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mAnasataraMgiNI supplement
 puShpakShetra's anugAmin & his anuyAyins are at least taking some action on navyonmAda. Certain ideologies can onl… twitter.com/i/web/status/1… 1 hour ago
 Imagine having a dream where the American hero spiderman bursts out of the bathtub & bounces from wall to wall befo… twitter.com/i/web/status/1… 1 hour ago
 RT @EPButler: Indian Religions and the Concept of God: An Online Workshop, 1314 Feb 2023 logicandreligion.com/vaishnavaconc… 1 hour ago
 The Okunevo had a rather complex ancestry for their time with the IE Afanasievo from Yamnaya, the Baikal Early neol… twitter.com/i/web/status/1… 20 hours ago
 Technooptimists being uncaring about demography & biological evolution might even be somewhat forgiven. But not ca… twitter.com/i/web/status/1… 20 hours ago
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Recent Posts
 The Vyomavyāpin in the Pāśupatatantra and a discursion on ninefold Rudramantras
 BhāskaraII’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 stotras, 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 Śaṃkarasaṃhitā
 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 IndoEuropean aspects of the Anatolian tradition
 The death of Miss Lizzie Willink
 IndoEuropean 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 impressions1
 A note on Śrī, Viṣṇu and śṛṅgāra
 Are civilizational cycles the norm?
 On the rise of the mātṛkās and the goddess Cāmuṇḍā
 Huns, Uralics, and empires of the steppe
 Some observations on the LekkerkerkerZeckendorf decomposition of integers
 Subjective and objective insight
 On the passing of E.O. Wilson

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February 2023 M T W T F S S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 
Pages
Categories
Search this Blog
Archives
mAnasataraMgiNI supplement
 puShpakShetra's anugAmin & his anuyAyins are at least taking some action on navyonmAda. Certain ideologies can onl… twitter.com/i/web/status/1… 1 hour ago
 Imagine having a dream where the American hero spiderman bursts out of the bathtub & bounces from wall to wall befo… twitter.com/i/web/status/1… 1 hour ago
 RT @EPButler: Indian Religions and the Concept of God: An Online Workshop, 1314 Feb 2023 logicandreligion.com/vaishnavaconc… 1 hour ago
 The Okunevo had a rather complex ancestry for their time with the IE Afanasievo from Yamnaya, the Baikal Early neol… twitter.com/i/web/status/1… 20 hours ago
 Technooptimists being uncaring about demography & biological evolution might even be somewhat forgiven. But not ca… twitter.com/i/web/status/1… 20 hours ago
Top Posts

Recent Posts
 The Vyomavyāpin in the Pāśupatatantra and a discursion on ninefold Rudramantras
 BhāskaraII’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 stotras, 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 Śaṃkarasaṃhitā
 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 IndoEuropean aspects of the Anatolian tradition
 The death of Miss Lizzie Willink
 IndoEuropean 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 impressions1
 A note on Śrī, Viṣṇu and śṛṅgāra
 Are civilizational cycles the norm?
 On the rise of the mātṛkās and the goddess Cāmuṇḍā
 Huns, Uralics, and empires of the steppe
 Some observations on the LekkerkerkerZeckendorf decomposition of integers
 Subjective and objective insight
 On the passing of E.O. Wilson

