Ramanujan cab numbers: a recreational mathematics activity

The story of the Indian mathematician Srinivasa Ramanujan is inspiring. None is more inspiring thanthe story of the Ramanujan cab number 1729 and the sequence of numbers defined by the equation:x^3 + y^3 = p^3 + q^3where x, y, p and q are distinct positive integers. 1729 is the smallest number that can be expressedas the sum of two cubes in two different ways:10^3 + 9^3 = 12^3 + 1^3 = 1729We introduce teaching activities and software that can inspire people and help them enjoy thesebeautiful mathematical creations.

BRAHMAGUPTA AND THE CONCEPT OF ZERO

This paper attempts to reconstruct the possible reasoning process that led the Indian mathematician Brahmagupta in 628 A.D. to the formulation of two controversial rules for arithmetic involving the number zero; rules which, contradict the modern arithmetic. This paper outlines a possible explanation of the issue based on similar reasoning.

Remembering Ramanujan

Mathematicians like Guido Grandi, Ernesto Cesaro and others found novel way of assigning finite sum to divergent series. This created a new scope of understanding leading to analytic continuation of real valued functions. One among such methods was called ``Ramanujan Summation'' proposed by Indian Mathematician Srinivasa Ramanujan. In this paper, I try to highlight how Ramanujan could have possibly arrived at those values by looking through his notebook jottings and extending further to provide Geometrical meaning behind those values obtained by him. Finally, I provide a novel way to arrive at the general formula obtained by Ramanujan regarding his summation of zeta function.

श्रीनिवास रामानुजन: एक सहज गणितज्ञ

Indian mathematician, Srinivas Ramanujan, lived a brief life. However, even in such a short period, he was successful in creating such ripples in the field of mathematics ,especially the research of the infinite series, that have made him immortal. This article throws light upon the extremely modest life this mathematical genius led and also on the beautiful mind we were privileged to have had among us.

Effectiveness of Vedic Mathematics in the Classrooms

Vedic Mathematics was discovered by Indian mathematician Jagadguru Shri Bharathi Krishna Tirtha in the period between A.D. 1911 and 1918. Later the findings were published in form of a book on Vedic Mathematics by Tirthaji Maharajwho was also known as Bharati Krsna. Bharati Krsna was born in 1884 and died in 1960. He was a brilliant student, obtaining the highest honours in all the subjects he studied, including Sanskrit, Philosophy, English, Mathematics, History and Science. When he heard what the European scholars were saying about the parts of the Vedas which were supposed to contain mathematics he resolved to study the documents and find their meaning. Between 1911 and 1918 he was able to reconstruct the ancient system of mathematics which we now call Vedic Mathematics.

The Great Art

This chapter discusses the origins of the art of algebra, beginning with the possibility that it may have come from the Greeks or from the Hindus. However, the Brahmins of northern India had some idea of algebra long before the Arabians learned it, contributed to it and brought that art to Spain in the late eleventh century. The Brahmasphutasiddhanta, written by the Indian mathematician Brahmagupta in 628, not only advanced the mathematical role of zero but also introduced rules for manipulating negative and positive numbers, methods for computing square roots, and systematic methods of solving linear and limited types of quadratic equations. The chapter also considers the contriburions of Abu Jafar Muhammad ibn Musa al-Khwārizmī and suggests that negative numbers originated in China, where they had been used since the beginning of the first millennium.

A classification of Kaprekar constant

The number 6174 has the well-known property that it equals the difference between the numbers formed by rearranging its digits in descending and ascending orders :Numbers with this property are called Kaprekar constants after the Indian mathematician D. R. Kaprekar [1]. Similarly, the general process of finding the difference between numbers formed by rearranging digits in descending and ascending orders is called the Kaprekar process.