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 Good map  illustrates some historical processes. The 2 words pur & grama>gaon are already seen in the RV & mean f… twitter.com/i/web/status/1… 13 hours ago
 RT @UnSubtleDesi: Remember this image? This is PFI members meeting members of Turkish “NGO” connected to Al Qaeda in 2018. This meeting has… 13 hours ago
 While of the different shAkhA, if there are regions of doubt one could consult the kANva text produced by svAminAth… twitter.com/i/web/status/1… 13 hours ago
 Europe is being taught what it means to be a vassal, a lesson H were administered by the former overlord of the pa~nchanetra. 14 hours ago
 indrANI from the va~Nga country of the pAla age https://t.co/XzZfNKO8vp 15 hours ago
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 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
 Turagapadādi

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September 2022 M T W T F S S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 
Pages
Categories
Search this Blog
Archives
mAnasataraMgiNI supplement
 Good map  illustrates some historical processes. The 2 words pur & grama>gaon are already seen in the RV & mean f… twitter.com/i/web/status/1… 13 hours ago
 RT @UnSubtleDesi: Remember this image? This is PFI members meeting members of Turkish “NGO” connected to Al Qaeda in 2018. This meeting has… 13 hours ago
 While of the different shAkhA, if there are regions of doubt one could consult the kANva text produced by svAminAth… twitter.com/i/web/status/1… 13 hours ago
 Europe is being taught what it means to be a vassal, a lesson H were administered by the former overlord of the pa~nchanetra. 14 hours ago
 indrANI from the va~Nga country of the pAla age https://t.co/XzZfNKO8vp 15 hours ago
Top Posts

Recent Posts
 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
 Turagapadādi

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September 2022 M T W T F S S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Category Archives: art
Some poems
Below are some poems in English by our brother. He sends us his compositions in a much more transient medium making them hard to preserve or share. Hence, we decided to anthologize those we could recover and present them here … Continue reading
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Turagapadādi
This note stems from a recent conversation with a friend, where he pointed out that the graph representing all possible positions the horse (knight) can take on the chessboard from a given starting square produces interesting graphs. It struck us … Continue reading
Generating simple radially symmetric art
Many people experience beauty in structures with bilateral, radial and rotational symmetries with or without recursion. The recursive or nested structure are the foundation of the beauty in fractal form, the generation of which has become increasingly easy for the … Continue reading
Posted in art, Life
Tagged art, art and science, Generative Art, Geometric construction, geometry
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The phantoms of the bonepipe2
Vidrum had been introduced to a synesthetic patient by a neurologist colleague. The patient’s manifestation of synesthesia left a rather profound impact on him; thus, when he had a break of an hour in his duties, wanting to explore the … Continue reading
Posted in art, Heathen thought, Life
Tagged biochemistry, chemistry, death, ghost, ghosts, pandemic, Story
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Making an illustrated Nakṣatrasūkta and finding the constellation for a point in the sky
The illustrated Nakṣatrasūkta Towards the latter phase of the Vedic age, multiple traditions independently composed sūktas that invoked the pantheon in association with their home nakṣatras as part of the śrauta Nakṣatreṣṭi or related gṛhya homas. Of these oldest and … Continue reading
Posted in art, Heathen thought, History, Scientific ramblings
Tagged astronomy, atharva veda, atharvaveda, globular clusters, history of science, nakShatras, nebula, nebulae, Rigveda, stars, Veda, vedic, Yajurveda
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Modulo rugs of 3D functions
Consider a 3D function . Now evaluate it at each point of a integer lattice grid. Compute corresponding to each point and plot it as a color defined by some palette that suits your aesthetic. The consequence is a what … Continue reading
Posted in art, Scientific ramblings
Tagged arithemetic, factorization, mathematical entity, mathematics, modulo, prime numbers, recreational geometry
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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 tale of the dolmendweller
The exams were over and the last semester of toil was all that stood between Vidrum and the dim glimmer he saw at the end of his metaphorical tunnel. He finally had some free time that he wished to savor … Continue reading
Posted in art, Heathen thought, Life
Tagged Army of Islam, communism, ghost, ghosts, Marxism, social parasitism, socialism, society, Story
