Cognition of the circle in ancient India

2013

Some Geometrical Concepts in earlier Indian works will be discussed. This talk includes a brief discussion on few topics including: the Sulba Sutras, Pythagorus Theorem, Transfer a Square into a Circle, Square Root of 2, Some trigonometry in ancient Indian works, the Vastu Shilpa Shastra, use of Geometry in Sulbha sutras to calculate the roots of the quadratic equation.

[The paper “Visual Grammar in South Asia: Meaning of Mathematics in Antiquity” on the occasion of Science and Technology in Premodern Asia: Coffee Break Conference, Oxford 2018, was presented for the session Mathematics & Astronomy chaired by Matt Kimberley, Research Curator, Asian & African Collections, The British Library.] Design defines a culture’s aesthetic. In ancient South Asia, society and craftsmen understood the value of mathematical adornment for cult purpose. Through learned skill the mathematically defined space on pottery, seals and sculpture display geometric patterns. The Flower of Life pained on the funerary pottery and the Hagal Rune incorporated in the hieroglyphic text on the Indus Valley tablet seals are repeated on the offering trays of Gandhara. From Swastika to series of Vesica Pisces, the arrangement of space extend to elaborate arrangement of symbolic motifs on disc stones, Pi-disks, homage tablets and seals, which are by themselves marvels in mathematical precision. The geometric elements on wide range of votive objects communicate faith in celestial spheres. The link between mathematics and astronomy is particularly discernible in the arched entrance to Lomas Rishi cave on the Barabar Hills in Bihar, India, which is similar to the first-century CE ivory torana gateway found in the royal stash in Begram, Afghanistan. The imagery on the Syrian arch high on symmetry and balance comparable to the Grand Royal Arch of the Freemasons not only convey meaning but the different moods of astronomical body in movement. By questioning the cognitive foundation on which such exceptional sacred objects were produced it is possible to uncover prior knowledge.

History of Science in South Asia

This article addresses on history of mathematics (specially one of its specific branch, geometry) in Sri Lanka. Despite the large amount of research on the history of mathematics in India, China and the Middle East, that on Sri Lanka still remains limited. Sri Lanka had close relations with all these regions from ancient times and knowldge on mathematics should not be an alien subject there. This article tries to address the paucity of research on the history of mathematics in Sri Lanka while emphasizing the local character of that ancient knowldge.

International Journal of Statistics and Applied Mathematics, 2025

This article explores the geometric knowledge from the Sulba Sutra and its relevance to school geometry using historical research methods collecting historical documents and analyzing them. Key assumptions, theory, theorems and practices were taken from Vedic texts Sulba Sutra and school mathematics texts. It examines key assumptions (Postulates) of Vedic ritual geometry, such as the construction of altars using precise proportions, alongside the Jatya Tribhuj (early right-angled triangle) and the Bhoja Koti Karna Nayana (Sulba theorem on right-angled triangles). Additional topics include shape transformations, symmetry, and the use of mean proportion. The research traces the mathematical content in various Sulba Sutras and their historical development. Similarly, a correlation of contents in school mathematics was established logically. The study concludes that Vedic ritual geometry's principles align with fundamental school geometry topics. Incorporating these concepts into school curricula can enhance students' engagement and understanding by linking abstract mathematical ideas to historical and cultural practices. This approach promotes hands-on, inclusive learning, blending ancient geometric knowledge with modern education for a culturally responsive teaching framework.

