into parallel (concentric) small circles; the pair of parallel planes tangent to the sphere are
417:). A great circle lies on a plane passing through the center of the sphere, so its extrinsic radius is equal to the radius of the sphere itself, and its extrinsic center is the sphere's center. A small circle lies on a plane
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is a point in the boundary of the small circle. Therefore, knowing the radius of the sphere, and the distance from the plane of the small circle to C, the radius of the small circle can be determined using the
Pythagorean
240:(the unique furthest other point on the sphere). For any pair of distinct non-antipodal points, a unique great circle passes through both. Any two points on a great circle separate it into two
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Every circle has two antipodal poles (or centers) intrinsic to the sphere. A great circle is equidistant to its poles, while a small circle is closer to one pole than the other.
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is a circle, which can be interpreted extrinsically to the sphere as a
Euclidean circle: a locus of points in the plane at a constant
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The sphere's intersection with a second sphere is also a circle, and the sphere's intersection with a concentric
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through these poles, passing through the sphere's center and perpendicular to the parallel planes, is called the
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analogous to a straight line in the plane. A great circle separates the sphere into two equal
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and is the shortest path between the points, and the longer is called the
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547:(2014), "On the works of Euler and his followers on spherical geometry",
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A spherical circle with zero geodesic curvature is called a
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Mathematical expression of circle like slices of sphere
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A circle with non-zero geodesic curvature is called a
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478:, paired with their opposite meridian in the other
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501:Proceedings of the Edinburgh Mathematical Society
193:. If the sphere is embedded in three-dimensional
64:but its sources remain unclear because it lacks
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95:Learn how and when to remove this message
470:the only great circle. By contrast, all
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147:) from a given point on the sphere (the
377:is the center of the small circle, and
163:relative to the sphere, analogous to a
181:, and the curves analogous to planar
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527:A treatise on spherical trigonometry
362:{\displaystyle BC^{2}=AB^{2}+AC^{2}}
606:. You can help Knowledge (XXG) by
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413:) from a point in the plane (the
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441:is a pair of antipodal circles.
41:
572:; Leathem, John Gaston (1901),
1:
578:(Revised ed.), MacMillan
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373:is the center of the sphere,
288:circles are sometimes called
466:are small circles, with the
456:geographic coordinate system
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300:Extrinsic characterization
218:Intrinsic characterization
171:; the curves analogous to
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514:10.1017/S0013091500037020
430:of the parallel circles.
111:Small circle of a sphere.
50:This article includes a
493:Allardice, Robert Edgar
435:right circular cylinder
79:more precise citations.
575:Spherical Trigonometry
545:Papadopoulos, Athanase
482:, form great circles.
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197:, its circles are the
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497:"Spherical Geometry"
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213:Fundamental concepts
123:(often shortened to
439:right circular cone
201:of the sphere with
407:Euclidean distance
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161:geodesic curvature
141:spherical distance
117:spherical geometry
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52:list of references
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537:978-1-4181-8047-8
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16:(Redirected from
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71:Please help
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18:Small circle
522:Casey, John
233:hemispheres
226:, and is a
185:are called
175:are called
77:introducing
647:Categories
555:: 53–108,
486:References
480:hemisphere
286:Concentric
562:1409.4736
476:longitude
472:meridians
460:parallels
290:parallels
254:major arc
250:minor arc
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524:(1889),
507:: 8–16,
495:(1883),
464:latitude
424:diameter
391:embedded
382:theorem.
369:, where
228:geodesic
85:May 2024
658:Circles
468:Equator
454:In the
450:Geodesy
401:with a
183:circles
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133:points
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275:arcs
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149:pole
119:, a
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