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The aftermath: A polynomial equation
This is merely the tailpiece to the last tale of the strange hauntings. A reader may wonder why expend so many words on a high school problem. While the ball could have fitted into the socket, it rolled away. As … Continue reading
Posted in art, Life, Scientific ramblings
Tagged mathematics, polynomial, series sum, Story
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The blue bottle and the talent show
This story itself is haunted. The deaths Seeing Vidrum intently gaze at something on his phone with an expression of near disbelief Kalakausha asked: “Vidrum, what are you looking at? We need to be leaving shortly. We have to buy … Continue reading
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Tagged Geometric construction, geometry, geometry box, recreational geometry, Story
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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
Leaves from the scrapbook4
As described here these entries are from the scrapbook of the second of the caturbhaginī, Vrishchika. Entry 1; kāmāturā, year Siddhārthin of the first cycle: Indrasena departed for grad school last week and I am feeling a bit of loneliness … Continue reading
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Tagged aphanosaurs, mercurials, Mohammedanism, politics, rasa, Story
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Packing constants for polygonal fractal maps
Among the very first programs which we wrote in our childhood was one to generate the famous Sierpinski triangle as an attractor using the “Chaos Game” algorithm of Barnsley. A couple of years later we returned to it generalize it … Continue reading
Posted in art, Scientific ramblings
Tagged chaos, complex numbers, fractal, fractals, geometry, Golden Ratio, IFS, polygons, recreational geometry
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Creating patterns through matrix expansion
People who are seriously interested in emergent complexity and pattern formation might at some point discover matrix expansion for themselves. It is a version of string rewriting that allows one to create complex patterns. For me, the inspiration came from … Continue reading
Posted in art, Scientific ramblings
Tagged art and science, fractal, fractals, geometry, IFS, mathematics, recreational geometry
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A dinnertime conversation
A complete version of this apolog will currently not be visible to the public. Things had cooled off a bit on the political front after the assassination of the Prime Minister Pratap Simha by a massed drone attack. On the … Continue reading
The second strike
PDF version Childhood Thrice a week, starting Fridays, Lootika’s mother taught her daughters mantrasiddhānta after dinner. She had covered the praxis of the secret mantras of the Vīṇāśikhā and had moved on to relevant sections of the Jayadrathayāmala and the … Continue reading
The incredible beauty of certain Hamiltonian mappings
In our teens we studied Hamiltonian functions a little bit as part of our attempt to understand classical and quantum physics. A byproduct of it was a superficial interest in the geometry of some of the mappings arising from such … Continue reading
Posted in art, Scientific ramblings
Tagged fractal, fractals, geometry, Hamiltonian, mathematical entity, mathematics, Oscillator, physics, recreational geometry, recursion
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Triangles, Hexes and Cubes
One philosophical question which we have often ponder about is: Are numbers “real”? One way to approach this question is via figurate numbers, where numbers directly manifest as very tangible geometry. This idea has deep roots in our tradition: as … Continue reading
The SatijaKetoja system
Satija and Ketoja discovered an interesting dynamical system in course of the study of the Schrödinger equation for one electron in a two dimensional periodic lattice on a uniform magnetic ﬁeld. While this equation and its variants have several uses … Continue reading
Posted in art, Scientific ramblings
Tagged attractors, Cauchy distribution, Cauchy flights, Central Limit Theorem, chaos, fractal, fractals, geometry, Ketoja, mathematics, physics, Satija
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Some simple maps specifying strange attractors
This note may be read a continuation of: Some reminiscences of our study of chaotic maps2 While the story of the chaotic 2D attractors began with the simplelooking maps of Henon and Lozi, by the early 1990s the highpoint was … Continue reading
Posted in art, Scientific ramblings
Tagged attractors, chaos, chaotic flows, fractal, fractals, geometry, mathematics
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Citrabhānu’s cubes
The Hindus unlike their yavana cousins preferred algebra to geometry. Yet on occasions they could indulge in geometric games for demostrating proofs of algebraic relations. We see a bit of this in the Āryabhaṭa school and the great BhāskaraII, but … Continue reading
