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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: recreational geometry
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 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 certain interesting heartshaped curves, which are distinct from the … Continue reading
Posted in Scientific ramblings
Tagged circle, conic sections, conics, curves, ellipse, Geometric construction, geometry, heartcurve, hyperbola, ovals, parabola, recreational geometry
The incredible beauty of certain Hamiltonian mappings
In our teens we studied Hamiltonian functions a little bit as part of our attempt to understand classical and quantum physics. A byproduct of it was a superficial interest in the geometry of some of the mappings arising from such … Continue reading
Posted in art, Scientific ramblings
Tagged fractal, fractals, geometry, Hamiltonian, mathematical entity, mathematics, Oscillator, physics, recreational geometry, recursion
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
Citrabhānu’s cubes
The Hindus unlike their yavana cousins preferred algebra to geometry. Yet on occasions they could indulge in geometric games for demostrating proofs of algebraic relations. We see a bit of this in the Āryabhaṭa school and the great BhāskaraII, but … Continue reading
The Meru and Nārāyaṇa’s cows: Words and fractals
The fractals described herein are based on and inspired by the work of the mathematicians Rauzy, MendesFrance, Monnerot and Knuth. Some their works, especially the first of them, are dense with formalism. Here we present in simple terms the means … Continue reading
Posted in art, Scientific ramblings
Tagged complex numbers, fractal, fractals, geometry, Golden Ratio, mathematics, Narayana cow sequence, recreational geometry, recursion
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