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mAnasataraMgiNI supplement
 RT @Paracelsus1092: There's a distinct possibility that Late Neolithic societies had a caste system, with those of higher huntergatherer/W… 1 hour ago
 chikkA and sundarabikShu seem to be shoring up the emperor of the middle kingdom against his rebels. 2 hours ago
 Lol seems to be taking a leaf off de Nobili's "veda". 13 hours ago
 nature.com/articles/s4200…\\ A rather remarkable study. The authors propose that infection by the apicomplexan parasit… twitter.com/i/web/status/1… 16 hours ago
 RT @DavidEvans_ROM: Happy #FossilFriday— here’s the beautifully preserved skull of the strange archosauriform Vancleavea from the Coelophys… 17 hours ago
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Recent Posts
 Cārucitrābhisambodhi
 RV 10.78
 The turning of the yugacakra
 A sampler of Ramanujan’s elementary results and their manifold ramifications
 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

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Pages
Categories
Search this Blog
Archives
mAnasataraMgiNI supplement
 RT @Paracelsus1092: There's a distinct possibility that Late Neolithic societies had a caste system, with those of higher huntergatherer/W… 1 hour ago
 chikkA and sundarabikShu seem to be shoring up the emperor of the middle kingdom against his rebels. 2 hours ago
 Lol seems to be taking a leaf off de Nobili's "veda". 13 hours ago
 nature.com/articles/s4200…\\ A rather remarkable study. The authors propose that infection by the apicomplexan parasit… twitter.com/i/web/status/1… 16 hours ago
 RT @DavidEvans_ROM: Happy #FossilFriday— here’s the beautifully preserved skull of the strange archosauriform Vancleavea from the Coelophys… 17 hours ago
Top Posts

Recent Posts
 Cārucitrābhisambodhi
 RV 10.78
 The turning of the yugacakra
 A sampler of Ramanujan’s elementary results and their manifold ramifications
 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

Join 696 other followers
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Tag Archives: conic sections
The shape of dinosaur eggs
Readers of these pages will know that we have a special interest in the geometry of ovals. One of the longstanding problems in this regard is: what is the curve that best describes the shape of a dinosaurian egg? While … Continue reading
Conic conquests: biographical and historical
PDF file of same article Studying mathematics with our father was not exactly an easygoing experience; nevertheless, it was the source of many a spark that inspired fruitful explorations and lifelessons. We recount one such thread here, and reflect on … Continue reading
Discovering bronze in the characteristic ellipse of right triangles
The arithmetic mean square of a right triangle An entire family of right triangles that includes all the different forms of right triangles defined in terms of the proportion of their legs can be obtained by setting their altitude to … Continue reading
Posted in Scientific ramblings
Tagged Bronze ratio, conic sections, conics, ellipse, Golden Ratio, mathematical entity, mathematics, right triangles, sequence, square, square root
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The mean hyperbola and other mean functions
Let be two numbers such that, We use to construct a specific rectangular hyperbola using one of the following methods: MethodI (Figure 1: this is based on an approach we described earlier) Figure 1 1) Mark point , which will … Continue reading
The hearts and the intrinsic Cassinian curve of an ellipse
Introduction This investigation began with our exploration of pedal curves during the vacation following our university entrance exams in the days of our youth. It led to us discovering for ourselves certain interesting heartshaped curves, which are distinct from the … Continue reading
Posted in Scientific ramblings
Tagged circle, conic sections, conics, curves, ellipse, Geometric construction, geometry, heartcurve, hyperbola, ovals, parabola, recreational geometry
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The quotient triangle, the parabolahyperbola sequence, the remainder triangle and perfect numbers
The quotient triangle Consider a positive integer . Then for all do the floor operation . Say , we get , a sequence of quotients of the division . If we do this for all we get the quotient triangular … Continue reading
Posted in Scientific ramblings
Tagged composite numbers, conic sections, conics, division, geometry, mathematics, Nicomachus, pi, prime numbers, Ramanujan
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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
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
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 Apollonian parabola
Some say that Archimedes and Apollonius of Perga (modern Murtina in Turkey; the center of the great yavana temple of the goddess Artemis in the days of Apollonius) were the two great yavanas who might have rivaled Karl Gauss or … Continue reading
Posted in History, Scientific ramblings
Tagged Apollonius, conic sections, conics, Geometric construction, geometry, history, mathematics, parabola
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A personal discursion on conic sections
The brothers Menaechmus and Dinostratus, as per the last great yavana sage Proclus, were associates of the Plato, who made some of the most profound discoveries in the yavana knowledge systems. Indeed, their discoveries might be considered one of the … Continue reading
Posted in art, Heathen thought, Life
Tagged Altar, Apollo, conic sections, Delian, Delos, geometry, parabola, Plato
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Fancies of the parabola and hyperbola
Many revolutionsofthesun ago we were seeking a device that could construct a parabola. We made a discovery in this connection that is exceedingly elementary Euclid for mathematicians, but for us it was an insightgiving philosophical revelation. A parabola can be … Continue reading
Posted in Life, Scientific ramblings
Tagged conic sections, conics, Geometric construction, geometry, hyperbola, parabola, recreational geometry
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