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- Bhāskara-II’s polygons and an algebraic approximation for sines of pi by x
- Origins of the serpent cult and Bhāguri’s snake installation from the Sāmaveda tradition
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mAnasa-taraMgiNI supplement
- RT @Pradeep_M_Nair: @HappySi99321047 @Shivaji_81 @ShefVaidya @GuhanRamya @gajanansinamdar @srivaraha_67 @LaxmiSeshaiyer @mmpandit @ramiyeng… 12 hours ago
- O gods of heaven and earth! This thing exceeds all expectations: tell me about Shingopana https://t.co/mrfyoyGfau 1 day ago
- The Mesozoic trainwreck piles up: Shidaisaurus, Diandongosaurus, Diandongosuchus...🤯 twitter.com/blog_supplemen… https://t.co/WFiAtsfnCo 1 day ago
- The Eulerian spiral integrals https://t.co/HAp6xm3Rtv 1 day ago
- It seems to miss the fact that many dinosaurs are still around 👀 https://t.co/WT0UXkzj6f 1 day ago
Top Posts
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Recent Posts
- Some ruminations on asteroids and meteoritic falls
- Comet C/2022 E3 (ZTF)
- The Vyomavyāpin in the Pāśupata-tantra and a discursion on nine-fold Rudra-mantra-s
- Bhāskara-II’s polygons and an algebraic approximation for sines of pi by x
- Origins of the serpent cult and Bhāguri’s snake installation from the Sāmaveda tradition
- Two simple stotra-s, sectarian competition, and the Varāha episode from the archaic Skandapurāṇa
- The zombie obeys: a note on host manipulation by parasites and its ecological consequences
- Cārucitrābhisambodhi
- RV 10.78
- The turning of the yugacakra
- A sampler of Ramanujan’s elementary results and their manifold ramifications
- A catalog of attractors, repellors, cycles, and other oscillations of some common functional iterates
- The wink of the Gorgon and the twang of the Lyre
- Some poems
- The Kaumāra cycle in the Skandapurāṇa’s Śaṃkara-saṃhitā
- Some notes on the runiform “Altaic” inscriptions and the early Turk Khaghanates: Orkhon and beyond
- Vikīrṇā viṣayāḥ: India and the Rus
- Alkaios’ hymn to the Dioskouroi: Hindu parallels
- Some notes on the Indo-European aspects of the Anatolian tradition
- The death of Miss Lizzie Willink
- Indo-European expansions and iconography: revisiting the anthropomorphic stelae
- Geopolitical summary: March 2022
- Human retroviruses, sociology of science, and biographical ruminations
- Transcripts of conversations: the addiction principle:
- Phantom impressions-1
- A note on Śrī, Viṣṇu and śṛṅgāra
- Are civilizational cycles the norm?
- On the rise of the mātṛkā-s and the goddess Cāmuṇḍā
- Huns, Uralics, and empires of the steppe
- Some observations on the Lekkerkerker-Zeckendorf decomposition of integers
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Tag Archives: Hindu mathematics
Bhāskara-II’s polygons and an algebraic approximation for sines of pi by x
Unlike the Greeks, the Hindus were not particularly obsessed with constructions involving just a compass and a straightedge. Nevertheless, their pre-modern architecture and yantra-s from the tāntrika tradition indicate that they routinely constructed various regular polygons inscribed in circles. Of … Continue reading
A sampler of Ramanujan’s elementary results and their manifold ramifications
As we have remarked before, Ramanujan seemed as if channeling the world-conquering strides of Viṣṇu, when he single-handedly bridged the lacuna in Hindu mathematics from the days of the brāhmaṇa-s of the Cerapada to the modern era. Starting around the … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, combinatorics, complex numbers, figurate numbers, Gamma function, Geometric construction, geometry, Hindu, Hindu mathematics, irrational numbers, mathematical entity, mathematics, numbers, prime numbers, recreational geometry, Riemann, sequence, series sum, zeta function
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Some biographical reflections on visualizing irrationals
In our childhood, our father informed us that, though the school told us that , it was not valid. However, he added that for “small fractions” [Footnote 1] it was a great approximation. Moreover, the numerical problems, which we would … Continue reading
Two exceedingly simple sums related to triangular numbers
This note records some elementary arithmetic pertaining to triangular numbers for bālabodhana. In our youth we found that having a flexible attitude was good thing while obtaining closed forms for simple sums: for some sums geometry (using methods of proofs … Continue reading
Posted in Scientific ramblings
Tagged geometry, Hindu mathematics, mathematical entity, mathematics, proof, sequence, series sum, sum
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Johannes Germanus Regiomontanus and his rod
Even before we had become acquainted with the trigonometric sum and difference formulae or calculus are father had pointed to us that there was an optimal point at which one should stand to observe or photograph features on vertical structures, … Continue reading
Bhāskara’s dual square indeterminate equations
PDF for convenient reading Figure 1. Sum and difference of squares amounting to near squares. In course of our exploration of the bhūjā-koṭi-karṇa-nyāya in our early youth we had observed that there are examples of “near misses”: . Hence, we … Continue reading
Posted in Heathen thought, Scientific ramblings
