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Learn about the mathematical concept of four-dimensional space (4D), which is the extension of three-dimensional space (3D) with one more dimension. Explore the history, geometry, and applications of 4D space in physics, mathematics, and philosophy.
5 ημέρες πριν · Learn about the basic concepts and properties of four-dimensional geometry, such as hyperspheres, hypercubes, and polytopes. Find formulas, examples, and references for further exploration of the fourth dimension.
14 Απρ 2023 · Learn how to visualize and imagine the fourth dimension by extruding a cube in a direction perpendicular to the third dimension. Explore the properties and characteristics of tesseracts, the 4D analogues of cubes, and how they differ from our 3D world.
26 Απρ 2017 · Learn how to create and project a 4D hypercube, a 4-dimensional analogue of a cube, using stereographic projection. Explore the mathematical and physical implications of higher-dimensional space and time with examples and resources.
The following images link to interactive models of some of the four-dimensional objects we've studied. To use the interactive versions, your browser must support WebGL, and you must have JavaScript enabled in your browser.
Explore 4D objects and their projections, slices, and volumes in this interactive website. Discover how 4D space differs from 2D and 3D space and how to visualize 4D universes.
5 Ιαν 2018 · By placing together two specially designed 2D setups, two separate teams of researchers - one in Europe and one in the US - were able to catch a glimpse of this fourth spatial dimension through what's known as the quantum Hall effect, a certain way of restricting and measuring electrons.
