# Tag Archives: irrational numbers

## A sampler of Ramanujan’s elementary results and their manifold ramifications

As we have remarked before, Ramanujan seemed as if channeling the world-conquering strides of Viṣṇu, when he single-handedly bridged the lacuna in Hindu mathematics from the days of the brāhmaṇa-s of the Cerapada to the modern era. Starting around the … Continue reading

## A catalog of attractors, repellors, cycles, and other oscillations of some common functional iterates

One of the reasons we became interested in functional iterates was from seeking an analogy for the effect of selective pressure on the mean values of a measurable biological trait in a population. Let us consider a biological trait under … Continue reading

## Some observations on the Lekkerkerker-Zeckendorf decomposition of integers

In our youth, we learned of a nice arithmetic theorem of Lekkerkerker (more popularly known after Zeckendorf; hereinafter L-Z) that relates to the famous Mātrā-meru sequence : 0, 1, 1, 2, 3, 5, 8… defined by the recurrence relationship . … Continue reading

## Some biographical reflections on visualizing irrationals

In our childhood, our father informed us that, though the school told us that , it was not valid. However, he added that for “small fractions” [Footnote 1] it was a great approximation. Moreover, the numerical problems, which we would … Continue reading

## Bhāskara’s dual square indeterminate equations

PDF for convenient reading Figure 1. Sum and difference of squares amounting to near squares. In course of our exploration of the bhūjā-koṭi-karṇa-nyāya in our early youth we had observed that there are examples of “near misses”: . Hence, we … Continue reading

## Trigonometric tangles

Let us define a define the trigonometric tangle as the following parametric function: where can be a rational number or an irrational number. and are any real number. If is a rational number and then we get a tangle petals … Continue reading