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mAnasataraMgiNI supplement
 A point to note: iShTaka has an Iranic cognate &, as we discussed before, even a Tocharian one. However, it atteste… twitter.com/i/web/status/1… 9 hours ago
 The match between the teacher and student is a critical issue. What guNas are considered great in a student might… twitter.com/i/web/status/1… 10 hours ago
 Rare objects of beauty that bring pleasure to their enjoyer are sought by many but not gained by most, leading to s… twitter.com/i/web/status/1… 10 hours ago
 RT @bharadvajatmaja: Kevin Turner lived amongst the Buryat Mongols, learnt from them & became a shaman himself. He recalls his experience… 11 hours ago
 n!+1 is prime for n=1, 2, 3, 11 I don't know of any n after that which yields a prime. 1 day 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

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Pages
Categories
Search this Blog
Archives
mAnasataraMgiNI supplement
 A point to note: iShTaka has an Iranic cognate &, as we discussed before, even a Tocharian one. However, it atteste… twitter.com/i/web/status/1… 9 hours ago
 The match between the teacher and student is a critical issue. What guNas are considered great in a student might… twitter.com/i/web/status/1… 10 hours ago
 Rare objects of beauty that bring pleasure to their enjoyer are sought by many but not gained by most, leading to s… twitter.com/i/web/status/1… 10 hours ago
 RT @bharadvajatmaja: Kevin Turner lived amongst the Buryat Mongols, learnt from them & became a shaman himself. He recalls his experience… 11 hours ago
 n!+1 is prime for n=1, 2, 3, 11 I don't know of any n after that which yields a prime. 1 day 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: Euler
Bhāskara’s dual square indeterminate equations
PDF for convenient reading Figure 1. Sum and difference of squares amounting to near squares. In course of our exploration of the bhūjākoṭikarṇanyāya in our early youth we had observed that there are examples of “near misses”: . Hence, we … Continue reading
Posted in Heathen thought, Scientific ramblings
Tagged arithmetic, bhAskara, Euler, fibonacci, figurate numbers, Geometric construction, geometry, Hindu knowledge, Hindu mathematics, history of science, irrational numbers, line, mathematics, numbers, Pythagorean triples, recreational geometry, square, square root, squares
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Two squares that sum to a cube
Introduction This note records an exploration that began in our youth with the simple arithmetic question: Sum of the squares of which pair integers yields a perfect cube? Some obvious cases immediately come to mind: . In both these cases … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, Brahmagupta, cube, Euler, Gauss, Hindu mathematics, mathematical entity, mathematics, numbers, prime numbers, Ramanujan, square
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From Plato to Euler and back
This is primarily meant as an educational handout on some very basic theorems of geometry that one might have studied in school. Some educated adults whom we asked about these had either forgotten them or claimed to have never studied … Continue reading
Posted in Scientific ramblings
Tagged Euler, geometry, Plato, Platonic ideals, polygons, polyhedra, polyhedron, space
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Reflections on our journey through the aliquot sums and sequences
The numerology of aliquot sums and perfect numbers The numerology of the Pythagorean sages among the old yavanas is one of the foundations of science and mathematics as we know it. One remarkable class of numbers which they discovered were … Continue reading
Counting primes, arithmetic functions, Ramanujan and the like
We originally wished to have a tailpiece for our previous note that would describe more precisely the relationship between the Möbius function and the distribution of prime numbers. However, since that would have needed a bit of a detour in … Continue reading
Posted in History, Scientific ramblings
Tagged complex numbers, Euler, Gauss, mathematics, prime numbers, Ramanujan, Riemann
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Of lives of men; of times of menII
Of lives of men; of times of menI Vidrum: “When we attended the discussions at the Right Wing Debate club we heard the president Rammandir Mishra repeatedly emphasize that South Asian civilization was not a ‘historycentric’ civilization and that historycentricism … Continue reading
Posted in Heathen thought, History, Life
Tagged ancient Hindu thought, Euler, Gauss, Hindu, Hindu knowledge, Hindu science, Hindus, history, Ramanujan, Riemann, Story, world history
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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
Some personal reflections on Carl Gauss, Bernhard Riemann and associated matters
The biochemist Albert SzentGyörgyi had famously remarked that as he successively, journeyed for a better understanding of life from cell biology, to physiology, to pharmacology, to bacteriology, to biochemistry, to physical chemistry to quantum mechanics he lost life between his … Continue reading
Posted in History, Life, Scientific ramblings
Tagged Einstein, Euclid, Euler, Gauss, geometry, Greek thought, Noneuclidean geometry, Riemann, Thabit ibn Kurra
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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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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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