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 A layman’s overview of the arithmetic of encryption
 Divisionmultiplication parabolas, triplications, and quadratic residues
 A brief overview of the last campaign of Chingiz Khan and the issue of succession in the Mongol empire
 The mean hyperbola and other mean functions
 A Political roundup August 15 2018
 The geometric principles behind discrete dynamical systems based on the generalized Witch of Agnesi
 Reflections on our journey through the aliquot sums and sequences
 The ghost in the tattered Gattermann
 The hearts and the intrinsic Cassinian curve of an ellipse
 The mathematics class
 Residues of squares, sequence curiosities and parabolas galore
 A poll on peoples’ beliefs on reincarnation
 Making of a modernday mantraśāstra pamphlet
 Some words on mathematical truth, scientific conviction and the sociology of science
 A note on the least prime divisor sequences of 2p plus or minus 1
 A note on āmreḍitas in the Ṛgveda and issues of word distribution
 The amazonian banana republic: the strīrājya in Hindu tradition
 Sītā in the pyre
 A sequence related to prime counting
 Convergence to a palindrome
 A problem from 600 CE and some curiosities of Āryabhaṭa’s kuṭṭaka algorithm
 A brief note on some new developments regarding the genomics of Indians
 The remarkable behavior of a map displaying derived from a simple model for a biological conflict
 A day at school
 Mongolica: Qubilai Khan’s campaign to destroy the Southern Song
 The quotient triangle, the parabolahyperbola sequence, the remainder triangle and perfect numbers
 Counting primes, arithmetic functions, Ramanujan and the like
 Our autodiscovery of the Möbius and Mertens sequences
 Mongolica: Knowledge preservation and generation, Bolad Aqa and the like
 Civilizational collapse, complexity, innovation and neomania
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Tag Archives: sequence
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
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
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
Posted in Scientific ramblings
Tagged Gauss, mathematics, prime numbers, sequence
Some novel observations concerning quadratic roots and fractal sequences
Disclaimer: To our knowledge we have not found the material presented here laid out here presented in completeness elsewhere. However, we should state that we do not follow the mathematical literature as a professional and could have missed stuff. Introduction … Continue reading
Posted in Scientific ramblings
Tagged floor, fractal, fractals, integers, quadratic equation, quadratic root, sequence, square root
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
Posted in art, Heathen thought, History, Scientific ramblings
Tagged AryabhaTa, Euler, figurate numbers, Gauss, Geometric construction, geometry, hex, Hindu mathematics, nIlakaNTha somayAjin, recreational geometry, sequence, series sum, square, sum, triangular
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
Posted in art, Scientific ramblings
Tagged conic sections, conics, fractal, fractals, Geometric construction, geometry, Golden Ratio, Hofstader, mathematics, recreational geometry, recursion, sequence