Journal of Northeastern University, 2022

Every religion has its own identity which is scripted in various religious texts in the form of sacred diagrams, motifs, etc. The power of these holy apices depends on the worshiper's beliefs and their satisfaction. Every natural geometry signifies its shape, size, character, and principles. Every aspect of an element present in the Universe can be analyzed through their governing attributes like-point, line, distance, angle, etc. The religious geometry of Hindu diagrams called Sri Yantra and Mandala, both are being an enigma in the whole Universe. It is a metaphysical philosophy which deals beyond the reality. Here, the paper proposes four strategies that can endeavors to reveal the mystic curtain of these religious diagrams over the world. First, study the geometrical configuration of the Sri Yantra and Mandala. Second, establishment of the fractal linkages between these sacred geometries. Third, construction of Sri Yantra and three suitable groups of Mandala. Lastly, interaction of the Mandala and Sri Yantra with the internal spaces in the sanctum sanctorum of Rajarani temple. Therefore, it is tried to make the study approach unique on its own to provide a basic platform and create some space for religiously oriented researchers.

6th International Conference on Geometry and Graphics MONGEOMETRIJA 2018, 2018

The architecture and mathematics of ancient India based on the same principles of traditional geometry. The most important geometric constructions, which underlain the traditional Hindu architectural theory, were regular square grids, known as Vastu-Purusa Mandalas, and different Pythagorean triangles applied to proportioning of altars. In the paper it is demonstrated that these two as it may seem quite distant fields of geometry constitute mutually complementary processes. The regular square grids generate all possible Pythagorean triangles and the triangles in turn generate the more and more sophisticated square grids.

I have argued for the existence in (what Western Europe sees as) the Near East of a long-lived community of practical geometers -first of all surveyors -which was not or only marginally linked to the scribe school traditions, and which (with branchings) carried a stock of methods and problems from the late third millennium BCE at least into the early second millennium CE. The arguments for this conclusion constitute an intricate web, and I shall only repeat those of them which are of immediate importance for my present concern: the links between the geometrical section of Mahāvīra's Ganita-sāra-saṅgraha and the practical mathematics of the Mediterranean region in the classical ages.

Hindustan Book Agency, 2004

Open Access Journal of Astronomy, 2025

In the present paper a brief account of ancient astronomy covering the Pre-Siddhanta period and the Siddhanta Jyotish period is given. Five Siddhanta books supposed to be written by the sages are described and some other books on astronomy written by outstanding mathematicians and astronomers are also discussed. The historical development of Ancient Mathematics regarding various manuscripts is described with examples. In particular, the development of decimal systems and numerals with zero symbols are discussed in detail. Some concluding remarks are also given with a list of references in the end.

Geography in ancient India refers to the metaphysical exposition of interconnectedness of man with nature aiming to understand humanity's residence on the earth. In geography, the " geo-" refers to the biological idea of mother Earth, Gaia, and "-graphy " to a cultural connotation referring to subjective meaning of place – with human interference and connectedness (e.g. love) space transfers to place. This was a kind of " deep " geography, where historical-cultural-ecological-landscape concerns altogether make a sense of meaning and understanding. In the present era of 'global understanding', the messages of geography in ancient India is being accepted as a light-tower for ecological awareness that commonly envisioned in the frame of 'sacred ecology'. Zukav (1979: 217) remarks that " Hindu mythology is virtually a large scientific discovery. Hindu deities such as Shiva and Vishnu continuously dance the creation and destruction of universe ". The relevance for life is inherent in the Hindu religion with its pantheon of Gods; the Hindu view is God-filled space – of an animate universe. Initiated in the historical past, the Vedic, Puranic literature and treatises fully describe the sense of respect for nature and attempt to make awareness of the crisis calling for profound changes in the way human beings relate to the natural world (cf. Chaitanya 1983). Some of these examples are illustrated here. Attempts have also been made to elucidate the geography in ancient India, however most of such works considered the notion and framework of concept of the universe and the earth, astronomical and climatic aspects, the places known and the settlement patterns (cf. Dubey 1967). The description of regional identity and regional geography (natural and cultural landscapes) has further been taken into account with reference to the Puranas while emphasising some notions of cosmogony and cosmology (cf. Ali 1983), however less emphasis is laid on the 'geographical thought' and metaphysical context, which may be compared with the scientific notion of modern geography. In fact, most of these studies deal with literary interpretation of the epics and ancient literature (Dhussa 2008: 74-75).