The painting gives an idea of one-dimensional, two-dimensional and three-dimensional space, talks about the fourth dimension, and shows the construction of a hypercube.
Cartoon explaining four-dimensional space through the characters of Lewis Carroll's Alice in Wonderland.
The concept of the dimension of a point.
One-dimensional space.
A straight line in one-dimensional space, in addition to zero-dimensional objects - points, contains one-dimensional segments.
A moving ball for a one-dimensional observer manifests itself only through a section.
Passing through a straight line, the ball cuts out a point, a segment, a point.
Two-dimensional space.
A plane, in addition to zero-dimensional and one-dimensional objects, contains two-dimensional figures.
And here the ball manifests itself through a section - a point, a circle, a point.
We make a two-dimensional Alice from flat figures.
Two-dimensional Alice will not get out of the circle, three-dimensional Alice will.
Three-dimensional space.
A moving ball, a plane and a changing circle cut out by the ball.
Three-dimensional Alice in a ball.
The fourth dimension.
A cartoon explaining, using the image of Alice, the manifestation of four-dimensional objects through their three-dimensional projections and sections.
The projection of a four-dimensional ball (hypersphere) will be an ordinary ball.
If a four-dimensional ball passes through three-dimensional space, it appears as an ordinary ball, the radius of which first increases and then decreases to zero.
Hypercube.
When a point moves in a straight line, a one-dimensional segment appears.
When the segment moves, we get a two-dimensional square.
A flat square sweeps out a volumetric body - a cube.
The volumetric body, moving out of three-dimensional space, generates a four-dimensional hypercube.
The image uses the image of the Cheshire cat.
Hypercube projections.
If a cube is projected onto a plane, illuminating the skeleton of the cube from a point, we get a square in a square.
By analogy, the projection of a hypercube will be a cube in a cube.
Hypercube sections.
When a hypercube passes through a straight line, its sections will be segments of varying length.
Flat sections - point, triangle, hexagon, triangle, point.
Sections of a hypercube are convex polyhedrons.
The developments of the boundaries of a square, cube, and four-dimensional cube are shown.
Formulas for describing geometric objects.
A mathematical image of a hypercube.
Using the image of Alice to explain the use of the fourth coordinate in a mathematical formula.
Images of Alice and the use of the fourth coordinate - time.
In various fields of science and technology, problems arise that lead to multidimensional space.
Images of various spaces.
Cheshire cat.
Sphinx.
Hyperball, hypercube, One-dimensional space, Two-dimensional space, Three-dimensional space, Four-dimensional space, Sections, Geometric shapes
Lewis Carroll