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mAnasataraMgiNI supplement
 Aware of some R&AW+mil agents who really had a clear idea of marUnmAda's civilizational war &its scope, beyond oper… twitter.com/i/web/status/1… 17 minutes ago
 The wide and rapid spread of the Lumpy skin poxvirus in cattle across the desh is rather puzzling.There seem to be… twitter.com/i/web/status/1… 11 hours ago
 The rug of pi; the rate at which numbers under the z/tan(z) map reach the invariant convergent pi/4 https://t.co/CcLgt6jiHi 13 hours ago
 Galtonism has enabled deep penetration of western assets by the middle kingdom nbcnews.com/news/world/sci… 13 hours ago
 Any complex number under the map of the reciprocal of the logarithm of its square will converge to that number indi… twitter.com/i/web/status/1… 17 hours ago
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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 
Pages
Categories
Search this Blog
Archives
mAnasataraMgiNI supplement
 Aware of some R&AW+mil agents who really had a clear idea of marUnmAda's civilizational war &its scope, beyond oper… twitter.com/i/web/status/1… 17 minutes ago
 The wide and rapid spread of the Lumpy skin poxvirus in cattle across the desh is rather puzzling.There seem to be… twitter.com/i/web/status/1… 11 hours ago
 The rug of pi; the rate at which numbers under the z/tan(z) map reach the invariant convergent pi/4 https://t.co/CcLgt6jiHi 13 hours ago
 Galtonism has enabled deep penetration of western assets by the middle kingdom nbcnews.com/news/world/sci… 13 hours ago
 Any complex number under the map of the reciprocal of the logarithm of its square will converge to that number indi… twitter.com/i/web/status/1… 17 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

Join 692 other followers
Meta
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
Tag Archives: square
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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Difference of consecutive cubes, conics and a Japanese temple tablet
Introduction In our part of the world, someone with even a nominal knowledge of mathematics might be aware of the taxicab number made famous by the conversation of Ramanujan and Hardy: the smallest number that can be expressed as the … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, cube, ellipse, geometry, history of science, Japan, mathematics, numbers, parabola, recreational geometry, square
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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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An apparition of Mordell
Consider the equation: where is a positive integer 1, 2, 3… For a given , will the above equation have integer solutions and, if yes, what are they and how many? We have heard of accounts of people receiving solutions … Continue reading
Posted in Scientific ramblings
Tagged Bachet, cube, cubic, geometry, mathematical entity, mathematics, Mordell equation, numbers, prime numbers, quadratic, recreational geometry, square
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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 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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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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A strange Soviet construction
in our college days we used to visit the lālpustakbhaṇḍār in our city where Soviet books on science and mathematics were sold at a low price (alongside Marxian literature). They were a great resource that enormously contributed to our intellectual … Continue reading
Posted in Scientific ramblings
Tagged Geometric construction, geometry, mathematics, recreational geometry, Russia, square
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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
Between the rasArNava and the chitrabandhas
In the glorious summer we sought, through the secret practice, the enlightenment, which the elixir of viveka confers upon the lucky. We reclined in the holy land of bhArata, now sullied by the faded vigor of our peoples and the … Continue reading
Posted in art, Heathen thought, Life, Scientific ramblings
Tagged ashoka tree, bhAravi, D4, Dialium, entropy, histones, kAlidAsa, kirAtArjunIyam, lowcomplexity, posttranslational modification, Sanskrit, Saraca, sarvatobhadra, square, symmetry
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