The apparition of the Scottish surgeon
On a late summer evening, at the twilight hour, Somakhya accompanied by Lootika met Vidrum outside his home. Vidrum was supposed to show Somakhya something special he had found during a visit to the limestone excavations near his ancestral village. … Continue reading
Posted in art, Life, Scientific ramblings
Tagged anthropogenic, extinctions, fiction, ghost, ghosts, history of science, Story, tortoise, turtles
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The Meru and Nārāyaṇa’s cows: Words and fractals
The fractals described herein are based on and inspired by the work of the mathematicians Rauzy, MendesFrance, Monnerot and Knuth. Some their works, especially the first of them, are dense with formalism. Here we present in simple terms the means … Continue reading
Hofstadter and Nārāyaṇa: connections across space and time
The scientistphilosopher Douglas Hofstadter presents an interesting singleseeded sequence H in his book ‘Gödel, Escher, Bach: An Eternal Golden Braid’. It is generated by the recurrence relation, where …(1) Working it out one can see that it takes the form: … Continue reading
Wisdom from a tag system
The case of the mathematician Emil Post, like that of several others, indicates how the boundary between mania and mathematics can be a thin one. Nevertheless, Post discovered some rather interesting things that were to have fundamental implications the theory … Continue reading
Posted in art, Scientific ramblings
Tagged Collatz, complex numbers, computation, fractal, fractals, mathematics, tag systems
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Median and pedal triangles and derived fractals: an introductory account
It is rather easily seen that joining the midpoints of the sides of a triangle yields four congruent triangles that in turn are similar to the original triangle (Figure 1). This figure might be used to provided a selfevident geometric … Continue reading
Posted in art, Scientific ramblings
Tagged fractal, fractals, Geometric construction, geometry, mathematics, triangles
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Means and conics
By the time one reaches high school one learns that: (i) there are four means that one might find some use of in life (I know there are more though they are hardly used) – the arithmetic mean which is … Continue reading
The square root spiral and the Gamma function: entwined analogies
The topic discussed here is something on which considerable serious mathematical literature has published by P.J Davis, W. Gautschi and others. This partly historical narration is just a personal account of our journey through the same as a nonmathematician. As … Continue reading
Journeying through the fractal slopes of mount Meru with twoseeded recursive sequences
The Hindus have been fascinated by sequences and series from the beginning of their civilizational memory recorded in the Veda. This continues down to the medieval mathematician Nārāyaṇa paṇḍita, who discovered a general formula (sāmāsika paṅkti) that can be to obtain the … Continue reading
Posted in art, Scientific ramblings
Tagged fractal, fractals, Golden Ratio, Hofstadter, mathematics, recreational geometry, recursion
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bhujākoṭikarṇanyāyaḥ koṭijyānyāyaś ca
bhujākoṭikarṇanyāyaḥ koṭijyānyāyaḥ
Posted in art, Scientific ramblings
Tagged Geometric construction, geometry, mathematics, recreational geometry
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The two squares theorem
I do not know who might have discovered this simple relationship first. I stumbled upon it while drawing figures in the notebook during a seminar. Take any two squares such that they are joined at one side and the two … Continue reading
Posted in art, Scientific ramblings
Tagged cuboid, Geometric construction, geometry, linear, mathematics, recreational geometry, square
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Constructing a regular heptagon with hyperbola and parabola
There is little doubt that Archimedes was one of the greatest yavana intellectuals. He would also figure in any list of the greatest mathematicianscientists of all times. His work on the construction of a regular heptagon has not survived the … Continue reading
Posted in art, Scientific ramblings
Tagged complex numbers, conics, Gauss, Geometric construction, geometry, Greek, heptagon, hyperbola, mathematics, parabola, polygons, Thabit ibn Kurra
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Infinite bisections required for trisection of an angle
Figure 1: Selfevident demonstration of Figure 2: Application of the same as serial bisections to trisect the angle. In the example chosen here we have . In ten steps we get to which is a pretty close, though in principle … Continue reading
Posted in art, Scientific ramblings
Tagged Geometric construction, geometry, mathematics, recreational geometry, series sum, triangles, trisection
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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
