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INTRODUCTION
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Readers of the introductions to my web sites will have read (ad nauseum some might say!) of my love of geometry, and my early training in the axiomatic method of Euclid. Although Euclid’s method was deficient by modern standards, it was argued that studying Euclidean geometry with its logical analysis and emphasis on proof and deduction gave one a good basis for logical deduction in all of mathematics and beyond. I was never sure of the validity of this argument, but that didn’t matter: it was taken as an axiom!
Later in my career I learned some computer programming, becoming mildly proficient in the use of Pascal, and able to solve various numerical problems in this way. I found some satisfaction in this approach to mathematics, and felt that the logical reasoning used in this programming probably had more transference than Euclidean axiomatics. Several years later I became interested in fractal geometry, and with the help of Bill Beaumont, embarked on the construction of fractals using a version of turtle logo. It was not just satisfying, but really exciting to construct a program and see a complex fractal design emerge as the result. Which bring us to the present. I am convinced that there is intrinsic value in being able to write a program which produces an interesting visual result. In an age of internet access and broadband, where should one turn to follow this dream? For subject matter I have chosen linkages – a mathematical concept of both geometrical and historical interest. For programming I have chosen JavaSketchPad®. This program is available for free download, is straightforward to use, and (relatively!) easy to master. If you happen to own The Geometer’s Sketchpad®, you will be able to construct the programs directly. This obviously has its uses, but rather defeats the rationale of this site! You will also need to have some webpage creation program for producing .html pages. The chapters present the linkages in chronological order. However, this does not mean that the linkages appear in increasing order of complexity. If you plan to do your own programming, Chapter 2 deals with the simplest linkage. To the best of my knowledge, there has been no infringement of copyright in producing these pages. If some unintentional infringement has occurred, pleas advise the author. I hope you enjoy this work on linkages, and the use of JavaSketchPad® to produce the interactive web applets. Paul Scott (2008) |
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