
Pages
Categories
Search this Blog
Archives
mAnasataraMgiNI supplement
 Perhaps because I don't like solitary travel I find this world roving a rather aberrant practice. But more to the p… twitter.com/i/web/status/1… 2 days ago
 I was speaking to my parents about this very issue because someone came up to me & authoritatively tried to mention… twitter.com/i/web/status/1… 2 days ago
 A partial graph of researchers leading the development of modern physics with some additional vertices added. The d… twitter.com/i/web/status/1… 2 days ago
 Elektorornis a strange bird from the Burmese Cretaceous amber with a very long 3rd digit on its foot https://t.co/sC1hwnah66 2 days ago
 A web of who eats whom as preserved in the fossil record of the Yanliao and Jehol in what's today China. https://t.co/PH4NDvU8Un 2 days ago
Top Posts

Recent Posts
 Matters of religion: the Vāyavīyaṃ Kauberavratam
 The Platonic culmination of Euclid and the pentagonhexagondecagon identity
 Leaves from the scrapbook4
 From Plato to Euler and back
 Śivagaṇas and Andhakāsuravadha in the Vāmanapurāṇa
 Packing constants for polygonal fractal maps
 Cows, horses, sheep and goats
 Fraudulent science by Indians: some really bad news
 Leaves from the scrapbook3
 Mongolica: The Tangut empire
 Notes on the Bhadrasūkta, a hymn for felicity to the Vedic pantheon
 Liṅgakāmādisūtrāṇi
 Creating patterns through matrix expansion
 An apparition of Mordell
 A dinnertime conversation
 Newton’s cows
 A novel discrete map exhibiting chaotic behavior
 1859 CE and beyond: Some reflections
 Cricket in pictures
 The maṅgalācaraṇam of the Mānasollāsa
 The second strike
 Visualizing the Hindu divisibility test
 Fermat’s little theorem and the periods of the reciprocals of primes
 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
Meta
Tag Archives: sequence
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
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