Notational Places in Pāṭīgaṇitam: Difference between revisions
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[[Category:Mathematics in Pāṭīgaṇitam]] | [[Category:Mathematics in Pāṭīgaṇitam]] | ||
[[Category:General]] | [[Category:General]] | ||
Here we will know the names used to denote the place value of digits as mentioned in Pāṭīgaṇitam. | |||
==Verse== | |||
एकं दश शतमस्मात्सहस्रमयुतं ततः परं लक्षम् । | |||
प्रयुतं कोटिमथार्बुदमब्ज खर्वं निखर्वं च ॥ ७ ॥ | |||
तस्मान् महासरोजं शङ्कुं सरितां पतिं ततस्त्वन्त्यम् । | |||
मध्यं परार्द्धमाहुर्यथोत्तरं दशगुणं तज्ज्ञाः ॥ ८ ॥ | |||
==Translation== | |||
ekam , daśa , śatam , sahasram , ayutam , lakṣam , prayutam, koṭiḥ, arbudam , abjam , kharvaḥ, nikharvaḥ , mahāsarojam , śaṅku , saritapati , antyam , madhyam and parārdham are each stated to be ten times the preceding by those who have a knowledge of them.<ref>{{Cite book|last=Shukla|first=Kripa Shankar|title=The Pāṭīgaṇita of Śrīdharācārya|publisher=Lucknow University|year=1959|location=Lucknow|pages=2}}</ref> | |||
{| class="wikitable" | |||
!Name | |||
!Indian Notation | |||
!Power | |||
Notation | |||
!Indian System | |||
|- | |||
|एकम् (''ekam'') | |||
|<small>1</small> | |||
|10<sup>0</sup> | |||
|One | |||
|- | |||
|दश (''daśa'') | |||
|<small>10</small> | |||
|10<sup>1</sup> | |||
|Ten | |||
|- | |||
|शतम् (''śatam'') | |||
|<small>100</small> | |||
|10<sup>2</sup> | |||
|One hundred | |||
|- | |||
|सहस्रम् (''sahasram'') | |||
|<small>1,000</small> | |||
|10<sup>3</sup> | |||
|One thousand | |||
|- | |||
|अयुतम् (''ayutam'') | |||
|<small>10,000</small> | |||
|10<sup>4</sup> | |||
|Ten thousand | |||
|- | |||
|लक्षम् (''lakṣam'') | |||
|<small>1,00,000</small> | |||
|10<sup>5</sup> | |||
|One Lakh | |||
|- | |||
|प्रयुतम् (''prayutam'') | |||
|<small>10 ''lakṣam''</small> | |||
|10<sup>6</sup> | |||
|Ten Lakhs | |||
|- | |||
|कोटिः (''koṭiḥ'') | |||
|<small>10 ''prayutam''</small> | |||
|10<sup>7</sup> | |||
|One crore | |||
|- | |||
|अर्बुदम् (''arbudam'') | |||
|<small>10 ''koṭiḥ''</small> | |||
|10<sup>8</sup> | |||
|Ten crore | |||
|- | |||
|अब्जम् (''abjam'') | |||
|<small>10 ''arbudam''</small> | |||
|10<sup>9</sup> | |||
|Hundred crore | |||
|- | |||
|खर्वः (''kharvaḥ'') | |||
|<small>10 ''abjam''</small> | |||
|10<sup>10</sup> | |||
|Thousand crore | |||
|- | |||
|निखर्वः (''nikharvaḥ'') | |||
|<small>10 ''kharvaḥ''</small> | |||
|10<sup>11</sup> | |||
|Ten thousand crore | |||
|- | |||
|महासरोजम् (''mahāsarojam'' ) | |||
|<small>10 ''nikharvaḥ''</small> | |||
|10<sup>12</sup> | |||
|One lakh crore | |||
|- | |||
|शङ्क़ुः (''śaṅkuḥ'') | |||
|<small>10 ''mahāsarojam''</small> | |||
|10<sup>13</sup> | |||
|Ten lakh crore | |||
|- | |||
|सरिता-पति (''sarita-pati'') | |||
|<small>10 ''śaṅkuḥ''</small> | |||
|10<sup>14</sup> | |||
|Crore of crore | |||
|- | |||
|अन्त्यम् (''antyam'') | |||
|<small>10 ''sarita-pati''</small> | |||
|10<sup>15</sup> | |||
|Ten crores of crore | |||
|- | |||
|मध्यम् (''madhyam'') | |||
|<small>10 ''antyam''</small> | |||
|10<sup>16</sup> | |||
|Hundred crores of crore | |||
|- | |||
|परार्द्धम् (''parārdham'') | |||
|<small>10 ''madhyam''</small> | |||
|10<sup>17</sup> | |||
|Thousand crores of crore | |||
|}Here each number is 10 times the previous number. ''daśa'' is 10 times of ''ekam. śatam'' is 10 times of ''daśa. sahasram'' is 10 times of ''śatam'' etc. | |||
==See Also== | |||
[[पाटीगणितम् में 'सांकेतिक स्थान']] | |||
==References== | |||
<references /> | |||
Latest revision as of 14:00, 1 September 2023
Here we will know the names used to denote the place value of digits as mentioned in Pāṭīgaṇitam.
