Is Pi different in non-Euclidean space?
Yes. π is a mathematical constant usually defined as the ratio of the circumference of a circle to its diameter in Euclidean geometry. In general relativity, space and spacetime are non-Euclidean geometries. The ratio of the circumference to diameter of a circle in non-Euclidean geometry can be more or less than π.
How the area of sphere is 4 pi r 2?
The Greek mathematician Archimedes discovered that the surface area of a sphere is the same as the lateral surface area of a cylinder having the same radius as the sphere and a height the length of the diameter of the sphere. Lateral Surface Area of the Cylinder =2πr(2r)=4πr2 . …
How many edges does a sphere have?
Edges. An edge is where two faces meet. For example a cube has 12 edges, a cylinder has two and a sphere has none.
What is the surface and volume of the sphere in hyperbolic form?
I was trying to find surface and volume of sphere in spherical space (considered as a cap of Euclidean 4D hypersphere), and eventually obtained formulas that seem to work: 2 π ( 1 − cos ( 2 r) / 2) for volume. Considering the analogy between formula for area of circle and for surface of sphere, the hyperbolic formulas should be 2 π ( cosh
Is the radius of a hyperbolic n-sphere is isometric to Euclidean radius?
Consequently, in hyperbolic ( n + 1) -space an n -sphere of radius r is isometric to a Euclidean n -sphere of Euclidean radius R sinh ( 2 r R) − 2 r).
What is the volume of a sphere with radius r?
A sphere with radius r has a volume of 34πr3 and a surface area of 4πr2. A sphere has several interesting properties, one of which is that, of all shapes with the same surface area, the sphere has the largest volume.
What is the surface area of a sphere equal to?
We established that the surface area of a sphere is equal to the surface area of the cylinder that circumscribes it, so …. Establishing the Surface area equation, is the first stage of establising the Volume of a Sphere which makes for some very interesting reading also!