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Tagged art, complex variable, geometry, recreational geometry, trigonometry
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Doubling the cube with ellipses
The problem of doubling of the cube which emerged in the context of the doubling of the cubical altar of the great god Apollo cannot be solved using just a straightedge and a compass. It needs one to construct a … Continue reading
Posted in art, Scientific ramblings
Tagged conic sections, conics, Delian, Delos, doubling the cube, ellipse, Geometric construction, geometry, mathematics
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The magic of the devaogdoad
Classical Hindu tradition holds that the ogdoad of devas corresponding to their directions is: Indra: East; Agni: Southeast; Yama: South; Nirṛti: Southwest; Varuṇa: West; Vāyu: Northwest; Kubera: North; Īśāna: Northeast. The central position might be occupied in certain traditions by … Continue reading
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
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
Deliberations on richness and beauty: discovery of some multiparameter iterative maps
As we have explained in the earlier notes (1, 2, 3), the second major factor in our exploration of 2D strange attractors maps, IFS and other fractals was the aesthetic experience they produced. Around that time we came across a … Continue reading
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Tagged chaos, fractal, fractals, Generative Art, geometry, mathematics
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Some reminiscences of our study of chaotic maps2
Continued from part1 The second two dimensional map we studied in our early days was that of Lozi: where and are constants. It becomes immediately evident that this map is conceptually similar to the Henon map, using the absolute value … Continue reading
Posted in art, Life, Scientific ramblings
Tagged attractors, chaos, fractal, fractals, geometry, Gingerbread Man, Henon, logistic map, Lozi, mathematics, strange attractors, tent map
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Some elementary lessons from iterative fractal maps
The famous Sierpinski gasket was one of the first fractals we wrote code for when we got access to a computer. It impressed us enormously that an intricate object with selfsimilarity over all scales could be generated by a rather … Continue reading
Posted in art, Life, Scientific ramblings
Tagged biology, developmental biology, evodevo, evolution, fractal, fractals, geometry, mathematics, recreational geometry, recursion, science, temple
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Some reminiscences of our study of chaotic maps1
Starting in our teens, we began our exploration of chaotic (strange) attractors emerging from simple iterative maps, numerical solution of ordinary differential equations and other fractals inspired by the work of Benoit Mandelbrot. It led us in two directions. First, … Continue reading
Posted in art, Scientific ramblings
Tagged art, attractors, beauty, chaos, fractal, fractals, Geometric construction, geometry, Henon map, iterative systems, mathematics, recreational geometry
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Paper folding, Sundara Rao and geometrical constructions
Paper folding, which we shall hereinafter refer to as origami without further discussion on the correctness of the usage, is believed to have had a long history in Japan. Some believe that some primitive form of origami might have been … Continue reading
Posted in art, Life, Scientific ramblings
Tagged doubling cube, Geometric construction, geometry, Japan, origami, paperfolding, religion, Sundara Rao, trisection of angle
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The professor’s war
It was the end of his work week. Vidrum came to the office of Vrishchika of long tresses; she had just started her lab at the medical school. Vrishchika put on her gloves and handed Vidrum a box: “Here is … Continue reading
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Tagged espionage, fiction, nucleotidyltransferase, oxytocin, science, Story, toxins
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Some lessons we learned from 3color totalistic cellular automata
Cellular automata (CA) have attracted people’s attention to different degrees over the past several decades since the early work of pioneers like Ulam and von Neumann. Remarkably von Neumann played with his earliest versions of CA using a graph paper … Continue reading
Ramanujan’s second construction for the approximate squaring of a circle
To experience the greatness of great men one has to relive or redo some acts of theirs to the best of ones ability. In ones youth such enactments might inspire one to make a bid for greatness. Whether this happens … 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
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
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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A journey through fractal objects
