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 RT @ANI: #WATCH  Defence Minister Rajnath Singh performs 'Shastra Pooja' at Auli Military Station in Chamoli, Uttarakhand on the occasion… 16 hours ago
 https://t.co/miuxsAc3tT 16 hours ago
 Good work: deviantart.com/prehistorybyli… 18 hours ago
 Some aspects of geopolitics are simply too dangerous to state plainly in public. The discerning will get how the so… twitter.com/i/web/status/1… 18 hours ago
 Probably at some level this is the tip of the iceberg of the penetration by marUmatta & also pa~nchanetramlechCha… twitter.com/i/web/status/1… 18 hours ago
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 A catalog of attractors, repellors, cycles, and other oscillations of some common functional iterates
 The wink of the Gorgon and the twang of the Lyre
 Some poems
 The Kaumāra cycle in the Skandapurāṇa’s Śaṃkarasaṃhitā
 Some notes on the runiform “Altaic” inscriptions and the early Turk Khaghanates: Orkhon and beyond
 Vikīrṇā viṣayāḥ: India and the Rus
 Alkaios’ hymn to the Dioskouroi: Hindu parallels
 Some notes on the IndoEuropean aspects of the Anatolian tradition
 The death of Miss Lizzie Willink
 IndoEuropean expansions and iconography: revisiting the anthropomorphic stelae
 Geopolitical summary: March 2022
 Human retroviruses, sociology of science, and biographical ruminations
 Transcripts of conversations: the addiction principle:
 Phantom impressions1
 A note on Śrī, Viṣṇu and śṛṅgāra
 Are civilizational cycles the norm?
 On the rise of the mātṛkās and the goddess Cāmuṇḍā
 Huns, Uralics, and empires of the steppe
 Some observations on the LekkerkerkerZeckendorf decomposition of integers
 Subjective and objective insight
 On the passing of E.O. Wilson
 Some words on mleccha cartels
 Relationships between incircles of the “equilateral triangles in a square” system
 The Rāmāyaṇa in numbers: meters, sarga and kāṇḍa structure
 Sneha, snowstorms, the sun and the moon in enigmatic ṛks
 The strange case of the Āpastamba sprite
 Agni as the divine commander in the Veda and the Purāṇa
 The birth defects of Dhṛtarāṣṭra and Pāṇḍu and related matters
 The rise of Navyonmāda, the subversion of the Mahāmlecchas, Cīnānusāra and beyond
 Some biographical reflections on visualizing irrationals

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Pages
Categories
Search this Blog
Archives
mAnasataraMgiNI supplement
 RT @ANI: #WATCH  Defence Minister Rajnath Singh performs 'Shastra Pooja' at Auli Military Station in Chamoli, Uttarakhand on the occasion… 16 hours ago
 https://t.co/miuxsAc3tT 16 hours ago
 Good work: deviantart.com/prehistorybyli… 18 hours ago
 Some aspects of geopolitics are simply too dangerous to state plainly in public. The discerning will get how the so… twitter.com/i/web/status/1… 18 hours ago
 Probably at some level this is the tip of the iceberg of the penetration by marUmatta & also pa~nchanetramlechCha… twitter.com/i/web/status/1… 18 hours ago
Top Posts

Recent Posts
 A catalog of attractors, repellors, cycles, and other oscillations of some common functional iterates
 The wink of the Gorgon and the twang of the Lyre
 Some poems
 The Kaumāra cycle in the Skandapurāṇa’s Śaṃkarasaṃhitā
 Some notes on the runiform “Altaic” inscriptions and the early Turk Khaghanates: Orkhon and beyond
 Vikīrṇā viṣayāḥ: India and the Rus
 Alkaios’ hymn to the Dioskouroi: Hindu parallels
 Some notes on the IndoEuropean aspects of the Anatolian tradition
 The death of Miss Lizzie Willink
 IndoEuropean expansions and iconography: revisiting the anthropomorphic stelae
 Geopolitical summary: March 2022
 Human retroviruses, sociology of science, and biographical ruminations
 Transcripts of conversations: the addiction principle:
 Phantom impressions1
 A note on Śrī, Viṣṇu and śṛṅgāra
 Are civilizational cycles the norm?
 On the rise of the mātṛkās and the goddess Cāmuṇḍā
 Huns, Uralics, and empires of the steppe
 Some observations on the LekkerkerkerZeckendorf decomposition of integers
 Subjective and objective insight
 On the passing of E.O. Wilson
 Some words on mleccha cartels
 Relationships between incircles of the “equilateral triangles in a square” system
 The Rāmāyaṇa in numbers: meters, sarga and kāṇḍa structure
 Sneha, snowstorms, the sun and the moon in enigmatic ṛks
 The strange case of the Āpastamba sprite
 Agni as the divine commander in the Veda and the Purāṇa
 The birth defects of Dhṛtarāṣṭra and Pāṇḍu and related matters
 The rise of Navyonmāda, the subversion of the Mahāmlecchas, Cīnānusāra and beyond
 Some biographical reflections on visualizing irrationals

