Related papers: Cognition of the circle in ancient India
In this article we review some key time cycles in ancient Indian astronomy, especially those that have emerged from researches in the past couple of decades expressing knowledge of the changing frame of earth's axis. The article also…
The earliest origins of mathematics in the Indian subcontinent is generally dated around 800-500 BCE when the {\em Sulbasutras} are thought to have been written. In this article we suggest that mathematical thinking in South Asia, in…
Textual and archaeological sources are used to provide a synoptic vision of the universe in India. This vision was based on an assumed equivalence of the outer and the inner cosmoses and it is embodied in architecture, music, and art. It…
Despite the extensive amount of scholarly work done on Indian mathematics in the last 200 years, the conditions under which it originated and evolved is still not clear. Often, one reads the ancient texts with the present concepts and…
The cyclic model of the universe has an old history in India. It has held the preeminent position regarding the origins of the universe, and it is described in astronomical texts, Puranic encyclopaedias, and philosophical literature. Within…
Recent analyses of Brahmagupta's discourse on the cyclic quadrilateral, and of Baudh\=ayana's approximate quadrature of the circle, have shown that it is useful to submit mathematical texts to a form of literary analysis. Several passages…
This paper, third in the series on Indian tradition of physics, describes conceptions of the cosmos with ideas that are clearly spelt out in texts such as Yoga Vasishtha.In particular, the conception of multiple universes that occurs often…
In this article I conduct a short review of the proofs of the area inside a circle. These include intuitive as well as rigorous analytic proofs. This discussion is important not just from mathematical view point but also because…
This paper presents textual evidence for an astronomical basis of the dimensions of the axis and perimeter in the plan of the Indian temple.
In this survey paper we give an historical and at the same time thematical overview of the development of ring geometry from its origin to the current state of the art. A comprehensive up-to-date list of literature is added with articles…
This work explores a possible course of evolution of mathematics in ancient times in India when there was no script, no place-value system, and no zero. Reviewing examples of time-reckoning, large numbers, sacrificial altar-making, and…
This paper describes Indian ideas of the early-Purana/Mahabharata times (centuries BC) on the nature of space, time and consciousness that would be of interest to the physicist. In order to simplify references, we quote mainly from…
Formulas about the side lengths, diagonal lengths or radius of the circumcircle of a cyclic polygon in Euclidean geometry, hyperbolic geometry or spherical geometry can be unified.
In point of fact the Indian tradition in mathematics is long and glorious. It dates back to earliest times, and indeed many of the Indian discoveries from 5000 years ago correspond rather naturally to modern mathematical results.
Inscribed angles are investigated in taxicab geometry with application to the existence and uniqueness of inscribed and circumscribed taxicab circles of triangles.
The early Greek and Indian cosmologies are summarized in this paper. The two traditions appear to have developed independently although after the time of Alexander they were consciously aware of each other. The focus and style of the two…
We show that many ancient Indian mythological legends are really allegorical depictions of astronomical and other physical phenomena of which the composers had a good idea. This detail enables us to also use techniques of astronomical…
We describe briefly the recent advances in understanding the distributed nature of computations in the (neural) network structure of the brain. We discuss if such artificial networks will be able to perform mathematics and natural sciences.…
This paper provides an overview of the birth and early development of Indian astronomy. Taking account of significant new findings from archaeology and literary analysis, it is shown that early mathematical astronomy arose in India in the…
We study some properties of a triad of circles associated with a triangle. Each circle is inside the triangle, tangent to two sides of the triangle, and externally tangent to the circle on the third side as diameter. In particular, we find…