Tag Archives: geometry

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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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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The incredible beauty of certain Hamiltonian mappings

In our teens we studied Hamiltonian functions a little bit as part of our attempt to understand classical and quantum physics. A byproduct of it was a superficial interest in the geometry of some of the mappings arising from such … Continue reading

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Triangles, Hexes and Cubes

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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The Satija-Ketoja system

Satija and Ketoja discovered an interesting dynamical system in course of the study of the Schrödinger equation for one electron in a two dimensional periodic lattice on a uniform magnetic field. While this equation and its variants have several uses … Continue reading

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Some simple maps specifying strange attractors

This note may be read a continuation of: Some reminiscences of our study of chaotic maps-2 While the story of the chaotic 2D attractors began with the simple-looking maps of Henon and Lozi, by the early 1990s the high-point was … Continue reading

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Citrabhānu’s cubes

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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