Can there be negative dimensions?

Can there be negative dimensions?

Dimension of a (finite dimensional) vector space is defined as the cardinality of a basis for the vector space. Since the cardinality cannot be negative, negative dimension for vector spaces is meaningless.

What is the dimension of a sphere?

Mathematicians often call the circle the 1-dimensional sphere, or S1. It’s defined to be the set of points in the plane that lie exactly 1 unit away from a central point, (0,0), or the origin. (To be more careful, this is the unit circle.

Can you have fractional dimensions?

A point has dimension 0, a line has dimension 1, and a plane has dimension 2. Well it is at most 1-dimensional, because one coordinate would certainly specify where a point is. However, you can get away with “less”, because the object is self-similar.

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What is a 5 dimensional sphere?

Hypersphere. A hypersphere in 5-space (also called a 4-sphere due to its surface being 4-dimensional) consists of the set of all points in 5-space at a fixed distance r from a central point P.

What do you call a 4 dimensional sphere?

The mathematical objects that live on the sphere in four dimensional space — the hypersphere — are both beautiful and interesting. The four dimensional sphere is a unique object, with properties both similar to and surprisingly different from those of our ordinary sphere.

What are the characteristics of sphere?

Important Facts: 1 A sphere is a symmetrical object 2 All the surface points of sphere are at equidistant from center 3 A sphere has only curved surface, no flat surface, no edges and no vertices.

What is the center of a sphere?

A sphere is three dimensional, geometrical shape, that has all its surface points equidistant from a common point. The distance between surface and the common point is the radius and the common point is called center of sphere.

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What does the -R in the radius of a sphere mean?

The -R seems “unnatural” at first, but in reality it is no trouble. It is not suggesting that the radius, the distance from the origin to the surface of the sphere is some how a negative quantity. More sharing options…

How do you draw a 4d-sphere?

To draw our 4D-sphere we need to depict a number of 3D-spheres as they change in time so that their 3D-points ( x,y,z) along with time t satisfy the previous equation. What could the radius of those 3D-spheres be, as a function of time?