Tesseract Calculator

Name: Tesseract - Geometry Calculator
Author: Jürgen Kummer

Calculations at a tesseract. This is a four-dimensional hypercube, the expansion of square (2D) and cube (3D) into a fourth dimension of space. This doesn't exist in our three-dimensional world, but can easily be calculated.
Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:

A = 24 \cdot a^{2}

V = 8 \cdot a^{3}

H = a^{4}

The edge length has a one-dimensional unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). Hypervolume has this unit to the power of four.

The physical world in which we live has three dimensions of space and one dimension of time. We are used to this and can imagine it. Mathematically, however, any whole number of dimensions is conceivable and calculable, but the human imagination is usually unable to keep up. Perhaps the easiest way is with the multidimensional extension of squares and cubes, since here every dimension is present in the same size. An n-dimensional hypercube with side length a has the hypervolume aⁿ. For the tesseract, it is n=4. Hyperdimensional objects have a hypervolume and several different dimensional surfaces with dimensions from 2 to n-1.
Four-dimensional objects were first described mathematically by the French-Italian mathematician and astronomer Joseph-Louis Lagrange in the 18th century. Albert Einstein combined the three spatial and one temporal dimensions into a four-dimensional space-time, thereby revolutionizing physics and providing a multitude of new theoretical insights and technical applications in practice, without which many things in our world today would not be understandable or functionable.

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