Posted in art
Tagged 3D Julia, fractal, fractals, geometry, Mandelbrot, recreational geometry, recursion
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śūlapuruṣasya vicāraḥ
Somakhya’s cousin Babhru and his family was visiting him during the vacation before they were to join university. After lunch he convinced Vidrum and Sharvamanyu to come over to his house when they got the chance for he thought more … Continue reading
Posted in art, Life, Politics
Tagged history, Oswald Spengler, Spengler, Story, world history
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A golden construction
Anyone with even a small fancy for geometrical matters would have at some point in their lives played with the golden ratio (). Indeed, we too have had our share of fun and games with the golden ratio. In course … Continue reading
Posted in art, Scientific ramblings
Tagged Generative Art, Geometric construction, geometry, Golden Ratio, mathematical entity, mathematics, vectors
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Nālikas
The first week of college had ended. Vidrum was returning from an eatery with his new friend Manjukeshi after an early supper. The two of them were rather surprised by the ferocious competitiveness of their classmates. Some refused to discuss … Continue reading
The first three squareable Lunes
For the sake of some readers we shall first define a lune: A lune is a concave closed region bounded by two circular arcs respectively with radii and and distance between their centers as , where . This region looks … Continue reading
Posted in art, Life, Scientific ramblings
Tagged area, circle, circumcenter, Geometric construction, geometry, lune, mathematics, quadrature of circle, squaring a circle
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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
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Tagged Geometric construction, geometry, mathematics, philosophy, triangles, trigonometry, van Aubel
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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
Posted in art, Life, Scientific ramblings
Tagged curves, evolutes, Geometric construction, geometry, leminiscates, mathematics, ovals, pedal curves, piriform
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svabhāṣāyāṃ śāstrīyā śikṣā
As PDF navame varṣe lūtikā tasyāḥ pañcavarṣīyāyai anujāyai varolyai dravyaśāstram aśikṣayat  lūtikā ‘vadat : “priye varoli dhyānena kārṇārpaṇaṃ kuru  atha vakṣyāmy amlakṣārasiddhāntaṃ ca lavaṇīkaraṇasya prayogaṃ ca  purve kāle svastyātreyeṇa+asmadīyena dravyavidā+amlakṣārasiddhāntaḥ proktaḥ  kāle ‘smin amlakṣārasiddhānto arrheniyas ca … Continue reading
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Tagged astronomy, chemistry, education, Sanskrit, Story
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The astroid, the deltoid and the fish within the fish
As this article needed a lot of figures with some mathematical notation it is being presented as a PDF file: The astroid, the deltoid and the fish within the fish
A biographical journey from conics to ovals
As this article needed a lot of figures with some mathematical notation it is being presented as a PDF file: A biographical journey from conics to ovals This may be read a continuation of earlier notes such as: Ovals, drops, tops … Continue reading
The cardioid and the arbelos: the scimitar and the axe
The arbelos of Archimedes, an object most wondrous; it brought pleasure to us, when stalked by enemies, as the old yavana by Romans, who ended for good his days. What is the mystery of the scimitar and the axe which … Continue reading
Posted in art, Life, Scientific ramblings
Tagged cardioid, Geometric construction, geometry, limacon, Mamikon, recreational geometry, visual calculus
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Der singende Knochen: śūlapuruṣāṇāṃ śūletyādi
That afternoon Vidrum was returning with a bunch of other friends whom he had taken through a tough course of climbing at a hilly locale. As they neared a certain road, he, Sharvamanyu, Somakhya and Lootika bade good bye to … Continue reading
Posted in art, Heathen thought, History, Life
Tagged ancient Hindu thought, folklore, folktales, Germanic, Germans, Gonzenbach, Greek, Grimm, Hindu, IndoAryan, Iranian, motifs, Odin, rudra, Story, Yezidi
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The ghosts of Tulagiri
Vrishchika was taking a few days off to visit her parents’ town before proceeding with her fellowship. Lootika had nearly completed moving her lab to Somakhya’s institute. She was happy that they could finally be together for good again and … Continue reading
śūlajanakāvya: Das Riesenspielzeug
Somakhya’s and Lootika’s families were returning from a ritual at the lessknown temple of the goddess Bhuvaneśvarī. They were there to worship a mysterious yantra, which is one of the rare examples of the depiction of a curve known as … Continue reading
The autumn days
