Rituals and Origins of Mathematics
Key Terms
- A. Seidenberg
- B. L. VAN DER WAERDEN
- Fritz Staal
- Amartya Kumar Dutta
- K. Plofker
- O. NEUGEBAUER
- Subhash Kak
- Radha Charan Gupta
- George Gheverghese Joseph
- Jan Gonda
- Geometry
- Algebra
- Geometrical Algebra
- Algebraic Geometry
- Rituals
- Ritual Origin of Geometry
- Ritual Origin of Counting
- Space
- Time
- Measuring of Space
- Counting of Time
- Greece
- Babylon
- Mesopotamia
- Gudea of Lagash
- Vedic India
- Egypt (Misr)
- China
- Tibet
- England
- Sulba Sutra
- Sulb – To Measure
- Migrations and Diffusions
- Culture, Knowledge, Traditions
- Circle and Square
- Heaven and Earth
- Vedic Mathematics
- Mesoamerica
Source: Awakening of Geometrical Thought in Early Culture
Source: Awakening of Geometrical Thought in Early Culture
Source: The ritual origin of geometry
Let us sum up the history of geometry from its beginnings in peg-and-cord constructions for circles and squares.
The circle and square were sacred figures and were studied by the priests for the same reason they studied the stars, namely, to know their gods better. The observation that the square on the diagonal of a rectangle was the sum of the squares on the sides found an immediate ritual application. Its elaboration in the sacrificial ritual gave it a dominant position in ancient thought and ensured its conservation for thousands of years. This initial elaboration took place well before 2000 B.C. By 2000 B.C., it was already old and had diffused parts of itself into Egypt and Babylonia (unless, indeed, one of these places was the homeland of the elaboration). These parts became the basis of a new development in these centers. The new, big development was the solution of the quadratic. A thousand years and more later, Greece inherited algebra from Babylonia, but its geometry has more of an Indian than a Babylonian look. It inherited geometric algebra, the problem of squaring the circle, the problem of expressing √2 rationally, and some notions of proof.
Source: Mathematics in India / Part 1: Geometry in Vedic and Sūtra literature
Source: The ritual origin of geometry
Source: The ritual origin of counting
Source: On the volume of a sphere
Source: The Ritual Origin of the Circle and Square
My Related Posts
Glimpses of Ancient Indian Mathematics
Rituals | Recursion | Mantras | Meaning : Language and Recursion
Myth of Invariance: Sound, Music, and Recurrent Events and Structures
Sounds True: Speech, Language, and Communication
Key Sources for Research
The ritual origin of counting.
Seidenberg, A.
Arch. Hist. Exact Sci. 2 (1962b), 1-40.
https://www.jstor.org/stable/41133226
The origin of mathematics.
Seidenberg, A. (1978).
Archive for History of Exact Sciences, 18, 301-342.
The ritual origin of geometry.
Seidenberg, A. (1961).
Archive for History of Exact Sciences, 1, 488-527.
https://link.springer.com/article/10.1007/BF00327767
“Geometry of the Vedic Rituals,”
A. SEIDENBERG 1983.
in F. STAAL (ed.), Agni, the Vedic Ritual of the Fire Altar, 2 vols., Berkeley, vol. 2.
The Ritual Origin of the Circle and Square
Seidenberg, A. (1981).
Archive for History of Exact Sciences 25, no. 4 (1981): 269–327.
https://www.academia.edu/5112088/The_Ritual_Origin_of_the_Circle_and_Square
http://www.jstor.org/stable/41133635.
The Separation of Sky and Earth at Creation,
A. Seidenberg (1959)
Folklore, 70:3, 477-482, DOI: 10.1080/0015587X.1959.9717190
https://www.tandfonline.com/doi/abs/10.1080/0015587X.1959.9717190
The Separation of Sky and Earth at Creation (II),
A. Seidenberg (1969)
Folklore, 80:3, 188-196, DOI: 10.1080/0015587X.1969.9716636
https://www.tandfonline.com/doi/pdf/10.1080/0015587X.1969.9716636
The Separation of Sky and Earth at Creation (III),
A. Seidenberg (1983)
Folklore, 94:2, 192-200, DOI: 10.1080/0015587X.1983.9716277
https://www.tandfonline.com/doi/abs/10.1080/0015587X.1983.9716277?src=recsys
On the volume of a sphere.
Seidenberg, A.
Arch. Hist. Exact Sci. 39, 97–119 (1988).
https://doi.org/10.1007/BF00348438
https://link.springer.com/article/10.1007/BF00348438#citeas
https://www.jstor.org/stable/41133846
“On the Area of a Semi-Circle,”
A. Seidenberg 1972.
Archive for History of Exact Sciences 9, 171–211.
