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mAnasa-taraMgiNI supplement
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Recent Posts
- Looking back at the goroga attacks and forward at geopolitical developments
- Khitans and Mongols: A story of deep and persistent connections-1
- The rise of the psychopath oligarchy
- The rise of yajña and Kauśika exceptionalism
- Tricakra
- Yantrasiddhi
- The dreadful apport
- 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
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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 long-standing 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 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
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
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Division-multiplication parabolas, triplications, and quadratic residues
Introduction Many strands of our investigations on conic-generating 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, Mephisto-Waltz, numbers, parabola, prime numbers, sequence
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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
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The quotient triangle, the parabola-hyperbola 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
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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
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 mathematician-scientists 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
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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 straight-edge 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
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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 yavana-s 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
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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, nine-point circle, orthocenter, Spieker point, triangles
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Fancies of the parabola and hyperbola
Many revolutions-of-the-sun 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 insight-giving philosophical revelation. A parabola can be … Continue reading
Posted in Life, Scientific ramblings
Tagged conic sections, conics, Geometric construction, geometry, hyperbola, parabola, recreational geometry
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