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Tag Archives: trigonometry
Johannes Germanus Regiomontanus and his rod
Even before we had become acquainted with the trigonometric sum and difference formulae or calculus are father had pointed to us that there was an optimal point at which one should stand to observe or photograph features on vertical structures, … Continue reading
A guillochelike trigonometric tangle
Coprimality, i.e., the situation where the GCD of 2 integers is 1 is one of the fundamental expressions of complexity. In that situation, two numbers can never contain the other within themselves or in multiples of them by numbers smaller … Continue reading
Posted in art, Scientific ramblings
Tagged arithmetic, curves, mathematical entity, mathematics, prime numbers, recreational geometry, spirograph, trigonometry
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The Mātrāmeru and convergence to a triangle
What is presented below will be elementary for someone with even just the mastery of secondary school mathematics. Nevertheless, even simple stuff might present points of interest to people who see beauty in such things. Consider the following question: Given … Continue reading
Posted in Scientific ramblings
Tagged fibonacci, geometry, Golden Ratio, mathematics, recreational geometry, sequence, triangles, trigonometry
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Sequences related to maps based on simple fractional functions
One of the pleasures of an unstructured youth in the precomputer era was what we called calculator games. As our father took his prized calculator with him to work we only got a little time with it in the evenings. … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, complex numbers, fibonacci, fractal, fractals, mathematics, nArAyaNa, numbers, sequence, trigonometry
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Some Nārāyaṇalike convergents and their geometric and trigonometric connections
While playing with an iterative geometric construction in our youth we discovered for ourselves a particular right triangle whose sides are in the proportion , where is the Golden Ratio. This triangle is of course famous as being the basis … Continue reading
Some notes on rational sector triangle triples
Rational points on a unit circle There are some events that happen in the course of ones life that might be considered historical or worldchanging. One such event from our lifetime is the proving of the Last Theorem of Fermat … Continue reading
The minimal triangle circumscribing a semicircle
Consider a fixed semicircle with center at and radius . Let be the isosceles triangle which circumscribes it (Figure 1). Figure 1 What will be the characteristics of the minimal form of the said triangle, i.e. triangle with minimum perimeter, … Continue reading
The Platonic culmination of Euclid and the pentagonhexagondecagon identity
Why did great sage Pāṇini compose the Aṣṭādhyāyī? There were probably multiple reasons but often you hear people say that he wanted to give a complete description of the Sanskrit language. That was probably one of his reasons but was … Continue reading
Posted in Heathen thought, Life
Tagged Geometric construction, geometry, Golden Ratio, Greek, Hindu, Plato, polygons, polyhedra, recreational geometry, religion, triangles, trigonometry
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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
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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
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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
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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
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
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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
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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
Āryabhaṭa and his sine table
Everyone and his son have written about Āryabhaṭa and his sine table. Yet we too do this because sometimes the situation arises where you have to explain things clearly to a layman who might have some education but is unfamiliar … Continue reading
Some meanderings among golden stuff2
Related stuff: Golden Ratio0 Golden Ratio1 If the golden ratio can fascinate erudite men of high IQ then what to say of simpletons like us. Hence, we shall here talk about some more trivia in this regard. The golden ratio … Continue reading
Leaves from the scrapbook
There were extensive memoirs in the form of electronic scrapbooks of Somakhya, Lootika and some members of their circle. Those in the know read the available excerpts due to matters of considerable interest being recorded in them. Other parts were … Continue reading
Posted in art, Life
Tagged chaos, Geometric construction, geometry, ghost, ghosts, LotkaVolterra, population dynamics, Story, triangles, trigonometry, trisection
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van Aubel’s theorem
The van Aubel’s theorem is a simple theorem which is comparable to the theorem attributed to the French conqueror Napoleon Bonaparte regarding triangles. It is easy to prove once you know the upāya, even as the yogins would say ānanda … Continue reading
Posted in art, Life, Scientific ramblings
Tagged Geometric construction, geometry, mathematics, philosophy, triangles, trigonometry, van Aubel
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Partitions, perforations and tilings
We are “geometric” in our thinking – perhaps, we are hence a little more Greek or the old type Arya than the later Hindu (who is more algebraic) in mentality. Long back in college we were fascinated by implicit trigonometric … Continue reading
Posted in art, Life
Tagged ancient Hindu thought, Generative Art, mathematics, trigonometry
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Idiosyncratic synesthetic experiences in some trivial trigonometric identities
Mathematical objects, despite existing in a purely abstract “Platonic” realm, have the ability (perhaps by the very virtue of their Platonic idealism) to produce synesthetic experiences. We have often wondered in our life as to why the realization or experience … Continue reading
Posted in art, Heathen thought, Life
Tagged beauty, Euler, Geometric construction, Hindu, mathematics, philosophy, Platonic ideals, trigonometry
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