Systems of Numerations

From Vigyanwiki

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 Moon Earth has only one Moon
Rūpa Form Form is unique for each individual
Bhūmi Earth Earth is one
2 Netra Eye Humans have two eyes
Yamala Twin Twins
Aśvinī Twin Devatās Nāsatya, Dasra - Twin Aśvinī Devatas.
3 Guṇa Quality Sattva, Rajas, Tamas - 3 Qualities
Rāma Rāma Paraśurāma, Balarāma, Dāśarathi Rāma
4 Veda Veda Ṛg, Yajur, Sāma and Atharva - 4 Vedas
5 Bhūta Elements Earth, Water, Fire, Air and Ākāśa - 5 elements
Mahayajña Sacrifice Devayajña, Pitṛyajña, Manuyajña, Manuṣyayajña, Bhūtayajña - Pañcamahāyajña
6 Vedāṅga 6 auxiliary disciplines of Hinduism Śikṣā, Vyākaraṇa, Kalpa, Nirukta, Jyotiṣa, Candas
Rasa Taste Sweet, salt, sour, pungent, astringent, and bitter
7 Muni, Ṛsi Sage kaśyapa atri vasiṣṭha viśvāmitra gautama jamadagni bhāradhvāja
Parvata Mountain
Svara Musical Note Seven notes in Indian music - ṣaḍja, ṛśabha, gāndhāra, madhyama pañcama, dhaivata, niśāda.