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 While many H go blue in the face denying a relatively obvious thing like the Aryan invasion they often ignore the 2… twitter.com/i/web/status/1… 23 hours ago
 RT @pinakasena: I had made a thread on finding a Rāga using Kaṭapayādi Saṅkhyā, now there is also a mathematical way of identifying the Sva… 23 hours ago
 A novel way of looking at relationships between population samples modern & ancient using Manhattan distance & then… twitter.com/i/web/status/1… 23 hours ago
 RT @Gopalee67: @blog_supplement शठे शाठ्यमाचरेदिति नीति:। अत्र अहिंसाविचार:न कर्तव्य:। स्वरक्षार्थं किमपि योग्यं कार्यं करणीयमेव। अन्यथा स… 2 days ago
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Recent Posts
 Packing constants for polygonal fractal maps
 Cows, horses, sheep and goats
 Fraudulent science by Indians: some really bad news
 Leaves from the scrapbook3
 Mongolica: The Tangut empire
 Notes on the Bhadrasūkta, a hymn for felicity to the Vedic pantheon
 Liṅgakāmādisūtrāṇi
 Creating patterns through matrix expansion
 An apparition of Mordell
 A dinnertime conversation
 Newton’s cows
 A novel discrete map exhibiting chaotic behavior
 1859 CE and beyond: Some reflections
 Cricket in pictures
 The maṅgalācaraṇam of the Mānasollāsa
 The second strike
 Visualizing the Hindu divisibility test
 Fermat’s little theorem and the periods of the reciprocals of primes
 A layman’s overview of the arithmetic of encryption
 Divisionmultiplication parabolas, triplications, and quadratic residues
 A brief overview of the last campaign of Chingiz Khan and the issue of succession in the Mongol empire
 The mean hyperbola and other mean functions
 A Political roundup August 15 2018
 The geometric principles behind discrete dynamical systems based on the generalized Witch of Agnesi
 Reflections on our journey through the aliquot sums and sequences
 The ghost in the tattered Gattermann
 The hearts and the intrinsic Cassinian curve of an ellipse
 The mathematics class
 Residues of squares, sequence curiosities and parabolas galore
 A poll on peoples’ beliefs on reincarnation
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Tag Archives: trigonometry
A novel discrete map exhibiting chaotic behavior
The map proposed by R. Lozi over 40 years ago is one of the simplest two dimensional maps that exhibits chaotic behavior and generates a wide range of interesting structures. The map may be defined thus: where are real parameters. … Continue reading
Posted in Scientific ramblings
Tagged attractors, chaos, chaotic flows, dynamics, fractal, fractals, geometry, mathematics, trigonometry
The remarkable behavior of a map displaying derived from a simple model for a biological conflict
One of the simplest yet profound mathematical models for biological growth emerged sometime in the middle of the 1800s due to the work of Verhulst. It describes population growth thus: let be the population of the organism at time . … Continue reading
Posted in Scientific ramblings
Tagged biological conflict, biology, chaos, dynamics, ellipse, geometry, mathematical entity, mathematics, polygons, trigonometry
Sine rugs
Consider a square lattice with uniform vertical and horizontal spacing of a quantum . This can be represented as an array of complex numbers of the form: . For our purposes we chose . Thus the lattice comprises of all … Continue reading
Posted in art, Scientific ramblings
Tagged art, complex variable, geometry, recreational geometry, trigonometry
Trigonometric tangles3: the fractals
See also: https://manasataramgini.wordpress.com/2016/05/06/theastroidthedeltoidandthefishwithinthefish/ 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
Posted in art, Scientific ramblings
Tagged complex numbers, curves, epicycloid, fractal, fractals, geometry, hypocycloid, mathematical entity, mathematics, recreational geometry, recursion, Riemann, trigonometry, Weierstrass
Euler’s squares
On account of our fascination with the geometry of origami (albeit not wellendowed in mathematical capacity) we discovered for ourselves shortly after our father had taught us trigonometry that, We had earlier shown the origami proof for that. But it … Continue reading
Posted in Scientific ramblings
Tagged Euler, Geometric construction, geometry, Golden Ratio, mathematics, pi, recreational geometry, square, trigonometry
Trigonometric tangles2
We had earlier described our exploration of the spirograph, hypocycloids, epicycloids and related curves. In course of our study of the śaiva tantras of the kaula tradition we started thinking about a remarkable piece of imagery mentioned in them. Tantras … Continue reading
Posted in art, Heathen thought, Life, Scientific ramblings
Tagged circles, circular waves, curves, epicycloid, Generative Art, hypocycloid, mathematics, religion, trigonometry
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
Posted in art, Scientific ramblings
Tagged curves, geometry, irrational numbers, mathematical entity, mathematics, recreational geometry, trigonometry