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Learn about the mathematical concept of four-dimensional space (4D), its history, geometry, and applications in physics and mathematics. Explore the visualization methods, examples, and properties of 4D objects such as the tesseract and the Minkowski space.
Minkowski space is a mathematical description of spacetime in special relativity, combining space and time into a four-dimensional model. It has a non-Euclidean metric, a Poincaré group of transformations, and a spacetime interval that is independent of frame of reference.
Spacetime is a four-dimensional continuum that fuses the three dimensions of space and the one dimension of time. It is a fundamental concept in relativity, where spacetime is curved by mass and energy, and different observers perceive events differently.
Learn about the geometry and group structure of rotations in four-dimensional Euclidean space, denoted by SO (4). Find out the types, properties and examples of simple, double and isoclinic rotations, and their relation to quaternions.
Hermann Minkowski was a mathematician who created the geometry of numbers and Minkowski space, and influenced the theory of relativity. He taught at universities in Germany, Poland, and Switzerland, and was a friend and colleague of David Hilbert and Albert Einstein.
A spinor is a complex vector that transforms differently depending on the path of rotation in Euclidean or Minkowski space. Spinors are used to describe the intrinsic angular momentum, or spin, of subatomic particles.
The metric tensor is the fundamental object of study in general relativity, capturing the geometric and causal structure of spacetime. The flat space metric (or Minkowski metric) is the metric used in special relativity and has a diagonal matrix with one negative and three positive eigenvalues.
Euclidean space is the fundamental space of geometry, which can be defined as a vector space with an inner product. Learn about the history, axioms, and properties of Euclidean spaces of any dimension, and how they relate to physical space and geometry.
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