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...
View ArticleSome words on mathematical truth, scientific conviction and the sociology of...
Sometime in the bronze age more than one group of humans, including our own Aryan ancestors, discovered that the squares of the two legs of a right triangle sum up to the square of the hypotenuse. This...
View ArticleMaking of a modern-day mantra-śāstra pamphlet
Originally, all mantra instructions were oral, keeping with the spirit of the śruti. But over time, starting probably around the Mauryan age, written manuals began to supplement the oral teachings....
View ArticleA poll on peoples’ beliefs on reincarnation
Using the Twitter’s poll tool we conducted a poll which gave the below results: Reincarnation happens: Believe so but there is no evidence for it: 52% Sure, have the evidence for it: 20% No, just...
View ArticleResidues 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....
View ArticleThe mathematics class
It was a dreary autumn day, the same year Lootika had joined their school. The apabhraṃśa class had just gotten over. Somakhya’s head was spinning with all the confusing genders of the vulgar...
View ArticleThe hearts and the intrinsic Cassinian curve of an ellipse
Introduction This investigation began with our exploration of pedal curves during the vacation following our university entrance exams in the days of our youth. It led to us discovering for ourselves...
View ArticleThe ghost in the tattered Gattermann
Vidrum had dropped by to see Somakhya and Lootika when they had just started their household together. They had reconstituted a fairly elaborate lab in the biggest room of their home. They had also...
View ArticleReflections 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 yavana-s is one of the foundations of science and mathematics as we know it. One remarkable...
View ArticleThe geometric principles behind discrete dynamical systems based on the...
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...
View ArticleA Political roundup August 15 2108
As I remarked to a friend, much of the stuff in (geo)politics which is relevant to us is what we have predicted before based on the relatively straightforward model of mleccha-marūnmattābhisaṃdhi i.e....
View ArticleThe 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: Method-I (Figure 1: this is based on an approach we described earlier) Figure 1 1)...
View ArticleA brief overview of the last campaign of Chingiz Khan and the issue of...
Succession is always an important issue in history. The legacy of a mighty ruler and/or founder of an empire might quickly unravel if the issue of succession is left unresolved. In Hindu history the...
View ArticleDivision-multiplication parabolas, triplications, and quadratic residues
Introduction Many strands of our investigations on conic-generating integer sequences, word fractals and cellular automaton models for pattern formation came together in an unexpected manner while...
View ArticleA layman’s overview of the arithmetic of encryption
Life as an encryption-decryption 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...
View ArticleFermat’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 4-symbol...
View ArticleVisualizing 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...
View ArticleThe second strike
PDF version Childhood Thrice a week, starting Fridays, Lootika’s mother taught her daughters mantra-siddhānta after dinner. She had covered the praxis of the secret mantra-s of the Vīṇāśikhā and had...
View ArticleThe maṅgalācaraṇam of the Mānasollāsa
In PDF format A conversation with a friend brought my mind back to the Mānasollāsa, the encyclopedia of the great Cālukya emperor Someśvara-deva. Below is the maṅgalācaraṇam of that work. The last...
View ArticleCricket in pictures
We may say that cricket has nearly passed us by. In our youth we played and watched the game quite a bit. While in secondary school we were fairly interested in cricket statistics. The sources for...
View Article