In space geometry, a spherical spindle ‘ is a part or subset of the spherical surface limited by two maximum circumferences , or each of the subsets in which two maximum circumferences split into a spherical surface [1] .
Summary
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- 1 Items
- 2 Area
- 3 Symmetry
- 4 References and notes
- 5 See also
Elements
Among the elements of the spherical spindle it is worth mentioning as elements
Spindle sides
The maximum circumferences that generate it are called the spindle sides .
The maximum circumferences are those whose center coincides with the center of the sphere : each maximum circumference divides the surface of the sphere into two equal halves. Two maximum circumferences always intersect at two opposite points, ends of the corresponding common diameter.
Axis
The diameter formed by the intersection points of the two maximum circumferences.
Spindle angle
It is the dihedral angle formed by the planes that contain the two maximum circumferences.
Example;
The portion of the peel that exactly covers a slice of the orange, gives the geometric spindle ide
The surface of the Earth between the London and Paris meridians
Area
equals the area of the sphere multiplied by the ratio of the spindle angle measurement and 360º.
A = 4 πr 2 n / 360, where n is the measure of the dihedral angle. [2]
Symmetry
The spindle has planar symmetry:
- one with respect to the plane perpendicular to its axis
- Another regarding the bisector plane of its dihedron.
