Exploring Dimensions
What do we mean when we talk about dimensions?
• The 0-dimensional point (no length, width, or height) is a shadow of a line…
• The 1-dimensional line (length or width or height) is a shadow of a square…
• The 2-dimensional square (length and width, or width and height) is a shadow of a cube…
• The 3-dimensional cube (length and width and height) is the shadow of an (unfolded) hypercube.
“Shadows of Higher Dimensions” by Paul Micarelli
Polyhedra: 3D Multifaceted forms Inside Out!
3D Cardstock Net and Model PDFs
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The Geometry of Architecture:
Even Contemporary Complex Structures Can Be Viewed
As a Collection of Smaller Simple Prisms or Curved Forms
All shapes in human design or in nature can be composed of simpler shapes that can be described.
The listing helps focus your mind on the prisms that need to be cut to assemble the model. Using descriptive language (larger than, smaller than, largest, smallest, height, width, length) will help in scaling the model.
Once you know how many parts are needed and the amount of foam board they will each require, you can begin by drawing a net (a two-dimensional plan for a three-dimensional shape) for the largest element. The next prism will be smaller than the first but scaled to the proportions of your image or vision.
While the naming of shapes can be completed in a sketchbook, journal, or by using a printed out photo, Google Drawing includes several tools that can be helpful. Two files below suggest some options, and can be saved as copies in your own Google Drive as a pattern for your own designs.
The listing helps focus your mind on the prisms that need to be cut to assemble the model. Using descriptive language (larger than, smaller than, largest, smallest, height, width, length) will help in scaling the model.
Once you know how many parts are needed and the amount of foam board they will each require, you can begin by drawing a net (a two-dimensional plan for a three-dimensional shape) for the largest element. The next prism will be smaller than the first but scaled to the proportions of your image or vision.
While the naming of shapes can be completed in a sketchbook, journal, or by using a printed out photo, Google Drawing includes several tools that can be helpful. Two files below suggest some options, and can be saved as copies in your own Google Drive as a pattern for your own designs.
Gabby C.--The Burrow--Naming the Shapes
Cora T.--Hamilton Hall--Naming the Shapes
The Kids Should See This: Tiling the Plane with Pentagons
Greece: Plato, Platonic Solids,
and "Discovering" Math
Euler's Rule
The ancient Greeks discovered and defined five regular shapes, the Platonic solids in 300 BCE. Two thousand years later, Swiss mathematician Leonhard Euler discovered and defined a simple rule:
the number of faces, plus the number of vertices (corners), equals the number of edges plus 2.
f + v = e + 2
f + v + e = 2
the number of faces, plus the number of vertices (corners), equals the number of edges plus 2.
f + v = e + 2
f + v + e = 2
4-Dimensional Geometry