Tag Archives: curves

Trigonometric tangles-3: the fractals

See also: https://manasataramgini.wordpress.com/2016/05/06/the-astroid-the-deltoid-and-the-fish-within-the-fish/ This exploration began in days of youth shortly after we learned about complex numbers. It culminated only much later in adulthood when we discovered for ourselves a class of fractal curves related to a celebrated curve discovered … Continue reading

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Trigonometric tangles-2

We had earlier described our exploration of the spirograph, hypocycloids, epicycloids and related curves. In course of our study of the śaiva tantra-s of the kaula tradition we started thinking about a remarkable piece of imagery mentioned in them. Tantra-s … Continue reading

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Trigonometric tangles

Let us define a define the trigonometric tangle as the following parametric function: where can be a rational number or an irrational number. and are any real number. If is a rational number and then we get a tangle petals … Continue reading

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Knotting a string: line, parabola, conchoid and knot

The basic construction In course of studying various methods of constructing conics we stumbled upon a means of using the relationship between uniform circular motion (UCM) and simple harmonic motion (SHM) to construct four distinct loci with common procedure. They … Continue reading

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Ovals, drops, tops, eights, pears and the like

Ovals, drops, tops, eights, pears and the like This piece may be seen as a continuation of the earlier one on our journey through the world of ovals. As it needed a lot of figures and some mathematical notation it … Continue reading

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