Higher-dimensional in the context of "Tesseract"

Play Trivia Questions online!

 or

Skip to study material about Higher-dimensional in the context of "Tesseract"
Ad spacer

⭐ Core Definition: Higher-dimensional

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.

In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. 10 dimensions are used to describe superstring theory (6D hyperspace + 4D), 11 dimensions can describe supergravity and M-theory (7D hyperspace + 4D), and the state-space of quantum mechanics is an infinite-dimensional function space.

↓ Menu

>>>PUT SHARE BUTTONS HERE<<<
In this Dossier

Higher-dimensional in the context of Point (geometry)

In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical spaces. As zero-dimensional objects, points are usually taken to be the fundamental indivisible elements comprising the space, of which one-dimensional curves, two-dimensional surfaces, and higher-dimensional objects consist.

In classical Euclidean geometry, a point is a primitive notion, defined as "that which has no part". Points and other primitive notions are not defined in terms of other concepts, but only by certain formal properties, called axioms, that they must satisfy; for example, "there is exactly one straight line that passes through two distinct points". As physical diagrams, geometric figures are made with tools such as a compass, scriber, or pen, whose pointed tip can mark a small dot or prick a small hole representing a point, or can be drawn across a surface to represent a curve.

↑ Return to Menu

Higher-dimensional in the context of Level set

In mathematics, a level set of a real-valued function f of n real variables is a set where the function takes on a given constant value c, that is:

When the number of independent variables is two, a level set is called a level curve, also known as contour line or isoline; so a level curve is the set of all real-valued solutions of an equation in two variables x1 and x2. When n = 3, a level set is called a level surface (or isosurface); so a level surface is the set of all real-valued roots of an equation in three variables x1, x2 and x3. For higher values of n, the level set is a level hypersurface, the set of all real-valued roots of an equation in n > 3 variables (a higher-dimensional hypersurface).

↑ Return to Menu
LINKED FROM (PARENTS)
← Point (geometry) ← Point (mathematics) ← Level set ← Point set
LINKS TO (CHILDREN)
Square (geometry) → Cube → Tesseract → Line segment → Square → Physics → Mathematics → Space (mathematics) → Mathematical object → Coordinates → Point (geometry) → Line (geometry) → One-dimensional space → Surface (mathematics) → Boundary (mathematics) → Cylinder (geometry) → Sphere → Two-dimensional space → Latitude → Longitude → Two-dimensional Euclidean space → Euclidean plane → Three-dimensional → Classical mechanics → Space → Time → Absolute space and time → Four-dimensional space → Electromagnetism → Spacetime → Event (relativity) → Observer (special relativity) → Minkowski space → Gravity → Pseudo-Riemannian manifold → General relativity → Superstring theory → Hyperspace → Supergravity → M-theory → Quantum mechanics → Function space →