Verse
एकं दश शतमस्मात्सहस्रमयुतं ततः परं लक्षम् ।
प्रयुतं कोटिमथार्बुदमब्ज खर्वं निखर्वं च ॥ ७ ॥
तस्मान् महासरोजं शङ्कुं सरितां पतिं ततस्त्वन्त्यम् ।
मध्यं परार्द्धमाहुर्यथोत्तरं दशगुणं तज्ज्ञाः ॥ ८ ॥
Translation
ekam , daśa , śatam , sahasram , ayutam , lakṣam , prayutam, koṭiḥ, arbudam , abjam , kharvaḥ, nikharvaḥ , mahāsarojam , śaṅku , saritapati , antyam , madhyam and parārdham are each stated to be ten times the preceding by those who have a knowledge of them.[1]
| Name | Indian Notation | Power
Notation |
Indian System |
|---|---|---|---|
| एकम् (ekam) | 1 | 100 | One |
| दश (daśa) | 10 | 101 | Ten |
| शतम् (śatam) | 100 | 102 | One hundred |
| सहस्रम् (sahasram) | 1,000 | 103 | One thousand |
| अयुतम् (ayutam) | 10,000 | 104 | Ten thousand |
| लक्षम् (lakṣam) | 1,00,000 | 105 | One Lakh |
| प्रयुतम् (prayutam) | 10 lakṣam | 106 | Ten Lakhs |
| कोटिः (koṭiḥ) | 10 prayutam | 107 | One crore |
| अर्बुदम् (arbudam) | 10 koṭiḥ | 108 | Ten crore |
| अब्जम् (abjam) | 10 arbudam | 109 | Hundred crore |
| खर्वः (kharvaḥ) | 10 abjam | 1010 | Thousand crore |
| निखर्वः (nikharvaḥ) | 10 kharvaḥ | 1011 | Ten thousand crore |
| महासरोजम् (mahāsarojam ) | 10 nikharvaḥ | 1012 | One lakh crore |
| शङ्क़ुः (śaṅkuḥ) | 10 mahāsarojam | 1013 | Ten lakh crore |
| सरिता-पति (sarita-pati) | 10 śaṅkuḥ | 1014 | Crore of crore |
| अन्त्यम् (antyam) | 10 sarita-pati | 1015 | Ten crores of crore |
| मध्यम् (madhyam) | 10 antyam | 1016 | Hundred crores of crore |
| परार्द्धम् (parārdham) | 10 madhyam | 1017 | Thousand crores of crore |
Here each number is 10 times the previous number. daśa is 10 times of ekam. śatam is 10 times of daśa. sahasram is 10 times of śatam etc.
See Also
पाटीगणितम् में 'सांकेतिक स्थान'
References
- ↑ Shukla, Kripa Shankar (1959). The Pāṭīgaṇita of Śrīdharācārya. Lucknow: Lucknow University. p. 2.
