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Symbolic Geometry, Golden Spirals, and Descartes-Geometry

Denis Monasse
Journal / Anthology

Mathematica in Education
Year: 1993
Volume: 2
Issue: 3
Page range: 3-6

Symbolic algebra has become familiar to a growing population of students and professional users but symbolic geometry is just emerging from the shade. Descartes-Geometry has been developed to cover all the domains of Euclidean geometry from graphics art to CAD, desktop publishing and, of course, education. The present package deals with 2D geometry, the 3D part being still under testing. It is written as a Mathematica library program and can be considered as an advanced language built on Mathematica graphics functions. There are specific virtues to symbolic geometry: the calculations being exact, the figures are rigorous and theorems can be proven or, at least, suggested by the constructions. Another aspect is the generalization of functional programming which can define families of figures. The example chosen here to illustrate this technique is the golden spiral which is made of arcs and circles deduced from each other by a set of given rules. Fractal geometry is one among many other fields of application which can be contemplated: wall, papers, mosaics, molecular modeling, integrated electronic circuits, etc. Step by step, we shall show how to specify the relevant geometric objects. Geometric functions will then be coded to generate the spiral.

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