or log in with
The surface of a sphere consists of the set of points which are all at the same distance from a given point in space.
surface of sphere, great circle, mathematics, geometry, surface
A sphere is defined by the set of points which are all at a fixed distance (r ) from a given point in space (P ). Here r is the radius of the sphere.
If this distance is smaller than r it results in a spherical body, if it is exactly equal to r it results in a spherical surface.
The intersection of a sphere with a plane, which passes through the centre of the sphere, is called the great circle of the sphere. This is demonstrated by pressing the ´Animation´ button.
The area of a great circle is
and the area of the four great circles together is
which is the formula of the surface area of the sphere.
In other words, 4 great circles can cover the entire surface of the sphere. Of course, this does not work in reality, this is only a theoretical experiment.
A sphere is the set of points which are all within the same distance from a given point in space.
Colour a map with the fewest number of colours possible, so that no two adjacent regions have the same colour.
The Möbius strip and the Klein bottle are special two-dimensional surfaces with only one side.
This animation presents the formulas to calculate the perimeter and area of shapes as well as the surface area and volume of solids.
Calculating the volume of a sphere is possible using an appropriate cylinder and cone.
The sum of the volume of the ´tetrahedrons´ gives an approximation of the volume of the sphere.
This animation demonstrates geometric rotation, a type of geometric transformation both in plane and space.
Rotating a geometric shape around a line within its geometric plane as an axis results in a solid of revolution.