Generalizing curves with logo-including polygonal patterns Papert introduced the LOGO environment in which we make a curve using LOGO commands (FORWARD, ROTATE). We call this geometry as turtle geometry. This environment has influenced many researchers and designers of computers and mathematics education. But the curve that we can make using LOGO command is elementary or too difficult. Polygon and circle is elementary and making other curves is difficult. In this paper, we introduce the method of drawing some other curves mediating new command. First, we study epicycloid and hypocycloid in the historical and the physical context. And we introduce the method of making epicycloid and hypocycloid using vector addition. Next we study the polygon patterns of this curve. Finally, we extend the method for making more general curve and we improve the computer environment using this metaphor.
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References in zbMATH (referenced in 4 articles )
Showing results 1 to 4 of 4.
- Feurzeig, Wallace: Logo vignettes: early teachable moments (2013)
- Feurzeig, Wallace: Toward a culture of creativity: a personal perspective on Logo’s early years and ongoing potential (2010)
- Kim, Hwa Kyung; Song, Min Ho: Generalizing curves with LOGO -- including polygonal patterns (2010)
- Griva, Igor; Shanno, David F.; Vanderbei, Robert J.; Benson, Hande Y.: Global convergence of a primal-dual interior-point method for nonlinear programming (2008)