Vidrum had just finished up with his last patient for the day. Before heading out to his office one of his assistants offered him a rich halvā. He curtailed his temptation reminding himself how bad it could be for one’s … Continue reading
Posted in art
Tagged crocodiles, cultured brains, gods, psychedelics, Story, West Africa
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The social, phantasmagorical and historical journey
It was some time just before the first vacations of Somakhya and Lootika’s first year in the preuniversity college. Lootika’s family was visiting a nearby temple of the massive ape Hanūmat on a Saturday evening. In the sabhāgṛha of the … Continue reading
Posted in art, Heathen thought, History
Tagged Abrahamism, ancient Hindu thought, AntiHindu, Army of Islam, arthashAstra, Hindu, Hindu knowledge, Story
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The winding narration of deaths and counterdeaths
It is said that Śiva transforms continually into many forms for his own enjoyment; not all of those are enjoyed by the consciousness housed in a paśu *∆*∆*∆* It was the time around Dīpāvalī, an year after when Somakhya and … Continue reading
A note on the pantheon of the Indian Saura tradition
The Indian Sauramata (or the Hindu sect of the Sun) is an amalgam of two distinct layers [Footnote 1]: 1) The endogenous layer of solar deities going back to the Veda and 2) the neomorphic layer of Iranic origin which … Continue reading
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Tagged Aditya, agni, ancient Hindu thought, atharvaveda, indra, Iranian, Rigveda, Sanskrit, solar worship, vaiShNava, varuNa, Veda
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This time it is the big man’s story
Vidrum was hurrying back to his office after a quick dinner. As he did so he mentally rued the fact that every time he found his way out of one problem in life a new one came upon him. Once … Continue reading
śūlapuruṣacatvārakam3: A method for the analysis of history
Somakhya, standing beside a pillar outside his university department, glanced at his watch with a tinge of irritation as he waited for Lootika to show up. She was to bring her sister Vrishchika from the medical school, which was some … Continue reading
Posted in art, History, Life
Tagged ancient Hindu thought, AntiHindu, AntiIndia, Darwin, Geopolitics, Germans, history, homology, India, Nietzsche, philosophy, Spengler, Story
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The ponderous tale of the tombstones
“Since you are recording the diverse Vaidrumas would you record the tombstone variation? While other matters like the sloths of South America, the megalithic culture of India, cave paintings, or even WW2 might be more interesting to the occasional reader … Continue reading
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Tagged Abrahamism, ancient Hindu thought, AntiHindu, AntiIndia, bhairava, China, English tyranny, Hindu, Hindu ritual, history, Story
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upakathā of previous: śūlapuruṣacatvārakam2
upakathā of previous: śūlapuruṣacatvārakam1 It was a Saturday afternoon. The caturbhaginīs had returned from their weekly visit to the museum library and were in a huddle at their home. Lootika was seated on the floor and was classifying and labeling … Continue reading
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Tagged ancient Hindu thought, comparative philosophy, Darwin, human existence, mahAbharata, Nietzsche, Schopenhauer, Story
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upakathā of previous: śūlapuruṣacatvārakam
It was a bright spring day, when the vaṭakinī mahotsava was being celebrated. Several families from the town were arriving early in the morning at a shrine, which contained a gigantic image of the terrible ape Hanūmat. Even as Somakhya … Continue reading
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Tagged ancient Hindu thought, Gauss, Nietzsche, philosophy, Schopenhauer, science, Spengler, Story
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The dream motif
Vidrum was nearing the road to his house. Instinctively, he felt his backpack and found it to be unzipped. Then to his utter disappointment he found that his box containing geometric instruments was missing. Anxious to get it back, he … Continue reading
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Tagged ancient Hindu thought, Army of Islam, beetles, staphylinids, Story, tantras
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The doctor and the speech at the rightwing thinktank
It was a late Friday afternoon and Vidrum had returned home early from the hospital. He spent some time in his garden making a ball from the paste of raintree pods, a messy but immensely meditative activity, which his friend … Continue reading
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Tagged Abrahamism, ancient Hindu thought, AntiHindu, AntiIndia, Army of Islam, arthashAstra, brahmana, Story
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Polygonal recursion
Also see this
The caves
