# What strategies of concept creation and exploration would lead you to come up with the description of the fourth dimension that we saw?

This assignment is the third in the category of ‘Tell the Story of Concept Creation’. The Fourth Dimension is a concept that arises by looking at lower dimensions and creating an abstract idea (the fourth dimension) that is an analogy of the ways that lower dimensions behave. This assignment asks you to describe the process by which the concept of the fourth dimension is created and explored. In other words, put yourself in the position of a mathematician creating a coherent concept of the fourth dimension. What strategies of concept creation and exploration would lead you to come up with the description of the fourth dimension that we saw?Your essay should definitely include an explanation of the process you use to fill in the chart that shows the numbers of vertices, edges, 2D, 3D, and 4D faces of cubes of dimensions 0, 1, 2, 3, 4, and 5.As always, thinking through the process of how an idea could be discovered is a great way to understand the idea more deeply.Although there is no length requirement for this assignment, we anticipate that a thorough answer will require perhaps 3 pages.
VerticesEdges2D faces3Dfaces4D faces0D cube1D cube2D cube3D cube4D cube5D cube