Engaging all students with “impossible geometry” - eric

By lr wiest · 2010 · cited by 3 — segment of the film the fantastic world of m. c. escher (emner, 1980/2006) on impossible objects, including penrose's discussion of his impossible triangle. 7 pages
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Geometry is an area in which Australian students performed particularlypoorly on the 2007 Trends in International Mathematics and ScienceStudy (TIMSS) (Thomson, Wernert, Underwood, & Nicholas, 2008). Scoresfor Year 8 students fell significantly below the TIMSS scale average. Australianstudents thus need stronger preparation in geometry. One innovative area ofrecreational geometry that has rich potential to engage and challenge a widevariety of students is “impossible geometry.” An impossible geometric objectis a two-dimensional drawing that gives the impression of a viable three-dimensional figure, which in fact cannot exist. It is thus an optical illusionwhere the misperception requires careful analysis to detect and explain.Whereas individual parts of the figure may be possible, the object in its total-ity is not. Impossible geometry has been a subject of interest for some time.Necker discussed impossible objects in an 1832 journal article, and Penroseand Penrose particularly popular...
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