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Development of a spiral: from paradoxical 2 segments to infinity sided polygon It all began one day, while evaluating new exhibits for Spirals Forever, I suddenly wondered: How many sides are most spirals made of? What is the smallest number possible? What is the highest? Well (based solely on my own impression), the most common spirals are the six sided ones (hexagonal); then come the seven and eight sided spirals. On expo here we got outstanding versions by Makin's hexagonal, Kelley's heptagonal and Crook's octagonal. The highest number concept is not a scientific problem, as from math aspect it is infinity. As the number of sides grows up the individual side length becomes smaller and smaller, and towards infinity, the spiral becomes a simple circle. A midway example is the most distinctive eleven sided polygonal spiral by Gedeon Peteri. The degradation of sides is more interesting. Five sided spiral is less common, but still available, with one of the most beautiful on expo here by Kelley. The for cornered spiral began to appear as a logical paradox, as the visual rectangle is so much opposed to the spiral, but a few examples are still found, as our amazing piece by Martinez. Now the big problem was searching a three sided spiral. First was the question weather it exists at all or not. I assumed that mathematically there was no objection for triangular spiral, but alas, I could not find a single example for it. So I have no other choice but to spend a few hours playing with formulae to create the triangular core of a spiral as shown here. Now there was only the two sided spiral problem. Of course there is not a 2 sided spiral, so I had to accept a trick, that will deceive the eye. The best I could get is shown here, but if anyone can make a better deception  I will display it too. Now I had all I needed from two to infinity, and so I assembled this expo in the Lobby of Spirals Forever. Dr. Joseph Trotsky April 2000 

 

 

 