Where can I find some hands-on activities for my Applied Geometry classes? I want to do more activities with them that allow us to get out of the classroom. However, I want to use activities that use only inexpensive equipment because I usually buy the equipment myself. Thank you for your help.
From : Jenny, Applied Geometry teacherHi Jenny,
I can see wanting them 'out of their seats' but don't see 'out of the classroom' as critical (unless getting to a computer lab moves out of the classroom).
I have a wide variety of activities which I use, but this around either my university classroom OR around research/explorations.
Work with polydron, origami and mirrors (and MIRAs) - on symmetry. The CORE of modern geoemtry is in transformations and many of these are based on reflections and products of reflections.
These COULD include looking a molecules (models made from kits for chemists) and seeing which ones have mirrors, which ones have 'two forms' (stereo isomers) and which do NOT. Turns out this is something IMPORTANT in university Chemistry which students are ill prepared for. [Did you know that Caraway flavor and Spearmint flavour are the SAME MOLECULE - just stereo isomers! There is an even more scary story about the two stereo isomer forms of the drug Thalidamide!] This can be started with 2-D but is best done in 3-D - where we live (and die). Turns out that what students learn in schools can make them WORSE at doing 3-D symmetry as they pass from grade 7 to 9 to 11!
I work on the rigidity of frameworks. There are lots of examples one can do. At heart, STATICS is really about PROJECTIVE GEOMETRY. This can be explored with different media and constructions, including 'weaving popsicle sticks' to see which patterns stay in equilibrium and which 'fly apart' when you take your hands off. There is a LOT of geometry buried in these, - but it is projective geometry (three points on a line, three lines through a point).
Origami is great. Does not sound very 'applied' but there is a group of people in computer science working on 'computational origami'. Which 'folded shapes' can be unfolded? Sounds abstract - but think about folding and unfolding proteins (and I do) and it suddenly is more applied.
Here is something I saw from a teacher in Japan.
Take a triangular piece of cardboard. Support it underneath on a stand (a paper cup). Pour salt, or sand, over it. The sand runs off the edges and, in a while, there are 'ridges' in the sand on the triangle. What ARE those ridges as you look down on the triangle? They are the angle bisectors. Do the ridges all meet in a point? Yes.
What if we start with a square, a parallelogram, a general quad?
Now take a larger piece of carborad with three equal size holes in it (the 'vertices' of a triangle). Pour sand or salt over it. Again, after a while the sand creates some ridges. What are the ridges now? Why? (They are the right bisectors of the sides!).
What if we start with four holes? Which patterns are possible?
If you started with ENOUGHT scattered holes on the cardboard, your create something known as the Voronoi Diagram. Sounds abstract? It is used for everthing from deciding voting districts for polling booths to describing features in CAD-CAM. The 3-D version of this plays a BIG role in crystalography.
Try to model the plane patterns in something like Geometer's Sketchpad. There is a small free ware program called Voronoi I think I got from the Geometry Center a few years ago (for the Mac). Easy to use, plays out some important and fun concepts.Walter Whiteley
Mathematics and Statistics
Grad programs in Math and Stats, Computer Science, and Education,