thethinkingatom

Dimensions- 4D and 5D figures

“Are there 4d and 5d figures?”

In our surrounding we usually see 3d figures. We usually draw 2d figures. A line is 1d and a dot is 0d, but are there 4d and a 5d figures?

First, a dimension is a measurable extent of a specific kind, such as length, width, height, or depth. More broadly, it refers to an aspect, feature, or the overall size and scope of something. There are many types of dimensions. Some of which are:

0d: This is the first dimension. It does not have any such properties and is just a simple dot. It does not have any direction of measurement. A dot is the origin of all geometry.

A dot- The only type of 0d figure

1d: A 1d figure has only one direction of measurement, length. It is a line which can be drawn in any direction. It lacks width and depth. Because it exists along a single axis, the exact location of any point on a 1D figure can be identified using just one coordinate, much like reading a standard number line.

A line- The only 1d figure

2d: A 2d figure has length and width. They are used in simple drawings. They are flat closed figures called as polygons. As they have no depth or volume, they are measured by their area and perimeter. Examples of 2d figures are squares, triangles, circles nonagons etc. The least number of sides a 2d figure can have are 3. They can also have curved surfaces.

A list of 2d figures

3d: Three-dimensional (3D) figures are solid shapes that have three measurements: length, width, and height. Unlike flat 2D shapes, 3D figures take up physical space and volume. They are the most common type of figures that we see all around us. Examples of 3d figures are a cube, cylinder, sphere, pyramid, cone etc.

A 3d shape- Cube

4d:A 4-dimensional figure, or 4-polytope, is a geometric object extending into a fourth spatial dimension, perpendicular to length, width, and depth. It involves the aspect of time with other 3d figures embedded into another three dimensional figure of the same type. Time is embedded as a continuous coordinate axis that is mathematically unified with the three dimensions of space. Rather than seeing a static object, a 4D figure treats time as an axis of extension, tracing out the complete history of a 3D object as a singular, timeless 4D shape. An example of a 4d figure is a tesseract or also called as a hypercube.

Images of a tesseract/ hypercube

5d: A five-dimensional figure is a figure that has five independent dimensions. In 5D Euclidean geometry, complex figures are called polytopes. An example of a 5-polytope figure is a Penteract. Like a 4D figure a 5d figure includes the concept of time and multiple 4d figures. A Penteract is created by taking a 4D cube (a tesseract) and duplicating it, then connecting all the corresponding vertices together.