Tag Archives: Geometric construction

Triangles, Hexes and Cubes

Posted on October 23, 2017 by

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 →

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Citrabhānu’s cubes

Posted on September 22, 2017 by

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 →

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Hofstadter and Nārāyaṇa: connections across space and time

Posted on August 14, 2017 by

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 →

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Median and pedal triangles and derived fractals: an introductory account

Posted on August 3, 2017 by

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 self-evident geometric … Continue reading →

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Means and conics

Posted on July 22, 2017 by

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 →

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Leaves from the scrapbook-2

Posted on July 3, 2017 by

As described here these entries are from the scrapbook of Somakhya. Entry 11; Arasa, year Pramādin of the first cycle: It was our first day at Kshayadrajanagara. I had exhausted all that was there to talk with my cousins Mandara … Continue reading →

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Cobwebs on the golden hyperbola and parabola

Posted on June 17, 2017 by

The material presented here is rather trivial to those who have spent even a small time looking at chaotic systems. Nevertheless, we found it instructive when we first discovered it for ourselves while studying conics. Hence, as part of recording … Continue reading →

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