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- A modern glance at Nārāyaṇa-paṇḍita’s combinatorics-1
- Kaiṭabha, poison and death: meanderings through tradition
- Chaos, eruptions and root-convergence in one-dimensional maps based on metallic-sequence generating functions
- Big fruits and dead giants
- Pearl necklaces for Maheśvara
- Nārāyaṇa’s sequence, Mādhava’s series and pi
- Discovering bronze in the characteristic ellipse of right triangles
- Matters of religion: the Vāyavīyaṃ Kaubera-vratam
- The Platonic culmination of Euclid and the pentagon-hexagon-decagon identity
- Leaves from the scrapbook-4
- From Plato to Euler and back
- Śiva-gaṇa-s and Andhakāsura-vadha in the Vāmana-purāṇa
- Packing constants for polygonal fractal maps
- Cows, horses, sheep and goats
- Fraudulent science by Indians: some really bad news
- Leaves from the scrapbook-3
- Mongolica: The Tangut empire
- Notes on the Bhadra-sūkta, a hymn for felicity to the Vedic pantheon
- Liṅga-kāmādi-sūtrāṇi
- 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
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- The maṅgalācaraṇam of the Mānasollāsa
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- Visualizing the Hindu divisibility test
- Fermat’s little theorem and the periods of the reciprocals of primes
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Author Archives: mAnasa-taraMgiNI
A modern glance at Nārāyaṇa-paṇḍita’s combinatorics-1
For improved reading experience one may use the PDF version. Students of the history of Hindu mathematics are well-acquainted with Nārāyaṇa-paṇḍita’s sophisticated treatment of various aspects of combinatorics and integer sequences in his Gaṇita-kaumudī composed in 1356 CE. In that … Continue reading
Posted in Heathen thought, History, Scientific ramblings
Tagged combinatorics, Hindu mathematics, Hindu science, mathematical entity, mathematics, nArAyaNa
Kaiṭabha, poison and death: meanderings through tradition
For better reading try PDF version The medical Suśruta-saṃhitā, kalpasthāna, chapter 3 contains an unusual mythologem about the origin of poison. It clearly belongs to the Prājāpatya tradition and presents some unusual features. It presented in full below: prajām imām … Continue reading
Chaos, eruptions and root-convergence in one-dimensional maps based on metallic-sequence generating functions
Over the years we have observed or encountered certain natural phenomena that are characterized by rare, sudden eruptive behavior occurring against a background of very low amplitude fluctuations. We first encountered this in astronomy: most remarkably, in the constellation of … Continue reading
Posted in Scientific ramblings
Tagged Bronze ratio, chaos, chaotic maps, Copper Ration, curves, fractals, geometry, Golden Ratio, mathematics, recreational geometry, recursion, sequence, Silver Ratio
Big fruits and dead giants
The fruits of the elephants nāgo bilvam ivākramya pothayiṣyāmy ahaṃ śiraḥ | alabhyām icchatas tasya kīcakasya durātmanaḥ || Like an elephant seizing a bilva [fruit] I will crush the head of that evil Kīcaka who desires that which ought not … Continue reading
Posted in Heathen thought, Scientific ramblings
Tagged elephant, extinction, fossils, human existence, mammoths, mastodonts, megafauna, Megatherium, proboscidea, proboscidean, sloths
Pearl necklaces for Maheśvara
Śrīpati’s pearl necklace for Maheśvara The brāhmaṇa Śrīpati of the Kāśyapa clan was a soothsayer from Rohiṇīkhaṇḍa, which is in the modern Buldhana district of Maharashtra state. Somewhere between 1030 to 1050 CE he composed several works on mathematics, astronomy … Continue reading
Nārāyaṇa’s sequence, Mādhava’s series and pi
The coin-toss problem and Nārāyaṇa’s sequence If you toss a fair coin times how many of the possible result-sequences of tosses will not have a successive run of 3 or more Heads? The same can be phrased as given tosses … Continue reading
Posted in Heathen thought, History, Scientific ramblings
Tagged approximation for pi, coin toss, constant, Euclid, fibonacci, Geometric construction, geometry, Golden Ratio, hexagon, Hindu mathematics, history of science, mAdhava, mathematics, nArAyaNa, pentagon, pi, sequence, series sum, tribonacci
Discovering bronze in the characteristic ellipse of right triangles
The arithmetic mean square of a right triangle An entire family of right triangles that includes all the different forms of right triangles defined in terms of the proportion of their legs can be obtained by setting their altitude to … Continue reading
Posted in Scientific ramblings
Tagged Bronze ratio, conic sections, conics, ellipse, Golden Ratio, mathematical entity, mathematics, right triangles, sequence, square, square root
