by
Emily Englehardt.
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The two weeks of introduction are (mostly) done. Now you choose something to do. The sections below give you an idea of possibilities. I am often just as happy if you create a topic of your own.
First choose what you want to draw. Discrete objects such as the Platonic solids or hypersolids. Continuous functions such as a Møbius strip or Klein bottle. A good way to pursue it is to create shapes on the computer and try to draw them. Look at Justin's stuff on the web.
Remember that the goal of drawing in this class is to help you see.
| Drawing Drawing helps visualization. Choose what you want to visualize and draw that. Steve will have suggestions. A good way to proceed is to create a shape in Zometools or the computer and then draw it from various angles. Read Michael's "Beyond 3D" and Justin's drawing turorials. |
Building Zome tools are exquisitly created to create 3D and 4D objects, but feel free to use paper or pipecleaners as well. Unusual object to create: the Caesar and Szlazzi polyhedra. |
| GSP Continue the Paideia tradition of exploring 4D in sketchpad. The deal here is to begin all structures with a cube or hypercube. |
Relativity I am generally reluctant to allow this but the interest of some class members has persuaded me. The problem is that there are few ineresting shapes (the cone being the only one) and the load of required physics knowledge is great, so that this is mostly a studying option. Begin by learning what a light cone is in many contexts. |
| Graphing Calculator This program is as good with continuos objects as Sketchpad is with discrete ones. Begin by looking at the examples. You cannot spend too much time rotating the hypercube and the Klein bottle. First challange, rotate the hypercube to its octagonal aspect. Rotate the Klein bottle to the traditional view as shown in the model in my room. |
Shadowing and Slicing Once you have built a figure, look at its shadows. This is important because you cannot create a 4D object without perspective. All you can create is the shadow in 3D of a 4D object, so understanding shadows is helpful. Slicing can be seen on the links to the left. |
