The Notational Places in Āryabhaṭīyam: Difference between revisions
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Revision as of 19:08, 16 August 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'
