Title: The Hidden Art in a Dynamic Geometry Software Program
Abstract: The article demonstrates the mathematics and art that is involved in the construction of some fractal geometry objects using the Geometer’s Sketchpad. Introduction The Geometer’s Sketchpad is a dynamic geometry software program, which has been developed solely for mathematics educational purposes. Nevertheless, we may use some of its functions to explore the realm of visual art. This software program is based on the rules of geometric constructions using compass and straightedge. A recent development in this software utility is the capability of creating some fractal geometry figures using the iteration function. An old fractal geometry object is the Sierpinski Gasket that can be created in Sketchpad. In this article we briefly show how we can make a Sierpinski Gasket in Sketchpad, and then we use the technique to create many new and pleasing images. Constructing a Sierpinski Gasket Using Sketchpad We construct the equilateral triangle Δ and its interior in a way that the third vertex C is constructed based on the other two given points of A and B. We then construct the midpoints of its sides, as is presented in Figure 1.a. Now we want to iterate on ABC A and B . For this, we select A and B in order and click on “Iterate” on the Transform menu. Now in the dialog box we select A as its own image and select as the image of D B . With this action, we create a self-similar triangle with the scale factor of onehalf to be placed on the lower left part of our original triangle (Figure 1.b). To complete the gasket we should add two new mappings by choosing A and B again and clicking on “Structure” and choosing Add New Map. Then we make similar triangles on the top and on the right side (Figure c). (a) (b) (c) (d) Figure 1
Publication Year: 2008
Publication Date: 2008-01-01
Language: en
Type: article
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