**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.

**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 theline 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

http://www.davidhbailey.com/dhbpapers/india-sqrt.pdf

http://www.davidhbailey.com/dhbpapers/india-sqrt-encyc.pdf

**Sources for History of Indian Mathematics **

R. C. Ranjan

http://www.ece.lsu.edu/kak/ranjan1.pdf

**Agni Kunda**

R C Gupta

http://www.dli.gov.in/rawdataupload/upload/insa/INSA_1/20008275_1.pdf

**Ancient Indian Mathematics : an overview**

Dani

http://www.tifr.res.in/~archaeo/FOP/FoP%20papers/ancmathsources_Dani.pdf

**The Greatest Mathematical Discovery?**

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

**Theorm of square on the diagonal in Vedic Geometry**

V Mishra and S L singh

http://www.dli.gov.in/rawdataupload/upload/insa/INSA_1/20005b5f_157.pdf

**Mystical Mathematics of Ancient Planets**

R C Gupta

http://www.dli.gov.in/data_copy/upload/INSA/INSA_1/2000c950-31.pdf

**TECHNIQUES OF ANCIENT EMPIRICAL MATHEMATICS**

R.C. GUPTA*

http://www.insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol45_1_4_RCGupta.pdf

**Yantras**

R C Gupta

http://www.insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol42_2_4_RCGupta.pdf

**Sri Yantra**

http://www.insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol49_3_5_Pustynski.pdf

**Sri Yantra**

http://www.dli.gov.in/rawdataupload/upload/insa/INSA_1/20005b60_137.pdf

**INVESTIGATING THE DEVELOPMENT OF ARITHMETIC AND ALGEBRA IN VEDIC INDIA: TRIBUTE TO SWAMI DAYANANDA SARASWATI**

Gurudeo Anand Tularam

**Astronomy of the Vedic Altars**

S Kak

http://www.peturhalldorsson.com/papers/papers/VistasAst.pdf

**Astronomy of the Satapatha Brahmana**

S Kak

http://insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol28_1_2_SCKak.pdf

**The Astronomy of the Age of Geometric Altars**

S Kak

http://adsabs.harvard.edu/full/seri/QJRAS/0036/0000385.000.html

** **

**Sri Yantra**

http://www.cincinnatitemple.com/articles/SriYantra.pdf

**DAKS.IN.AGNI IN SULBASUTRAS – AN ASTRONOMICAL INTERPRETATION**

B S Shylaja

2013

http://www.insa.nic.in/writereaddata/UpLoadedFiles/IJHS/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**

http://www.sciencedirect.com/science/article/pii/0315086085900217

**Varāhamihira’s pandiagonal magic square of the order four**

Takao Hayashi

http://www.sciencedirect.com/science/article/pii/031508608790019X

**COMPUTING N : A MODERN GENERALIZATION OF ANCIEN**T

TECHNIQUE

VINOD MISHRA

http://www.insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol46_1_4_VMishra.pdf

**On the Pythagorean triples in the Sulvasutras**

S.G. Dani

http://www.math.tifr.res.in/~dani/pyth.pdf

** ****Indian Numerals**

RC Gupta

http://www.dli.gov.in/rawdataupload/upload/insa/INSA_1/20005af7_23.pdf

**ARCHAEO-ASTRONOMICAL SIGNIFICANCE OF THE VEDIC**

**DARSAPAURNAMASA ALTAR**

R N Iyengar and V H Satheeshkumar

http://insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol47_3_6_RNIyengar.pdf

**ENLARGEMENT OF VEDIS IN ****THE SULBASUTRAS**

PADMAVATI TANEJA AND NIDHI HANDA

http://www.insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol45_2_2_PTaneja.pdf

**Mathematics in Ancient India**

Amartya Kumar Dutta

**Part 2 Diophantine Equations**

http://111.93.135.171/ResonanceNew/Volumes/07/10/0006-0022.pdf

Henderson, David W.

**“Square roots in the Sulba sutras.” **

Geometry at Work: 39-45.

http://www.math.cornell.edu/~dwh/papers/sulba/sulba.html

**Applied Geometry of the Sulba Sutras**

John F. Price

https://xa.yimg.com/kq/groups/3167322/26725216/name/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.

http://www.dli.gov.in/rawdataupload/upload/insa/INSA_1/20005b58_4.pdf

Datta, Bibhutibhusan, and Avadhesh Narayan Singh.

** “History of Hindu mathematics.”**

(1935).

**Hindu Geometry**

B Datta and A N Singh

http://www.insa.nic.in/writereaddata/UpLoadedFiles/IJHS/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

http://people.sju.edu/~rhall/mathforpoets.pdf

**Landmarks of Science in Early India**

M Danino

http://www.iisc.ernet.in/prasthu/pages/PP_data/105.pdf

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

Georges Ifrah,

**The Universal History of Numbers, **

John Wiley and Sons, 2000.

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

**Mathematics in India**

By Kim Plofker

2009

Singh, Avadhesh Narayan.

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

**Magic Squares in India**