Author Archives: mAnasa-taraMgiNI

A sequence related to prime counting

The current note arose as an exploration branching off from the matter discussed in these earlier notes: this one and this one. As we saw before, Carl Gauss, while still in his teens, produced his first estimate of the prime … Continue reading

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Convergence to a palindrome

This is a brief account of a sequence we constructed inspired by Dattatreya Ramachandra Kaprekar. It is not known to us if he had discovered it in one of his obscure publications from a small town in the Maharatta country. … Continue reading

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A problem from 600 CE and some curiosities of Āryabhaṭa’s kuṭṭaka algorithm

Around 600 CE in the examinations of one of the Hindu schools of mathematics and astronomy one might have encountered a problem such as below (given by Bhāskara-I in his commentary on Āryabhaṭa’s Āryabhaṭīya): dvayādyaiḥ ṣaṭ-paryantair ekāgraḥ yo ‘vaśiṣyate rāśiḥ … Continue reading

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A brief note on some new developments regarding the genomics of Indians

When we wrote a previous article on this matter we had stated that new data will alter the details of our understanding of picture discussed therein. Indeed, two new manuscripts which were deposited in the past month by McColl et … Continue reading

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The remarkable behavior of a map displaying derived from a simple model for a biological conflict

One of the simplest yet profound mathematical models for biological growth emerged sometime in the middle of the 1800s due to the work of Verhulst. It describes population growth thus: let be the population of the organism at time . … Continue reading

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A day at school

It was the English class in school. The teacher, a swarthy man with somewhat liberal political leanings, strode into the class: “Today we shall be studying a poem by the white American poet Robert Frost, Fire and Ice. Dandadipa, stand … Continue reading

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Mongolica: Qubilai Khan’s campaign to destroy the Southern Song

The final act in Mongol conquest of China shows the military capability of Qubilai and why his grandfather, the great Khan had singled him out as the one who someday would adorn his throne. We shall place here a very … Continue reading

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