Mathematics and Society - OS X Lion Server

Background for Student Page:(Combinations of motions to compose music or designs is an interesting and challengingactivity.Here is a chance to discuss the "glide reflection" in geometry. This is a combinationof a translation and a reflection. Have students try this with a variety of shapes.First translate the figure, then reflect the image you get from the translation.Example:Experiment with the combining of other motions.it along a vertical axis. Rotate it 90 0 and reflectoriginal shape. If it is not identical, what motionSelect a geometric shape. Reflectit again. Compare the result to theor motions would make it so?Try various combinations with different shapes to find a specific set of combinationsthat will always give you your original figure back in the same spot.(Extensions:Those students interested in writing music could do so in several ways: Start with aseries of melodic notes, add measures by translating, reflecting, rotating, or combiningthe motions in a set pattern. One pattern could be established by throwing dice.The TWelve Tone Method givesan introduction to Schoenberg's method of composition that uses ideas similar to geometricmotions.Another extension of motions is tolook at the art work of M. C. Escher.If any of his books or poster printsare available, show them to students asexamples of the different motions. Seeif they can pick out the motion.Students might also be able toidentify different usage of these motionsin a marching band.(298