The Fourth Dimension
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Lesson Summary:
In this lesson, Ludwig Schlafli, a 19th century mathematician, discusses objects in the fourth dimension and introduces a series of 4-dimensional polyhedra. He explains how a point in each dimension is described by a certain amount of numbers, and proceeds to create 4-dimensional objects by analogy to 2-dimensional and 3-dimensional shapes. Schlafli shows how these shapes can be projected onto our 3-dimensional space to see their shadows and highlights some of his most impressive discoveries, including the 120 cell and the 600 cell, which have 120 and 600 faces respectively.
Lesson Description:
19th century mathematician Ludwig Schlafli discusses objects in the fourth dimension including a series of 4-dimensional polyhedra.
Questions answered by this video:
- What do 4-dimensional shapes look like?
- What is the 4th dimension?
- Who is Ludwig Schlafli?
- How can you visualize the fourth dimension?
- What is a simplex?
- What is a hypercube?
- What do a 24-cell, 120-cell and 600-cell look like?
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Staff Review
The speaker of this video works up to the fourth dimension by starting with a 1-dimensional line on a chalkboard. He then moves to a two dimensional coordinate plane. Still working on a chalkboard, the speaker makes 3-dimensional coordinate axes. Finally, a four-dimensional model is discussed. Points and lines are used to present the fourth dimension by analogy, and some 4-dimensional objects are shown and discussed in depth. -
