Tag Archives: mathematics

The mean hyperbola and other mean functions

Let be two numbers such that, We use to construct a specific rectangular hyperbola using one of the following methods: Method-I (Figure 1: this is based on an approach we described earlier) Figure 1 1) Mark point , which will … Continue reading

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The geometric principles behind discrete dynamical systems based on the generalized Witch of Agnesi

Consider the family of curves defined by the equation following parametric equation , where and It defines a family of probability distribution functions (PDFs): This can be seen from the above equations because Figure 1 Examples of these PDFs are … Continue reading

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Reflections on our journey through the aliquot sums and sequences

The numerology of aliquot sums and perfect numbers The numerology of the Pythagorean sages among the old yavana-s is one of the foundations of science and mathematics as we know it. One remarkable class of numbers which they discovered were … Continue reading

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Residues of squares, sequence curiosities and parabolas galore

Squares and their residues This is an exploration of number triangles in the same vein as some other such we have previously described . It resulted in some observations that seemed interesting to us. Some are perhaps trivial but some … Continue reading

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A note on the least prime divisor sequences of 2p plus or minus 1

Let be the sequence of prime numbers: 2, 3, 5, 7… Define the sequences such that . Then sequence is defined such that is the lowest prime divisor (LPD) of and sequence is defined so that is the LPD of … Continue reading

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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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