Paper Folding[折纸](PPT-38).ppt

How is the circle an ellipse? When the focal point F becomes the center of the circle, we have a circle that is constructed. Hyperbola: Definition Hyperbola: the locus of all points P in the plane the difference of whose distances r1=F1*P and r2=F2*P from two fixed points the foci F1 and F2 separated by a distance of 2c. Weisstein, Eric W. Hyperbola. From MathWorld--A Wolfram Web Resource. /Hyperbola.html GSP Construction Hyperbola Animation Equation of a hyperbola Animation Folding the hyperbola Construct a circle on a clean sheet of wax paper. Construct a fixed point F outside the circle. Fold points on the circle onto F, making at least 50 folds Points to ponder: the hyperbola How does the hyperbola relate to the ellipse? How do you relate the construction to the locus definition? How can you get to the equation of the ellipse it is not conveniently placed in the plane? References Origami. (2008, December 4, 2008). Retrieved December 7, 2008, from /wiki/Origami Anderson, E. M. (1999, February 13, 2004). Origami history. Retrieved December 7, 2008, from /history/ Bogomolny, A. (1996). Paper folding geometry. Retrieved December 7, 2008, from /pythagoras/PaperFolding/index.shtml Demaine, E. (2004). Retrieved December 7, 2008, from /6.885/fall04/ Demine, E., Benbernou, N. (2007). Geometric folding algorithms: Linkages, origami, polyhedra. Retrieved December 7, 2008, from /6.885/fall07/ Fuchs, D., Tabachnikov, S. (1999). More on paperfolding. The American Mathematical Monthly, 106(1), 9. Hatfield, L. L. Fold, plot, simulate, do algebra: Using technology to help students understand the parabola. Unpublished Prepublication draft journal article. University of Georgia. Hatfield, L. L. ConicsTE.gsp. Unpublished Geometers Sketchpad File. University of Georgia. Jeremy, C. a. (1999). History of Origami. Retrieved December 12, 2008, from /5402/history.html 01-1a References Joyce, D. E. (1997). Euclids Elements. Retrieved December 7, 2008, from