Tagged arithmetic, bhAskara, Euler, fibonacci, figurate numbers, Geometric construction, geometry, Hindu knowledge, Hindu mathematics, history of science, irrational numbers, line, mathematics, numbers, Pythagorean triples, recreational geometry, square, square root, squares
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Counting pyramids, squares and magic squares
Figure 1. Pyramidal numbers The following note provides some exceedingly elementary mathematics, primarily for bālabodhana. Sometime back we heard a talk by a famous contemporary mathematician (M. Bhargava) in which he described how as a kid he discovered for himself … Continue reading
Conic conquests: biographical and historical
PDF file of same article Studying mathematics with our father was not exactly an easy-going experience; nevertheless, it was the source of many a spark that inspired fruitful explorations and life-lessons. We recount one such thread here, and reflect on … Continue reading
Notes on miscellaneous brāhmaṇa passages from the Yajurveda
The upasthāna ritual is performed to let the sacrificial fire remain in residence after the primary oblations are complete. In the triple-fire śrauta rite this is done at the āhavanīya altar with several incantations specified in the saṃhitā-s of the … Continue reading
Posted in Heathen thought, History
Tagged Hindu, Hindu knowledge, Hindu mathematics, Hindu ritual, religion, Rigveda, ritual, Veda, vedic, Yajurveda
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Two squares that sum to a cube
Introduction This note records an exploration that began in our youth with the simple arithmetic question: Sum of the squares of which pair integers yields a perfect cube? Some obvious cases immediately come to mind: . In both these cases … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, Brahmagupta, cube, Euler, Gauss, Hindu mathematics, mathematical entity, mathematics, numbers, prime numbers, Ramanujan, square
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Some Nārāyaṇa-like convergents and their geometric and trigonometric connections
While playing with an iterative geometric construction in our youth we discovered for ourselves a particular right triangle whose sides are in the proportion , where is the Golden Ratio. This triangle is of course famous as being the basis … Continue reading
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
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
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Visualizing 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 divisibility tests for the first few … Continue reading
A problem from 600 CE and some curiosities of Āryabhaṭa’s kuṭṭaka algorithm
Around 600 CE in the examinations of one of the Hindu schools of mathematics and astronomy one might have encountered a problem such as below (given by Bhāskara-I in his commentary on Āryabhaṭa’s Āryabhaṭīya): dvayādyaiḥ ṣaṭ-paryantair ekāgraḥ yo ‘vaśiṣyate rāśiḥ … Continue reading
Posted in Heathen thought, Scientific ramblings
Tagged AryabhaTa, Golden Ratio, Hindu mathematics, kuTTaka, mathematics, prime numbers
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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
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
The square root spiral and the Gamma function: entwined analogies
The topic discussed here is something on which considerable serious mathematical literature has published by P.J Davis, W. Gautschi and others. This partly historical narration is just a personal account of our journey through the same as a non-mathematician. As … Continue reading
The magic of the deva-ogdoad
Classical Hindu tradition holds that the ogdoad of deva-s corresponding to their directions is: Indra: East; Agni: Southeast; Yama: South; Nirṛti: Southwest; Varuṇa: West; Vāyu: Northwest; Kubera: North; Īśāna: Northeast. The central position might be occupied in certain traditions by … Continue reading
Āryabhaṭa and his sine table
Everyone and his son have written about Āryabhaṭa and his sine table. Yet we too do this because sometimes the situation arises where you have to explain things clearly to a layman who might have some education but is unfamiliar … Continue reading
Euler and Ramanujan: primes, near integers and cakravāla
Mathematician Watson who worked on the famed notebooks said regarding some of Srinivasa Ramanujan’s equations: “a thrill which is indistinguishable from the thrill which I feel when I enter the Sagrestia Nuovo of the Capella Medici and see before me … Continue reading
Posted in Scientific ramblings
Tagged almost integers, diophantine, e, Hindu mathematics, mathematics, Monstrous moonshine, near integers, Pell, pi, Ramanujan
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Early Hindu mathematics and the exploration of some second degree indeterminate equations
The following is merely a record of our exploration as a non-mathematician/non-computer scientist of a remarkable (at least to us) class of numerical relationships. An equation like can be solved to obtain specific solutions as: . However, if we have … Continue reading
Chaos in the iterative Hindu square root method of the gaṇaka-rāja
For Hindus big numbers always mattered and our mathematics is quite reflection of this fascination. Since the earliest times, Hindus devised various methods to obtain square roots of numbers, especially approximations of irrational roots correct to multiple decimal places. The … Continue reading
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