Glimpses of Ancient Indian Mathematics

Glimpses of Ancient Indian Mathematics

There is amazing mathematics used in Hindu Rituals in constructions of Vedis and Citis.  These are described in Sulba Sutras, Instruction Manuals for the Priests to use in creating Fire Altars.

Rituals are described in Shrauta and Grihya Sutras.

From Mathematics in Ancient India Part 1 Overview

The oldest known mathematics  texts in existence are the Sulba-sutras  of Baudhayana, Apastamba and Katyayana which form part of the literature of the Sutra period of the later Vedic age. The Sulba sutras had been estimated to have been composed around 800 B C (some recent researchers are suggesting earlier dates). But the mathematical knowledge recorded in these sutras (aphorisms) are much more ancient ; for the Sulba authors emphasize that they were merely stating facts already known to the composers of the Brahmanas and Samhitas of the early Vedic age.

The Sulbasutras give a compilation of the results in mathematics that had been used for the designing and constructions of the various elegant Vedic fire-altars right from the dawn of civilization.The altars had rich symbolic significance and had to be constructed with accuracy. The designs of several of these brick-altars are quite involved for instance, there are constructions depicting a falcon in fight with curved wings, a chariot wheel complete with spokes or a tortoise with extended head and legs!  Constructions of the ̄fire-altars are described in an enormously developed form in the Satapatha Brahmana (c. 2000 B C ; vide [3]); some of them are mentioned in the earlier Taittiriya Samhita (c. 3000 B C ; vide [3]); but the sacrificial ̄fire-altars are referred without explicit construction in the even earlier Rig Vedic Samhitas, the oldest strata of the extant Vedic literature. The descriptions of the fire-altars from the Taittiriya Samhita onwards are exactly the same as those found in the later Sulbasutras.

From  Ancient Indian Mathematics : an overview

A major part of the body of mathematical knowledge from the Vedic period that has come down to us is from the Sulvasutras. The Sulvasutras are compositions aimed at providing instruction on the principles involved and procedures of construction of the vedis (altars) and agnis (fireplaces) for the performance of the yajnas, which were a key feature of the Vedic culture. The fireplaces were con- structed in a variety of shapes such as falcons, tortoise, chariot wheels, circular trough with a handle, pyre, etc (depending on the context and purpose of the par- ticular yajna) with sizes of the order of 20 to 25 feet in length and width, and there is a component of the Sulvasu ̄tras describing the setting up of such platforms with tiles of moderate sizes, of simple shapes like squares, triangles, and occasionally special ones like pentagons. Many of the vedis involved, especially for the yajnas for special occasions had dimensions of the order of 50 to 100 feet, and making the overall plan involved being able to draw perpendiculars in that setting. This was accomplished both through the method that is now taught in schools, involving perpendicularity of the line joining the centres of two intersecting circles with the line joining the two points of intersection, as also via the use of the converse of “Pythagoras theorem”; they were familiar with the “Pythagoras theorem”, and explicit statement of the theorem is found in all the four major Sulvasu ̄tras. The Sulvasu ̄tras also contain descriptions of various geometric principles and constructions, including procedures for converting a square into a circle with equal area, and vice versa, and a good approximation to the square root of 2 (see [4] for some details).



One of the best resource for published papers is Indian Journal of History of Science.


Key People:

  • Subhash Kak
  • Radha Charan Gupta
  • Vinod Mishra
  • A. Seidenberg
  • B Datta
  • S G Dani
  • A K Dutta
  • George Gheverghese Joseph.
  • Frits Staal
  • David Bailey
  • John Price
  • A. N. Singh
  • A. K. Bag
  • Kim Plofker
  • Georges Ifrah
  • R. N. Iyenger


Key Sources of Research:



Ancient Indian Square Roots: An Exercise in Forensic Paleo-Mathematics

David H. Bailey Jonathan M. Borwein

Click to access india-sqrt.pdf

Click to access india-sqrt-encyc.pdf




Sources for History of Indian Mathematics

R. C. Ranjan


Click to access ranjan1.pdf




Agni Kunda

R C Gupta

Click to access 20008275_1.pdf




Ancient Indian Mathematics : an overview


Click to access ancmathsources_Dani.pdf




The Greatest Mathematical Discovery?

