العربية
中国
Français
Deutsch
Ελληνική
हिन्दी
Italiano
日本語
Português
Русский
EspañolĀRYABHAṭA NUMERATION
(Redirected from Aryabhata numeration)
The ' numeration' is a system of numerals based on Sanskrit phonemes. It was intrudoced in the early 6th century by , in the first chapter titled ''Gītika Padam'' of his ''Aryabhatiya''. It attributes a numerical value to each syllable of the form consonant+vowel possible in Sanskrit phonology, from '' = 1 up to '' = 1018.
The basis of this number system is mentioned in the second stanza of the first chapter of Aryabhatiya.
The Varga (Group/Class) letters Ka to Ma are to be placed in the varga (square) places (1st,100th,10000th ...etc places) and Avarga letters like Ya, Ra , La .. have to be placed in Avarga places (10th,1000th,...etc places).
The Varga letters 'Ka' to 'Ma' have value from 1,2,3 .. up to 25 and Avarga letters 'Ya' to 'Ha' have value 30,40,50.. up to 100.In the Varga and Avarga letters, beyond the ninth vowel (place), new symbols can be used.
The values for vowels are as follows : i= 100 ; u = 10000, ru = 1000000 and so on.
Aryabhata used this number system for representing both small and large numbers in his mathematical and astronomical calculations. This system can even be used to represent fractions and mixed fractions. For example nga is 1/5, nja is 1/10 and Jhardam (jha=9:it's half) = 4 1/2
The traditional Indian digit order is reversed compared to the modern way. By consequence, Āryabhaa began with the ones before the tens; then the hundreds and the thousands; then the myriad and the lakh (= 105) and so on. ''(cf. Indian numbering system)''
''Here the complete table:''
★ Kurt Elfering: ''Die Mathematik des Aryabhata I. Text, Übersetzung aus dem Sanskrit und Kommentar''. Wilhelm Fink Verlag, München, 1975, ISBN 3-7705-1326-6
★ Georges Ifrah: ''The Universal History of Numbers. From Prehistory to the Invention of the Computer''. John Wiley & Sons, New York, 2000, ISBN 0-471-39340-1.
★ B. L. van der Waerden: ''Erwachende Wissenschaft. Ägyptische, babylonische und griechische Mathematik''. Birkhäuser-Verlag, Basel Stuttgart, 1966, ISBN 3-764-30399-9
The ' numeration' is a system of numerals based on Sanskrit phonemes. It was intrudoced in the early 6th century by , in the first chapter titled ''Gītika Padam'' of his ''Aryabhatiya''. It attributes a numerical value to each syllable of the form consonant+vowel possible in Sanskrit phonology, from '' = 1 up to '' = 1018.
| Contents |
| History |
| Example |
| Numeral table |
| References |
History
The basis of this number system is mentioned in the second stanza of the first chapter of Aryabhatiya.
The Varga (Group/Class) letters Ka to Ma are to be placed in the varga (square) places (1st,100th,10000th ...etc places) and Avarga letters like Ya, Ra , La .. have to be placed in Avarga places (10th,1000th,...etc places).
The Varga letters 'Ka' to 'Ma' have value from 1,2,3 .. up to 25 and Avarga letters 'Ya' to 'Ha' have value 30,40,50.. up to 100.In the Varga and Avarga letters, beyond the ninth vowel (place), new symbols can be used.
The values for vowels are as follows : i= 100 ; u = 10000, ru = 1000000 and so on.
