The Notational Places in Āryabhaṭīyam: Difference between revisions

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*In Mahāvīrācārya's Gaṇitasārasaṅgraha - 10<sup>24</sup> (mahākṣobham - महाक्षोभम्)
*In Mahāvīrācārya's Gaṇitasārasaṅgraha - 10<sup>24</sup> (mahākṣobham - महाक्षोभम्)
==See Also==
==See Also==
[https://alpha.indicwiki.in/index.php?title=%E0%A4%86%E0%A4%B0%E0%A5%8D%E0%A4%AF%E0%A4%AD%E0%A4%9F%E0%A5%80%E0%A4%AF%E0%A4%AE%E0%A5%8D_%E0%A4%AE%E0%A5%87%E0%A4%82_%27%E0%A4%B8%E0%A4%BE%E0%A4%82%E0%A4%95%E0%A5%87%E0%A4%A4%E0%A4%BF%E0%A4%95_%E0%A4%B8%E0%A5%8D%E0%A4%A5%E0%A4%BE%E0%A4%A8%27 आर्यभटीयम् में 'सांकेतिक स्थान']
[[आर्यभटीयम् में 'सांकेतिक स्थान']]
==References==
==References==
<references />
<references />
[[Category:Mathematics in Āryabhaṭīyam]]
[[Category:Mathematics in Āryabhaṭīyam]]

Revision as of 14:08, 31 July 2023

Introduction

Here we will know the place values as per Āryabhaṭīyam.

Verse

एकं च दश च शतं च सहस्रं त्वयुतनियुते तथा प्रयुतम् ।

कोट्यर्बुदं च वृन्दं स्थानात् स्थानं दशगुणं स्यात् ॥

Translation

Ekam (units place), daśa (tens place) , śatam (hundreds place), sahasram (thousands place) , ayutam (ten thousands place) , niyutam (lakhs place) , prayutam (ten lakhs place) , koṭiḥ (crores place), arbudam (ten crores place), vṛndam (hundred crores place) are respectively from place to place , each ten times the preceding.[1]

Position Name Place Value
1 Ekam (एकम्) 1
2 Daśa (दश) 10
3 Śatam (शतम्) 100
4 Sahasram (सहस्रम्) 1000
5 Ayutam (अयुतम्) 10000
6 Niyutam (नियुतम्) 100000
7 Prayutam (प्रयुतम्) 1000000
8 Koṭiḥ (कोटिः) 10000000
9 Arbudam (अर्बुदम्) 100000000
10 Vṛndam (वृन्दम्) 1000000000
109 108 107 106 105 104 103 102 101 100
0 0 0 0 0 0 0 0 0 0
hundred crores place ten crores place crores place ten lakhs place lakhs place ten thousands place thousands place hundreds place Tens place Units place

In this śloka Āryabhaṭa defines 10 place values. In India numbers larger than (109) were in use.

Examples -

  • In Yajurveda - 1019 (lokaḥ - लोकः)
  • In Vālmīkirāmāyaṇa - Yuddhakāṇḍa 28th sarga - 1060 (mahaughaḥ - महौघः)
  • In Bhāskarācāryā's (2nd) Līlāvatī - 1017 (Parārdham -परार्धम् )
  • In Mahāvīrācārya's Gaṇitasārasaṅgraha - 1024 (mahākṣobham - महाक्षोभम्)

See Also

आर्यभटीयम् में 'सांकेतिक स्थान'

References

  1. ↑ Āryabhaṭīyam (Gaṇitapādaḥ) (in Saṃskṛta). Delhi: Samskrit Promotion Foundation. 2023. pp. 3–5.{{cite book}}: CS1 maint: unrecognized language (link)
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