
Pages
Categories
Search this Blog
Archives
mAnasataraMgiNI supplement
 षट्पादतन्त्रीमधुराभिधानम् प्लवङ्गम् उदीरितकण्ठतालम् । आविष्कृतम् मेघमृदङ्गनादैः वनेषु सङ्गीतम् इव प्रवृत्तम्… twitter.com/i/web/status/1… 7 hours ago
 मेघकृष्णाजिनधरा धारायज्ञोपवीतिनः । मारुतापूरितगुहाः प्राधीता इव पर्वताः ॥ Wearing the blackantelope skin of [m… twitter.com/i/web/status/1… 17 hours ago
 नवमासधृतं गर्भम् भास्कारस्य गभस्तिभिः । पीत्वा रसं समुद्राणां द्यौः प्रसूते रसायनम् ॥ Bearing for 9 months the em… twitter.com/i/web/status/1… 17 hours ago
 balloon Galtonism is at play. 18 hours ago
 1 of the mightiest characters of the rAmAyaNa was the ape vAlin. Among his great acts were the slaying of the dAnav… twitter.com/i/web/status/1… 1 day 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 
Pages
Categories
Search this Blog
Archives
mAnasataraMgiNI supplement
 षट्पादतन्त्रीमधुराभिधानम् प्लवङ्गम् उदीरितकण्ठतालम् । आविष्कृतम् मेघमृदङ्गनादैः वनेषु सङ्गीतम् इव प्रवृत्तम्… twitter.com/i/web/status/1… 7 hours ago
 मेघकृष्णाजिनधरा धारायज्ञोपवीतिनः । मारुतापूरितगुहाः प्राधीता इव पर्वताः ॥ Wearing the blackantelope skin of [m… twitter.com/i/web/status/1… 17 hours ago
 नवमासधृतं गर्भम् भास्कारस्य गभस्तिभिः । पीत्वा रसं समुद्राणां द्यौः प्रसूते रसायनम् ॥ Bearing for 9 months the em… twitter.com/i/web/status/1… 17 hours ago
 balloon Galtonism is at play. 18 hours ago
 1 of the mightiest characters of the rAmAyaNa was the ape vAlin. Among his great acts were the slaying of the dAnav… twitter.com/i/web/status/1… 1 day 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: conics
The shape of dinosaur eggs
Readers of these pages will know that we have a special interest in the geometry of ovals. One of the longstanding problems in this regard is: what is the curve that best describes the shape of a dinosaurian egg? While … Continue reading
Conic conquests: biographical and historical
PDF file of same article Studying mathematics with our father was not exactly an easygoing experience; nevertheless, it was the source of many a spark that inspired fruitful explorations and lifelessons. We recount one such thread here, and reflect on … Continue reading
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
Leave a comment
Divisionmultiplication parabolas, triplications, and quadratic residues
Introduction Many strands of our investigations on conicgenerating integer sequences, word fractals and cellular automaton models for pattern formation came together in an unexpected manner while investigating a simple integer sequence. While some of these connections have have been known … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, conics, fractal, fractals, geometry, mathematical entity, mathematics, MephistoWaltz, numbers, parabola, prime numbers, sequence
Leave a comment
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
Leave a comment
The quotient triangle, the parabolahyperbola sequence, the remainder triangle and perfect numbers
The quotient triangle Consider a positive integer . Then for all do the floor operation . Say , we get , a sequence of quotients of the division . If we do this for all we get the quotient triangular … Continue reading
Posted in Scientific ramblings
Tagged composite numbers, conic sections, conics, division, geometry, mathematics, Nicomachus, pi, prime numbers, Ramanujan
Leave a comment
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
Means and conics
By the time one reaches high school one learns that: (i) there are four means that one might find some use of in life (I know there are more though they are hardly used) – the arithmetic mean which is … Continue reading
Constructing a regular heptagon with hyperbola and parabola
There is little doubt that Archimedes was one of the greatest yavana intellectuals. He would also figure in any list of the greatest mathematicianscientists of all times. His work on the construction of a regular heptagon has not survived the … Continue reading
Posted in art, Scientific ramblings
Tagged complex numbers, conics, Gauss, Geometric construction, geometry, Greek, heptagon, hyperbola, mathematics, parabola, polygons, Thabit ibn Kurra
Leave a comment
Doubling the cube with ellipses
The problem of doubling of the cube which emerged in the context of the doubling of the cubical altar of the great god Apollo cannot be solved using just a straightedge and a compass. It needs one to construct a … Continue reading
Posted in art, Scientific ramblings
Tagged conic sections, conics, Delian, Delos, doubling the cube, ellipse, Geometric construction, geometry, mathematics
Leave a comment
The Apollonian parabola
Some say that Archimedes and Apollonius of Perga (modern Murtina in Turkey; the center of the great yavana temple of the goddess Artemis in the days of Apollonius) were the two great yavanas who might have rivaled Karl Gauss or … Continue reading
Posted in History, Scientific ramblings
Tagged Apollonius, conic sections, conics, Geometric construction, geometry, history, mathematics, parabola
Leave a comment
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
Leave a comment
Fancies of the parabola and hyperbola
Many revolutionsofthesun ago we were seeking a device that could construct a parabola. We made a discovery in this connection that is exceedingly elementary Euclid for mathematicians, but for us it was an insightgiving philosophical revelation. A parabola can be … Continue reading
Posted in Life, Scientific ramblings
Tagged conic sections, conics, Geometric construction, geometry, hyperbola, parabola, recreational geometry
Leave a comment