Table of Contents
What is the term for a plane that passes through the center of a sphere?
plane passing through the center of the sphere is called a great circle of the sphere.)
What lies on a sphere and divides the sphere into two hemispheres?
The Equator is an imaginary line around the middle of the Earth. It is halfway between the North and South Poles, and divides the Earth into the Northern and Southern Hemispheres.
How is sphere divided?
In a plane, a straight line is a geodesic. On a sphere, a great circle is a geodesic. A hemisphere is the half sphere formed by a plane intersecting the center of a sphere. The cut-line forming a hemisphere is a great circle….
| • | The radius of the sphere is r. |
|---|---|
| • | The height of the cylinder is h = 2r. |
What is the distance across the middle of a circle or sphere?
The distance from a circle’s center to a point on the circle is called the radius of the circle. A radius is a line segment with one endpoint at the center of the circle and the other endpoint on the circle.
Is a part of the sphere which is captured between two great circles?
The minor arc of a great circle between two points is the shortest surface-path between them. These great circles are the geodesics of the sphere. The disk bounded by a great circle is called a great disk: it is the intersection of a ball and a plane passing through its center.
What is meant by great circle route?
great circle route, the shortest course between two points on the surface of a sphere. It lies in a plane that intersects the sphere’s centre and was known by mathematicians before the time of Columbus. Navigational radio signals also follow great circle paths.
What is the basic geometric figures of sphere?
In spherical geometry, the basic concepts are point and great circle. However, two great circles on a plane intersect in two antipodal points, unlike coplanar lines in Elliptic geometry. In the extrinsic 3-dimensional picture, a great circle is the intersection of the sphere with any plane through the center.
How do you divide a sphere into equal areas?
One of the ways is to divide the sphere into N sectors of equal width, like segments of an orange. Each of the N pieces will have equal surface area. Another way is to divide the sphere into N sectors of equal width, and then to divide along the equator, so that each will be a half-segment.
How many planes are in a sphere?
Grade 9. A sphere will have infinite planes of symmetry through the center of the sphere since you can cut it through the center and both parts are equal.
What is the intersection of a plane and a sphere?
A great circle is the intersection a plane and a sphere where the plane also passes through the center of the sphere. Lines of longitude and the equator of the Earth are examples of great circles.
When does a plane cut a sphere into two equal parts?
When a plane cuts a sphere from any point on it, we get a circle. The size of the cross section may vary depending on the point of intersection of plane and sphere. If the plane passed through the center of sphere, then it divides the sphere into two equal parts (i.e. hemisphere).
How to determine the cross section of a sphere?
All cross-sections of a sphere are circles. Determine the cross-section area of the given cylinder whose height is 25 cm and radius is 4 cm. We know that when the plane cuts the cylinder parallel to the base, then the cross-section obtained is a circle. Therefore, the area of a circle, A = πr 2 square units.
How is a sphere like a two dimensional space?
Like a circle in a two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point in a three-dimensional space.
What do you call two points opposite each other on a sphere?
Two points which are opposite each other on the sphere are called antipodal points. In spherical geometry, we can say “two points determine a geodesic, unless they are antipodal points, in which case there are infinitely many geodesics joining them”.