David H. Bailey∗ Jonathan M. Borwein† May 8, 2011

Click to access decimal.pdf





Theorm of square on the diagonal in Vedic Geometry

V Mishra and S L singh

Click to access 20005b5f_157.pdf




Mystical Mathematics of Ancient Planets

R C Gupta

Click to access 2000c950-31.pdf







Click to access Vol45_1_4_RCGupta.pdf






R C Gupta

Click to access Vol42_2_4_RCGupta.pdf




Sri Yantra

Click to access Vol49_3_5_Pustynski.pdf




Sri Yantra

Click to access 20005b60_137.pdf





Gurudeo Anand Tularam;jsessionid=278E06CA597AC86D67817E8F7F028E30?sequence=1




Astronomy of the Vedic Altars

S Kak

Click to access VistasAst.pdf




Astronomy of the Satapatha Brahmana

S Kak

Click to access Vol28_1_2_SCKak.pdf





The Astronomy of the Age of Geometric Altars

S Kak




Sri Yantra

Click to access SriYantra.pdf






B S Shylaja


Click to access Vol48_2_6_BSShylaja.pdf




Use of Astronomical Principles in Indian Temple Architecture

B. S. Shylaja





The So-called Fibonacci Numbers in Ancient and Medieval India





Varāhamihira’s pandiagonal magic square of the order four

Takao Hayashi








Click to access Vol46_1_4_VMishra.pdf




On the Pythagorean triples in the Sulvasutras

S.G. Dani


Click to access pyth.pdf





Indian Numerals

RC Gupta

Click to access 20005af7_23.pdf








R N Iyengar and V H Satheeshkumar


Click to access Vol47_3_6_RNIyengar.pdf









Click to access Vol45_2_2_PTaneja.pdf





Mathematics in Ancient India

Amartya Kumar Dutta

Part 2 Diophantine Equations


Click to access 0006-0022.pdf

Part 1 Overview

Click to access Amartya.pdf






Henderson, David W.

“Square roots in the Sulba sutras.”

Geometry at Work: 39-45.




Applied Geometry of the Sulba Sutras

John F. Price

Click to access Applied+Geometry+in+SulbaSutras.pdf




Staal, Frits.

“Greek and Vedic geometry.”

Journal of Indian Philosophy 27.1 (1999): 105-127.





Seidenberg, Abraham.

“The origin of mathematics.”

Archive for history of exact sciences 18.4 (1978): 301-342.





Katz, Victor J., and Annette Imhausen.

The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook.

Princeton University Press, 2007.




Seidenberg, Abraham.

“The ritual origin of geometry.”

Archive for history of exact sciences 1.5 (1961): 488-527.





Seidenberg, Abraham.

“The ritual origin of counting.”

Archive for History of Exact Sciences 2.1 (1962): 1-40.





Seidenberg, Abraham.

“The ritual origin of the circle and square.”

Archive for History of Exact Sciences 25.4 (1981): 269-327.





Hindu Trigonometry




Bag, A. K.

“Ritual Geometry in India and its Parallelism in other Cultural areas.”

Indian J. Hist. Sci 25 (1990): 4-19.

Click to access 20005b58_4.pdf




Datta, Bibhutibhusan, and Avadhesh Narayan Singh.

“History of Hindu mathematics.”





Hindu Geometry

B Datta and A N Singh

Click to access Vol15_2_1_KSShukla.pdf





Ethnomathematics: A Multicultural View of Mathematical Ideas.


By Marcia Ascher.

Pacific Grove, CA (Brooks/Cole Publishing Co.). 1991. xii + 203 pp. including Index.




The Crest of the Peacock: Non-European Roots of Mathematics.

By George Gheverghese Joseph.

London (I. B. Tauris & Co., Ltd) and New York (St. Martin’s Press). 1991. xvi + 368 pp. including Bibliography and Index.




Math for Poets and Drummers

Rachel Wells Hall


Click to access mathforpoets.pdf




Landmarks of Science in Early India


M Danino

Click to access 105.pdf




Gupta, R. C.

“Yantras or Mystic Diagrams: A wide area for study in ancient and medieval Indian mathematics.”

Indian Journal of History of Science 42.2 (2007): 163.





Georges Ifrah,

The Universal History of Numbers,

John Wiley and Sons, 2000.





Archibald, R.

 “The Science of the Sulba. A Study in Early Hindu Geometry by Bibhutibhusan Datta.”

History of Science 22.1 (1934).




Mathematics in India

By Kim Plofker





Singh, Avadhesh Narayan.

History of Hindu mathematics: a source book. Parts I and II.

Asia Pub. House, 1962

Magic Squares in India

Dutta and Singh

Author: Mayank Chaturvedi

You can contact me using this email mchatur at the rate of AOL.COM. My professional profile is on

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