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- Matters of religion: the Vāyavīyaṃ Kaubera-vratam
- The Platonic culmination of Euclid and the pentagon-hexagon-decagon identity
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- From Plato to Euler and back
- Śiva-gaṇa-s and Andhakāsura-vadha in the Vāmana-purāṇa
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- Mongolica: The Tangut empire
- Notes on the Bhadra-sūkta, a hymn for felicity to the Vedic pantheon
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- Creating patterns through matrix expansion
- An apparition of Mordell
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- 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
- Division-multiplication 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
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Tag Archives: Geometric construction
The Platonic culmination of Euclid and the pentagon-hexagon-decagon identity
Why did great sage Pāṇini compose the Aṣṭādhyāyī? There were probably multiple reasons but often you hear people say that he wanted to give a complete description of the Sanskrit language. That was probably one of his reasons but was … Continue reading
Posted in Heathen thought, Life
Tagged Geometric construction, geometry, Golden Ratio, Greek, Hindu, Plato, polygons, polyhedra, recreational geometry, religion, triangles, trigonometry
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: Method-I (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 heart-shaped curves, which are distinct from the … Continue reading
Posted in Scientific ramblings
Tagged circle, conic sections, conics, curves, ellipse, Geometric construction, geometry, heart-curve, hyperbola, ovals, parabola, recreational geometry
The 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 apabhraṃśa that was dealt with in the … Continue reading
Posted in Life
Tagged fiction, Geometric construction, geometry, Story
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 Bhāskara-II, but … Continue reading
Hofstadter and Nārāyaṇa: connections across space and time
The scientist-philosopher Douglas Hofstadter presents an interesting single-seeded 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
