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 vigrahaNAd rAsabhAkramaNam 😉 https://t.co/ndSFMVxZ3n 16 hours ago
 RT @avataram: Universal Genève 1950s with cloisonné dial featuring Ma Kali, the goddess of time! https://t.co/KIDCcZcgYU 18 hours ago
 Stable Diffusion: A visitation https://t.co/oJc0p2mDrt 19 hours ago
 Phantoms of the living and the dead: Stablediffusion https://t.co/MpEypeTKTM 20 hours ago
 RT @shrikanth_krish: @gaurav_lele @van_vij @kaeshour @omarali50 @AmitMajmudar @razibkhan @blog_supplement I strongly recommend @blog_supple… 22 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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December 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 31 
Pages
Categories
Search this Blog
Archives
mAnasataraMgiNI supplement
 vigrahaNAd rAsabhAkramaNam 😉 https://t.co/ndSFMVxZ3n 16 hours ago
 RT @avataram: Universal Genève 1950s with cloisonné dial featuring Ma Kali, the goddess of time! https://t.co/KIDCcZcgYU 18 hours ago
 Stable Diffusion: A visitation https://t.co/oJc0p2mDrt 19 hours ago
 Phantoms of the living and the dead: Stablediffusion https://t.co/MpEypeTKTM 20 hours ago
 RT @shrikanth_krish: @gaurav_lele @van_vij @kaeshour @omarali50 @AmitMajmudar @razibkhan @blog_supplement I strongly recommend @blog_supple… 22 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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December 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 31
Tag Archives: 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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A catalog of attractors, repellors, cycles, and other oscillations of some common functional iterates
One of the reasons we became interested in functional iterates was from seeking an analogy for the effect of selective pressure on the mean values of a measurable biological trait in a population. Let us consider a biological trait under … Continue reading
Some observations on the LekkerkerkerZeckendorf decomposition of integers
In our youth, we learned of a nice arithmetic theorem of Lekkerkerker (more popularly known after Zeckendorf; hereinafter LZ) that relates to the famous Mātrāmeru sequence : 0, 1, 1, 2, 3, 5, 8… defined by the recurrence relationship . … Continue reading
Some biographical reflections on visualizing irrationals
In our childhood, our father informed us that, though the school told us that , it was not valid. However, he added that for “small fractions” [Footnote 1] it was a great approximation. Moreover, the numerical problems, which we would … Continue reading
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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Counting pyramids, squares and magic squares
Figure 1. Pyramidal numbers The following note provides some exceedingly elementary mathematics, primarily for bālabodhana. Sometime back we heard a talk by a famous contemporary mathematician (M. Bhargava) in which he described how as a kid he discovered for himself … Continue reading
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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Chaotic behavior of some floorsquared maps
Consider the one dimensional maps of the form: , where is the fractional part of What will be evolution of a under this map when or ? We can see that for it will tend converge. However, the behavior is … Continue reading
Posted in Scientific ramblings
Tagged attractors, chaos, fractal, fractals, geometry, Golden Ratio, mathematics, numbers
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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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Sequences related to maps based on simple fractional functions
One of the pleasures of an unstructured youth in the precomputer era was what we called calculator games. As our father took his prized calculator with him to work we only got a little time with it in the evenings. … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, complex numbers, fibonacci, fractal, fractals, mathematics, nArAyaNa, numbers, sequence, trigonometry
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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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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 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 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
Residues of squares, sequence curiosities and parabolas galore
Squares and their residues This is an exploration of number triangles in the same vein as some other such we have previously described . It resulted in some observations that seemed interesting to us. Some are perhaps trivial but some … Continue reading
Posted in Scientific ramblings
Tagged mathematical entity, mathematics, numbers, square root, squares, triangles
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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