Systems of Numerations

Introduction

Ancient Indians through the medium of poetry made Mathematics simplified and interesting. Through poetry it is easy to remember theorem or formulae and interesting also. The Science of Indian Mathematics was composed in many meters(chandas) of poetry. Ancient Indians found a unique way to express numbers in poetry. Hence the following two systems of number representation were born.

1. Bhūta-saṅkhyā system
2. Kaṭapayādi system

Bhūta-saṅkhyā

Bhūta-saṅkhyā is a system of representation of numbers where the numerals are expressed by certain words. The meanings of these words indicate numbers either naturally or by well known references in popular Indian literature. Bhūta-saṅkhyā is found in Chandassūtra of Piṅgala which was composed in 3rd Century BCE.

Representation of Numbers

Number '1' is represented by Candra which means moon. Moon is the only natural satellite of the earth which is unique. Any such unique object can be used for representing the number '1'. The other words popularly used to represent "1" are bhūmi (earth), rūpa (form) etc.

Number '2' is represented by any popular pairs, like the eyes, the hands, the Aśvinī twins.

Number '0' is represented by the word ākāśa (space) which stands for void.

Number '3' is represented by the word guṇa (triguṇa - three qualities namely Sattva, Rajas, and Tamas).

Number '4' is represented by the word Veda (Rig Veda, Yajur Veda , Atharva Veda, Sama Veda)

A common convention is used while using the words for representation of numbers. The Convention is to follow the rule "अङ्कानां वामतो गतिः" . It means that the numbers are to be read from right to left. Numbers expressed through the words are to be formed from the units place onwards.

aśvinī ākāśa guṇa kha candra rūpa bhūmi rāma bhūta bāṇa vāyu mahayajña ṛtu vedāṅga

List of words used as Bhūta-saṅkhyā

Numeral	Bhūta-saṅkhyā	Meaning	Details
0	Kha , Ākāśa	Space, Sky	Space represents void meaning zero
1	Candra Rūpa Bhūmi	Moon Form Earth	Earth has only one Moon Form is unique for each individual Earth is one
2	Netra Yamala Aśvinī	Eye Twin Twin Devatās	Humans have two eyes Twins Nāsatya, Dasra - Twin Aśvinī Devatas.
3	Guṇa Rāma	Quality Rāma	Sattva, Rajas, Tamas - 3 Qualities Paraśurāma, Balarāma, Dāśarathi Rāma
4	Veda	Veda	Ṛg, Yajur, Sāma and Atharva - 4 Vedas
5	Bhūta Mahayajña	Elements Sacrifice	Earth, Water, Fire, Air and Ākāśa - 5 elements Devayajña, Pitṛyajña, Manuyajña, Manuṣyayajña, Bhūtayajña - Pañcamahāyajña
6	Vedāṅga	Six auxiliary disciplines of Hinduism	Śikṣā, Vyākaraṇa, Kalpa, Nirukta, Jyotiṣa, Candas