Aryabhata used this number system for representing both small and large numbers in his mathematical and astronomical calculations. This system can even be used to represent fractions and mixed fractions. For example nga is 1/5, nja is 1/10 and Jhardam (jha=9:it's half) = 4 1/2
Example
| '''Example:'' 299, 792 458' | ||||
| 100 101 | 102 103 | 104 105 | 106 107 | 108 |
| 85, | 42, | 97, | 99, | 2 |
The traditional Indian digit order is reversed compared to the modern way. By consequence, Āryabhaa began with the ones before the tens; then the hundreds and the thousands; then the myriad and the lakh (= 105) and so on. ''(cf. Indian numbering system)''
Numeral table
''Here the complete table:''
| The 33 × 9 = 297 Sanskrit alphabetic numerical syllables | |||||||||||||
| Nine vowels or syllabics | -'' | -'' | -'' | -'' | -'' | -'' | -'' | -'' | -'' | ||||
| अ | इ | उ | ऋ | ऌ | ए | ऐ | ओ | औ | |||||
| × | 10 0 | 10 2 | 10 4 | 10 6 | 10 8 | 1010 | 1012 | 1014 | 1016 | ||||
| Five velar plosives | |||||||||||||
| '' - | क | 1 | क | कि | कु | कृ | कॄ | के | कै | को | कौ | ||
| '' - | ख | 2 | ख | खि | खु | खृ | खॄ | खे | खै | खो | खौ | ||
| '' - | ग | 3 | ग | गि | गु | गृ | गॄ | गे | गै | गो | गौ | ||
| '' - | घ | 4 | घ | घि | घु | घृ | घॄ | घे | घै | घो | घौ | ||
| '' - | ङ | 5 | ङ | ङि | ङु | ङृ | ङॄ | ङे | ङै | ङो | ङौ | ||
| Five palatal plosives | |||||||||||||
| '' - | च | 6 | च | चि | चु | चृ | चॄ | चे | चै | चो | चौ | ||
| '' - | छ | 7 | छ | छि | छु | छृ | छॄ | छे | छै | छो | छौ | ||
| '' - | ज | 8 | ज | जि | जु | जृ | जॄ | जे | जै | जो | जौ | ||
| '' - | झ | 9 | झ | झि | झु | झृ | झॄ | झे | झै | झो | झौ | ||
| '' - | ञ | 10 | ञ | ञि | ञु | ञृ | ञॄ | ञे | ञै | ञो | ञौ | ||
| Five retroflex plosives | |||||||||||||
| '' - | ट | 11 | ट | टि | टु | टृ | टॄ | टे | टै | टो | टौ | ||
| '' - | ठ | 12 | ठ | ठि | ठु | ठृ | ठॄ | ठे | ठै | ठो | ठौ | ||
| '' - | ड | 13 | ड | डि | डु | डृ | डॄ | डे | डै | डो | डौ | ||
| '' - | ढ | 14 | ढ | ढि | ढु | ढृ | ढॄ | ढे | ढै | ढो | ढौ | ||
| '' - | ण | 15 | ण | णि | णु | णृ | णॄ | णे | णै | णो | णौ | ||
| Five dental plosives | |||||||||||||
| '' - | त | 16 | त | ति | तु | तृ | तॄ | ते | तै | तो | तौ | ||
| '' - | थ | 17 | थ | थि | थु | थृ | थॄ | थे | थै | थो | थौ | ||
| '' - | द | 18 | द | दि | दु | दृ | दॄ | दे | दै | दो | दौ | ||
| '' - | ध | 19 | ध | धि | धु | धृ | धॄ | धे | धै | धो | धौ | ||
| '' - | न | 20 | न | नि | नु | नृ | नॄ | ने | नै | नो | नौ | ||
| Five labial plosives | |||||||||||||
| '' - | प | 21 | प | पि | पु | पृ | पॄ | पे | पै | पो | पौ | ||
| '' - | फ | 22 | फ | फि | फु | फृ | फॄ | फे | फै | फो | फौ | ||
| '' - | ब | 23 | ब | बि | बु | बृ | बॄ | बे | बै | बो | बौ | ||
| '' - | भ | 24 | भ | भि | भु | भृ | भॄ | भे | भै | भो | भौ | ||
| '' - | म | 25 | म | मि | मु | मृ | मॄ | मे | मै | मो | मौ | ||
| Four approximants or trill | |||||||||||||
| '' - | य | 30 | य | यि | यु | यृ | यॄ | ये | यै | यो | यौ | ||
| '' - | र | 40 | र | रि | रु | रृ | रॄ | रे | रै | रो | रौ | ||
| '' - | ल | 50 | ल | लि | लु | लृ | लॄ | ले | लै | लो | लौ | ||
| '' - | व | 60 | व | वि | वु | वृ | वॄ | वे | वै | वो | वौ | ||
| Three coronal fricatives | |||||||||||||
| '' - | श | 70 | श | शि | शु | शृ | शॄ | शे | शै | शो | शौ | ||
| '' - | ष | 80 | ष | षि | षु | षृ | षॄ | षे | षै | षो | षौ | ||
| '' - | स | 90 | स | सि | सु | सृ | सॄ | से | सै | सो | सौ | ||
| One glottal fricative | |||||||||||||
| '' - | ह | 100 | ह | हि | हु | हृ | हॄ | हे | है | हो | हौ | ||
References
★ Kurt Elfering: ''Die Mathematik des Aryabhata I. Text, Übersetzung aus dem Sanskrit und Kommentar''. Wilhelm Fink Verlag, München, 1975, ISBN 3-7705-1326-6
★ Georges Ifrah: ''The Universal History of Numbers. From Prehistory to the Invention of the Computer''. John Wiley & Sons, New York, 2000, ISBN 0-471-39340-1.
★ B. L. van der Waerden: ''Erwachende Wissenschaft. Ägyptische, babylonische und griechische Mathematik''. Birkhäuser-Verlag, Basel Stuttgart, 1966, ISBN 3-764-30399-9
This article provided by Wikipedia. To edit the contents of this article, click here for original source.
psst.. try this: add to faves
Featured Companies
| Dancing Moon Travel | |
| Alpine Interface Inc. | |
| Travelbugs, LLC | |
| Golf Holidays International |
