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Some elementary lessons from iterative fractal maps
The famous Sierpinski gasket was one of the first fractals we wrote code for when we got access to a computer. It impressed us enormously that an intricate object with self-similarity over all scales...
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Some reminiscences of our study of chaotic maps-2
Continued from part-1 The second two dimensional map we studied in our early days was that of Lozi: where and are constants. It becomes immediately evident that this map is conceptually similar to the...
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Matters of religion: “he becomes Naravāhanadatta”
Somakhya’s mother (SM) and Lootika’s mother (LM) ran into each other during their visit to the shrine of Rudra beside the river on a Monday evening. They sat at the platform below the vast aśvattha...
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A strange Soviet construction
in our college days we used to visit the lāl-pustak-bhaṇḍār in our city where Soviet books on science and mathematics were sold at a low price (alongside Marxian literature). They were a great resource...
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“Like the vidyādhara’s sword”
In old Hindu tradition a man who attained siddhi in his mantra practice was believed to become a vidyādhara whose might was manifest in the form his beautiful female partner who flew beside him...
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Deliberations on richness and beauty: discovery of some multi-parameter...
As we have explained in the earlier notes (1, 2, 3), the second major factor in our exploration of 2D strange attractors maps, IFS and other fractals was the aesthetic experience they produced. Around...
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loka-nīti-carcā
loka-nIticharchA vijaya-nāma mahā-mlecchānām bahuprajāvān bahupatnīvāṃś ca vyāpārī gṛha-krayāc chailūṣa-pradarśanāc ca mahādhany abhavat । sa marūnmattair abhibhṛtāṃ pūrvatana-mleccha-rāja-patnīm...
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The great faceless man
In the late Yajurvaidika upaniṣat, the Śvetāśvatara, which is the foundational text of the śaiva-śāsana, the god Rudra is described thus: na tasya pratimā asti yasya nāma mahad yaśaḥ। There is no one...
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The Rāmāyaṇa and a para-rāmāyaṇa in numbers-I: epic as religion
This note may be read as part of our studies on the Rāmāyaṇa and para-Rāmāyaṇa-s of which an earlier part is presented here. A study of the epic in Indo-European tradition suggests that there were two...
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Early Hindu mathematics and the exploration of some second degree...
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...
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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...
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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...
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Some visions of infinity from the past and our times
The great Hindu mathematician and astronomer Bhāskara-II’s work preserves a high-point of Hindu knowledge. His work contains ideas that are often seen as characterizing “modern” scientific...
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Trigonometric tangles
Let us define a define the trigonometric tangle as the following parametric function: where can be a rational number or an irrational number. and are any real number. If is a rational number and then...
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A prefatory narrative
Jhilleeka and Prachetas were visiting Lootika and Somakhya. Prithika, the daughter of the latter two was much excited as she resembled and was to resemble her youngest aunt in more than one way – they...
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Śarabha vidhi
The account of this rite continues from the prefatory narrative. Lootika: “There are several ways in which Rudra is worshipped as Śarabha conceived as the great dinosaur. We shall follow the way which...
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Trigonometric tangles-2
We had earlier described our exploration of the spirograph, hypocycloids, epicycloids and related curves. In course of our study of the śaiva tantra-s of the kaula tradition we started thinking about a...
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Euler’s squares
On account of our fascination with the geometry of origami (albeit not well-endowed in mathematical capacity) we discovered for ourselves shortly after our father had taught us trigonometry that, We...
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Marching onward in the American spring but where to?
We hear in the news that the students (and whoever else) at the University of California, Berkeley, are in state of ferment. This is unsurprising in itself given that the it has for long been the...
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Trigonometric tangles-3: the fractals
See also: https://manasataramgini.wordpress.com/2016/05/06/the-astroid-the-deltoid-and-the-fish-within-the-fish/ This exploration began in days of youth shortly after we learned about complex numbers....
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