Solids {sphere} can result when semicircle rotates around its diameter. Equation is x^2 + y^2 + z^2 <= r^2, where r is radius.
area
Area is 4 * pi * r^2, where r is radius.
volume
Volume is 4 * pi * r^3 / 3, where r is radius.
imaginary circle
Two spheres share imaginary circle.
secondaries
Great circles can pass through poles.
spherical distance
Geodesic has length {spherical distance}.
spherical polygon
Great-circle arcs can bound spherical surface region {spherical polygon}.
spherical surface
x^2 + y^2 + z^2 = r^2 defines spherical surface. Area is 4 * pi * r^2, where r is radius.
diameter
Diameter is perpendicular to sphere at both endpoints.
coordinates
Sphere coordinates are longitude (360 degrees) and latitude (180 degrees), because they define unique points. Longitudes are perpendicular to latitudes. For spinning spheres, longitudes are along general direction of spherical axis, and latitudes are perpendicular to spherical axis.
Spherical coordinates can be vertical and horizontal latitude, so axes are perpendicular, but two latitudes define two different points, so points must have one more coordinate, such as north or south. Spherical coordinates can be vertical and horizontal longitudes, with axes not always perpendicular, but two longitudes can define the same great circle, so points must have one more coordinate. Therefore, only longitude and latitude define sphere points using two numbers.
Mathematical Sciences>Geometry>Solid>Sphere
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Date Modified: 2022.0224