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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… 50 minutes ago
 chikkA and sundarabikShu seem to be shoring up the emperor of the middle kingdom against his rebels. 58 minutes ago
 Lol seems to be taking a leaf off de Nobili's "veda". 12 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… 15 hours ago
 RT @DavidEvans_ROM: Happy #FossilFriday— here’s the beautifully preserved skull of the strange archosauriform Vancleavea from the Coelophys… 16 hours ago
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 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… 50 minutes ago
 chikkA and sundarabikShu seem to be shoring up the emperor of the middle kingdom against his rebels. 58 minutes ago
 Lol seems to be taking a leaf off de Nobili's "veda". 12 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… 15 hours ago
 RT @DavidEvans_ROM: Happy #FossilFriday— here’s the beautifully preserved skull of the strange archosauriform Vancleavea from the Coelophys… 16 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: prime numbers
A sampler of Ramanujan’s elementary results and their manifold ramifications
As we have remarked before, Ramanujan seemed as if channeling the worldconquering strides of Viṣṇu, when he singlehandedly bridged the lacuna in Hindu mathematics from the days of the brāhmaṇas of the Cerapada to the modern era. Starting around the … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, combinatorics, complex numbers, figurate numbers, Gamma function, Geometric construction, geometry, Hindu, Hindu mathematics, irrational numbers, mathematical entity, mathematics, numbers, prime numbers, recreational geometry, Riemann, sequence, series sum, zeta function
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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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An arithmetic experiment and an unsolved problem
We realized that a simple arithmetic experiment we had performed in our youth is actually related to an unsolved problem in number theory. It goes thus: consider the sequence of natural numbers Then find the distance of to nearest prime … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, arithmetic mean, geometric mean, mathematical entity, mathematics, numbers, prime numbers, sequence
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Generalizations of the prime sieve and Pi
PDF version for better reading Eratosthenes, the preeminent yavana philosopher of early Ptolemaic Egypt [footnote 1], composed a hymn to the god Hermes of which only some fragments have come down to us. This connection to Hermes is evidently related … Continue reading
Posted in Heathen thought, Scientific ramblings
Tagged approximation for pi, circle, geometry, Greek, Greek thought, mathematical entity, mathematics, numbers, pi, prime numbers, sequence
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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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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
Pearl necklaces for Maheśvara
Śrīpati’s pearl necklace for Maheśvara The brāhmaṇa Śrīpati of the Kāśyapa clan was a soothsayer from Rohiṇīkhaṇḍa, which is in the modern Buldhana district of Maharashtra state. Somewhere between 1030 to 1050 CE he composed several works on mathematics, astronomy … Continue reading
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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Visualizing the Hindu divisibility test
Prologue This article continues on the themes covered by the last two (here and here) relating to factorization and the primitive root modulo of a prime number. Early in ones education one learns the divisibility tests for the first few … Continue reading
Fermat’s little theorem and the periods of the reciprocals of primes
From the genetic code to the proof of Fermat’s little theorem Nucleic acids encode the 20 amino acids found in the sequence of a protein using just 4 bases: A, G, T, C in DNA. Thus, the 4symbol nucleic acid … Continue reading
Posted in Life, Scientific ramblings
Tagged arithmetic, decimal, decimal cycle, Fermat little theorem, fractions, mathematics, prime numbers, sequence
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A layman’s overview of the arithmetic of encryption
Life as an encryptiondecryption cycle Encryption is a concept as old as life itself. The sequence of proteins, the primary purveyors of function in life as we know it, is encrypted within nucleic acids. It is decrypted by this remarkable … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, code, encryption, key, mathematics, numbers, prime numbers, RSA
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Divisionmultiplication parabolas, triplications, and quadratic residues
Introduction Many strands of our investigations on conicgenerating integer sequences, word fractals and cellular automaton models for pattern formation came together in an unexpected manner while investigating a simple integer sequence. While some of these connections have have been known … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, conics, fractal, fractals, geometry, mathematical entity, mathematics, MephistoWaltz, numbers, parabola, prime numbers, sequence
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The geometric principles behind discrete dynamical systems based on the generalized Witch of Agnesi
Consider the family of curves defined by the equation following parametric equation , where and It defines a family of probability distribution functions (PDFs): This can be seen from the above equations because Figure 1 Examples of these PDFs are … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, chaos, chaotic flows, dynamics, fractal, fractals, geometry, GumowskiMira, mathematics, numbers, prime numbers
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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
A note on the least prime divisor sequences of 2p plus or minus 1
Let be the sequence of prime numbers: 2, 3, 5, 7… Define the sequences such that . Then sequence is defined such that is the lowest prime divisor (LPD) of and sequence is defined so that is the LPD of … Continue reading
Posted in Scientific ramblings
Tagged Gauss, mathematical entity, mathematics, prime numbers, sequence
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A sequence related to prime counting
The current note arose as an exploration branching off from the matter discussed in these earlier notes: this one and this one. As we saw before, Carl Gauss, while still in his teens, produced his first estimate of the prime … Continue reading
Convergence to a palindrome
This is a brief account of a sequence we constructed inspired by Dattatreya Ramachandra Kaprekar. It is not known to us if he had discovered it in one of his obscure publications from a small town in the Maharatta country. … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, mathematical entity, mathematics, palindrome, prime numbers
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A problem from 600 CE and some curiosities of Āryabhaṭa’s kuṭṭaka algorithm
Around 600 CE in the examinations of one of the Hindu schools of mathematics and astronomy one might have encountered a problem such as below (given by BhāskaraI in his commentary on Āryabhaṭa’s Āryabhaṭīya): dvayādyaiḥ ṣaṭparyantair ekāgraḥ yo ‘vaśiṣyate rāśiḥ … Continue reading
Posted in Heathen thought, Scientific ramblings
Tagged AryabhaTa, Golden Ratio, Hindu mathematics, kuTTaka, mathematics, prime numbers
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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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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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Our autodiscovery of the Möbius and Mertens sequences
Recently, we were explaining to our friend the Möbius and the Mertens functions and their relationship to the prime number distribution. We also heard with some wonder from a physicist of a theoretical model where multiparticle states behave as bosons … Continue reading
Early Hindu mathematics and the exploration of some second degree indeterminate equations
The following is merely a record of our exploration as a nonmathematician/noncomputer scientist of a remarkable (at least to us) class of numerical relationships. An equation like can be solved to obtain specific solutions as: . However, if we have … Continue reading