The exam to qualify for preuniversity college was just over and a long vacation lay ahead. Vidrum was drained by the huge mental effort he had put into the exams to earn a seat at a respectable college. It was … Continue reading
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Tagged Abrahamism, AntiHindu, AntiIndia, ants, butterflies, flies, ghost, planchette, social parasitism, Story
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Some trivia on equilateral triangles and the like
One may ask why one needs to revisit elementary geometry that was usually studied at secondary school. The simple answer is it is a good recreation. But it is not like any recreation, because it also opens the doors to … Continue reading
Posted in art, Life, Scientific ramblings
Tagged centroid, circumcenter, conics, Euler line, incenter, Kiepert hyperbola, Nagel line, Nagel point, Napoleon, ninepoint circle, orthocenter, Spieker point, triangles
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The ditty of the desert road
He who eats once is a tyāgin; He who eats twice is a yogin; He who eats thrice is a bhogin; And he who eats four times a day is verily destined to be a rogin! Some find rest by … Continue reading
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Battle of the agents
As PDF It was the last day of school and the exams were to begin at the start of the next week. Following their parents stern instructions, Jhilleeka and Varoli decided not hangout after school and were returning home on … Continue reading
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Tagged ancient Hindu thought, fungi, land snails, shiva, skanda, Story
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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
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Tagged ancient Hindu thought, Generative Art, mathematics, trigonometry
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The Mandeldiamond: crystals emerge from an amorphous background
A closer look at realms within this “Terra Mysterium” Crystals by the shoreline: Crystals in the crevice – realm of craters:
The dance of the bhairava
bhairava on a cadaver from Nepal netrAku~nchanasAraNakramakR^itapravyaktanaktaM dino dikchakrAntavisarpisallarisaTAbhArAvaruddhAmbaraH  hastanyastakapAlakandaradarImuktAbhradhArAH pibann unmuktadhvanibhinnakarNakuharaH kravyAd ayaM nR^ityati  netra= eye; Aku~nchana= closing; sAraNa= opening; krama= periodic; kR^ita= act; pravyakta= manifest; naktaM= night; dinaH= day; dik= direction; chakra= circle; anta= ends; [dikchakrAnta= … Continue reading
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Tagged bhairava, Hindu, poetry, saiva, sanAtanadharma, Sanskrit, shaiva
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Some sketches of Indian wild life in vidyAkara’s anthology
sAndrasthUlanaloparodhaviShamAH shakyAvatArAH puras toyottIrNanivR^ittanakrajaTharakShuNNasthalIvAlukAH  vyaktavyAghrapadA~Nkapa~NktinichitonmudrArdrapa~NkodarAH saMtrAsaM janayanti ku~njasaritaH kAchAbhanIlodakAH  sAndra: thick; sthUla: large; nala: reed; uparodha: barrier; viShamAH: rough; shakya: possible; avatArAH: descents; puraH: first; toya: water; uttIrNa: descended; nivR^itta: climbed back; nakra: crocodile; jaThara: belly; kShuNNa: roughed … Continue reading
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Tagged bees, boar, crocodiles, dove, jackal, kavI, kAvya, naturalist, poetry, tiger, wildlife
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parjanya
Posted in art, Heathen thought
Tagged cloud, fractal, Generative Art, mantra, parjanya, Rigveda, vedic
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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
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Tagged beauty, Euler, Geometric construction, Hindu, mathematics, philosophy, Platonic ideals, trigonometry
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The cairn beyond the crag
It was the an early Indian summer morning. The type that makes one rise rapidly from bed rather than remain tucked in like the mornings in the cold northern lands. Vidrum had arisen from his bed and briskly jogged up … Continue reading
The verse of the sword
chitrabandhas are widely represented in classical works on kAvya. The bandhas of the form of the sword find mention in agnipurANa, the kAvyAlaMkAra of rudraTa and the praise of chaNDI by the other Kashmirian Anandavardhana. Swordshaped yantras comparable to the … Continue reading
Posted in art, Heathen thought, Scientific ramblings
Tagged chitrabandha, complementarity, kAvya, poetry, riboswitches, RNA, sword, umA
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The box
◊◊◊◊◊◊ Somakhya and Lootika raced up the metal rungs of the tall ladder which led to the bracket atop which sat the great water tank. There, ensconced from the spying eyes they did not know how much time passed in … Continue reading
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Tagged cemetery, fibrodysplasia ossificans progressiva, geometry box, ghosts, gravestone, mystery, Story
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