Tag Archives: conics

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

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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

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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

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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

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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

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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

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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

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