GREEK AND VEDIC GEOMETRY.
Staal, F. (1999).
Journal of Indian Philosophy, 27, 105-127.
https://link.springer.com/article/10.1023/A:1004364417713
The Mathematics of India
Concepts, Methods, Connections
a review by avinash sathaye
Mathematics in India
Part 1: Geometry in Vedic and Sūtra literature
By Amartya Kumar Dutta
Mathematics in India
Part 2: Computational Mathematics in Vedic and Sūtra Literature
Amartya Kumar Dutta
Mathematics in India
Part 3: The Decimal Notation and some Arithmetic Algorithms
Amartya Kumar Dutta
Mathematics in India
Part 4: Principles of Arithmetic
Amartya Kumar Dutta
Mathematics in India
Part 5: The Kuṭṭaka Algorithm
Amartya Kumar Dutta
Mathematics in India
Mathematics in India
Part 6: The Foundations of Algebra – Glimpses
Amartya Kumar Dutta
Mathematics in India.
K. Plofker,
The mathematics of Egypt, Mesopotamia, China, India, and Islam (ed. V. Katz), Princeton Univ. Press, Princeton, 2007.
Emergence of a New Era in the History of Indian Mathematics
Historiography of the Kerala School of Astronomy and Mathematics, 1820–2021: Some Highlights
By M.D. Srinivas
Geometry and Algebra in Ancient Civilizations.
B. L. VAN DER WAERDEN 1983.
Berlin.
The Exact Sciences in Antiquity
O. NEUGEBAUER 1962.
Princeton.
“On the Sulvasutras,”
G. Thibaut 1875.
J. Asiatic Society Bengal, vol. 44: 1.
Mathematics in Ancient India
1. An Overview
Amartya Kumar Dutta
RESONANCE I April .2002
https://www.ias.ac.in/article/fulltext/reso/007/04/0004-0019
Ancient Indian Leaps into Mathematics
B.S. Yadav
Man Mohan Editors
ISBN 978-0-8176-4694-3
DOI 10.1007/978-0-8176-4695-0
Springer New York Dordrecht Heidelberg London
Gaṇitānanda: Selected Works of Radha Charan Gupta on History of Mathematics
edited by K. Ramasubramanian
https://link.springer.com/book/10.1007/978-981-13-1229-8
Three Old Indian Values of π
Subhash Kak
The History of Mathematics: A Reader
John Fauvel and Jeremy Gray
1987
Is Mathematics Connected to Religion?
by Stanisław Krajewski
The penultimate version of the chapter to appear in: Sriraman, Bharat (ed) Handbook of the History and Philosophy of Mathematical Practice. Springer, Cham, 2022.
DOI https://doi.org/10.1007/978-3-030-19071-2_77-1
Indian Mathematics and Astronomy: Some Landmarks
Rao, S. Balachandra;
Jnana Deep Publications, Bangalore, 1994 (rev 98)
ISBN 81-9100962-0-6
https://www.cse.iitk.ac.in/users/amit/books/rao-1994-indian-mathematics-astronomy.html
The History of Mathematics
AN INTRODUCTION
David M. Burton
University of New Hampshire
The Crest of the Peacock. NonEuropean Roots of Mathematics
Joseph, George Gheverghese (1990),
London: Penguin Books.
“Agnicayana: the Piling Up of svayamatrnna,”
Kashikar, C. G. (1979),
Annals of the Bhandarkar Oriental Research Institute 60: 215–218.
The Science of Ritual,
Staal, Frits (1982),
Poona: Bhandarkar Oriental Research Institute.
AGNI. The Vedic Ritual of the Fire Altar, I-II,
Staal, Frits, in collaboration with C. V. Somayajipad and M. Itti Ravi Nambudiri (1983),
Berkeley: Asian Humanities Press.
“The Ignorant Brahmin of the Agnicayana,”
Staal, Frits (1978),
Annals of the Bhandarkar Oriental Research Institute 59: 337–348.
The Ritual Sutras,
Gonda, Jan (1977),
Wiesbaden: Otto Harrassowitz.