Join 697 other subscribers
Meta
February 2023 M T W T F S S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Tag Archives: triangles
Relationships between incircles of the “equilateral triangles in a square” system
This note relates to geometric relationships that may be likened to the Japanese templetablet problems. The inspiration for discovering and exploring it came from an origami construction presented by the pioneer in that field, Sundara Rao of Kumbhaghoṇa, in the … Continue reading
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
A great statistician, and biographical, numerical musings on ancient game
Recently my friend brought it to my attention that C. Radhakrishna Rao had scored a century. Born in 1920 CE to Doraswamy Nayadu and A. Laxmikanthamma from the Andhra country, he is one of the great mathematical thinkers and statisticians … Continue reading
Rāsabhanyāyaśikṣā
Vrishchika had been seeing several kids of patients affected by the chemical leak that had happened sometime ago. While she saw some purely for routine clinical practice, she was also particularly interested in the several cases exhibiting heterotaxy and had … Continue reading
The Mātrāmeru and convergence to a triangle
What is presented below will be elementary for someone with even just the mastery of secondary school mathematics. Nevertheless, even simple stuff might present points of interest to people who see beauty in such things. Consider the following question: Given … Continue reading
Posted in Scientific ramblings
Tagged fibonacci, geometry, Golden Ratio, mathematics, recreational geometry, sequence, triangles, trigonometry
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Some Nārāyaṇalike 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
Some notes on rational sector triangle triples
Rational points on a unit circle There are some events that happen in the course of ones life that might be considered historical or worldchanging. One such event from our lifetime is the proving of the Last Theorem of Fermat … Continue reading
The minimal triangle circumscribing a semicircle
Consider a fixed semicircle with center at and radius . Let be the isosceles triangle which circumscribes it (Figure 1). Figure 1 What will be the characteristics of the minimal form of the said triangle, i.e. triangle with minimum perimeter, … Continue reading
The Platonic culmination of Euclid and the pentagonhexagondecagon 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
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Residues of squares, sequence curiosities and parabolas galore
Squares and their residues This is an exploration of number triangles in the same vein as some other such we have previously described . It resulted in some observations that seemed interesting to us. Some are perhaps trivial but some … Continue reading
Posted in Scientific ramblings
Tagged mathematical entity, mathematics, numbers, square root, squares, triangles
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Median and pedal triangles and derived fractals: an introductory account
It is rather easily seen that joining the midpoints of the sides of a triangle yields four congruent triangles that in turn are similar to the original triangle (Figure 1). This figure might be used to provided a selfevident geometric … Continue reading
Posted in art, Scientific ramblings
Tagged fractal, fractals, Geometric construction, geometry, mathematics, triangles
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Infinite bisections required for trisection of an angle
Figure 1: Selfevident demonstration of Figure 2: Application of the same as serial bisections to trisect the angle. In the example chosen here we have . In ten steps we get to which is a pretty close, though in principle … Continue reading
Posted in art, Scientific ramblings
Tagged Geometric construction, geometry, mathematics, recreational geometry, series sum, triangles, trisection
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Some meanderings among golden stuff2
Related stuff: Golden Ratio0 Golden Ratio1 If the golden ratio can fascinate erudite men of high IQ then what to say of simpletons like us. Hence, we shall here talk about some more trivia in this regard. The golden ratio … Continue reading
Leaves from the scrapbook
There were extensive memoirs in the form of electronic scrapbooks of Somakhya, Lootika and some members of their circle. Those in the know read the available excerpts due to matters of considerable interest being recorded in them. Other parts were … Continue reading
Posted in art, Life
Tagged chaos, Geometric construction, geometry, ghost, ghosts, LotkaVolterra, population dynamics, Story, triangles, trigonometry, trisection
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van Aubel’s theorem
The van Aubel’s theorem is a simple theorem which is comparable to the theorem attributed to the French conqueror Napoleon Bonaparte regarding triangles. It is easy to prove once you know the upāya, even as the yogins would say ānanda … Continue reading
Posted in art, Life, Scientific ramblings
Tagged Geometric construction, geometry, mathematics, philosophy, triangles, trigonometry, van Aubel
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Some trivia on equilateral triangles and the like
One may ask why one needs to revisit elementary geometry that was usually studied at secondary school. The simple answer is it is a good recreation. But it is not like any recreation, because it also opens the doors to … Continue reading
Posted in art, Life, Scientific ramblings
Tagged centroid, circumcenter, conics, Euler line, incenter, Kiepert hyperbola, Nagel line, Nagel point, Napoleon, ninepoint circle, orthocenter, Spieker point, triangles
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