Awakening of Geometrical Thought in Early Culture
by Paulus Gerdes
https://conservancy.umn.edu/bitstream/handle/11299/149158/gerdes.pdf;sequence=1
Advancements of Ancient India’s Vedic Culture
by Stephen Knapp
DEVELOPMENT IN MATHEMATICS
By Stephan Knapp
Development in Mathematics
1 – Indian Third Wave West: Fertile Cresent and mathematics
N.S. Rajaram
Posted on Feb 19, 2013 by VOI
2 – Indian Third Wave West: From language to thought
N.S. Rajaram
Posted on Apr 7, 2013 by VOI
1 & 2 – Indo-Europeans: Their origins and the natural history of their languages
N.S. Rajaram
Posted on Dec 23, 2012 by VOI
3 – Indo-Europeans: Pashupati’s animals on the march
N.S. Rajaram
Posted on Jan 8, 2013 by VOI
Philosophical Problems of Mathematics in the Light of Evolutionary Epistemology
YEHUDA RAV
Séminaire de Philosophie et Mathématiques, 1988, fascicule 6
« Philosophical problems of mathematics in the light of evolutionary epistemology », , p. 1-30
<http://www.numdam.org/item?id=SPHM_1988___6_A1_0>
Aspect-Perception and the History of Mathematics
Akihiro Kanamori
August 17, 2017
A quest for exactness: machines, algebra and geometry for tractional constructions of differential equations. History and Overview
Pietro Milici.
[math.HO]. Université Paris 1 – Panthéon Sorbonne; Università degli studi di Palermo, 2015. English. NNT : . tel-01889365
https://theses.hal.science/tel-01889365/document
The Origins of Mathematics
The Origin of Mathematics.
Walicki, M. (1994).
THE VEDIC FOUNDATIONS OF THE ANCIENT PYRAMID CIVILIZATIONS
Milorad Ivanković
(Non-affiliated independent researcher) Vršac (Verschez), Serbia.
Vol.7 Issue 3 (July-Sept.) 2021
Click to access 1-26-VEDIC-FOUNDATIONS-ANCIENT-PYRAMID-CIVILIZATIONS.doc.pdf
A Brief History of Indian Science. From Mathematics to Medicine.
JULY 18, 2021
AUTHORED BY: SUBHASH KAK
https://cisindus.org/2021/07/18/a-brief-history-of-indian-science-from-mathematics-to-medicine/
A Brief History of Indian Science. Some Underlying Principles.
JULY 18, 2021
AUTHORED BY: SUBHASH KAK
https://cisindus.org/2021/07/02/a-brief-history-of-indian-science-1/
PRAJĀPATI-PURUSA AND VEDIC ALTAR CONSTRUCTION
James L Kelley
Geometrical Concepts in Indian Ancient Works
Bhavanari Satyanarayana
https://www.academia.edu/24450462/Geometrical_Concepts_in_Indian_Ancient_Works
Variations of the Vedic Unit “Prakrama” (Step) Applied for Measuring Length at Ritual Sites (With Excursus: “Prakramas in the Kerala Vedic Tradition”)
TESHIMA Hideki
Manuscript for contributing “Sciences of the Ancient World Matter 2” (ed. Karine CHEMLA, Agathe KELLER, et al., in preparation for publishing)
Pānini and Euclid: Reflections on Indian Geometry
Johannes Bronkhorst
2001, Journal of Indian Philosophy
https://www.academia.edu/3747402/Pānini_and_Euclid_Reflections_on_Indian_Geometry
WAS THERE SOPHISTICATED MATHEMATICS DURING VEDIC AGE?
AMARTYA KUMAR DUTTA
Equation Solving in Indian Mathematics
Rania Al Homsi
Department of Mathematics Uppsala University
Emergence of a New Era in the History of Indian Mathematics
Historiography of the Kerala School of Astronomy and Mathematics, 1820–2021: Some Highlights
By M.D. Srinivas
Bhavana, volume 6 issue 1 january 2022
A Bigger Altar Geometry & Ritual
Lawrence Brenton
Agni-kundas — a neglected area of study in the history of ancient Indian mathematics,
(Gupta, RC, 2003)
Indian Journal of History of Science, 38.1 (2003) 1-15.
Science of the Sacred
Ancient Perspectives for Modern Science
Compiled by
David Osborn
The Circle and the Square: Measure and Ritual in Ancient China,
Robert Poor (1995)
Monumenta Serica, 43:1, 159-210, DOI: 10.1080/02549948.1995.11731271
https://www.tandfonline.com/doi/pdf/10.1080/02549948.1995.11731271
In Square Circle: Geometric Knowledge of the Indus Civilization
Sitabhra Sinha∗, Nisha Yadav∗∗ and Mayank Vahia∗∗
*The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India. e-mail: sitabhra@imsc.res.in
**Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India.
The astronomy of the age of geometric altars
Subhash C. Kak∗
Quarterly Journal of the Royal Astronomical Society, vol. 36, 1995, pp. 385-396
Viewpoints which Matter 