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Template:Table Numeral Systems

The Template:IAST numeration is a system of numerals based on Sanskrit phonemes. It was introduced in the early 6th century by [[Aryabhata|Template:IAST]], 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 Template:IAST = 1 up to Template:IAST = 1018.

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; its half) = 4½

Example[]

Example:  299,792,458
100 101 102 103 104 105 106 107 108
 85,  42,  97,  99, 2
Template:Script Template:Script Template:Script Template:Script Template:Script
Template:IAST Template:IAST Template:IAST Template:IAST Template:IAST

The traditional Indian digit order is reversed compared to the modern way. By consequence, ĀryabhaTemplate:IASTa 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 is the complete table:

The   33 × 9  =  297   Sanskrit alphabetic numerical syllables
Nine vowels or syllabics   -Template:IPA -Template:IPA -Template:IPA -Template:IAST -Template:IAST -Template:IPA -Template:IPA -Template:IPA -Template:IPA  
         
    ×     10 0   10 2   10 4   10 6   10 8   1010   1012   1014   1016  
Five velar plosives                      
Template:IPA - 1  
Template:IPA
कि
Template:IPA
कु
Template:IPA
कृ
Template:IAST
कॢ
Template:IAST
के
Template:IPA
कै
Template:IPA
को
Template:IPA
कौ
Template:IPA
 
Template:IPA - 2  
Template:IPA
खि
Template:IPA
खु
Template:IPA
खृ
Template:IAST
खॢ
Template:IAST
खे
Template:IPA
खै
Template:IPA
खो
Template:IPA
खौ
Template:IPA
 
Template:IPA - 3  
Template:IPA
गि
Template:IPA
गु
Template:IPA
गृ
Template:IAST
गॢ
Template:IAST
गे
Template:IPA
गै
Template:IPA
गो
Template:IPA
गौ
Template:IPA
 
Template:IPA - 4  
Template:IPA
घि
Template:IPA
घु
Template:IPA
घृ
Template:IAST
घॢ
Template:IAST
घे
Template:IPA
घै
Template:IPA
घो
Template:IPA
घौ
Template:IPA
 
Template:IAST - 5  
Template:IAST
ङि
Template:IAST
ङु
Template:IAST
ङृ
Template:IAST
ङॢ
Template:IAST
ङे
Template:IAST
ङै
Template:IAST
ङो
Template:IAST
ङौ
Template:IAST
 
Five palatal plosives                      
Template:IPA - 6  
Template:IPA
चि
Template:IPA
चु
Template:IPA
चृ
Template:IAST
चॢ
Template:IAST
चे
Template:IPA
चै
Template:IPA
चो
Template:IPA
चौ
Template:IPA
 
Template:IPA - 7  
Template:IPA
छि
Template:IPA
छु
Template:IPA
छृ
Template:IAST
छॢ
Template:IAST
छे
Template:IPA
छै
Template:IPA
छो
Template:IPA
छौ
Template:IPA
 
Template:IPA - 8  
Template:IPA
जि
Template:IPA
जु
Template:IPA
जृ
Template:IAST
जॢ
Template:IAST
जे
Template:IPA
जै
Template:IPA
जो
Template:IPA
जौ
Template:IPA
 
Template:IPA - 9  
Template:IPA
झि
Template:IPA
झु
Template:IPA
झृ
Template:IAST
झॢ
Template:IAST
झे
Template:IPA
झै
Template:IPA
झो
Template:IPA
झौ
Template:IPA
 
Template:IPA - 10  
Template:IPA
ञि
Template:IPA
ञु
Template:IPA
ञृ
Template:IAST
ञॢ
Template:IAST
ञे
Template:IPA
ञै
Template:IPA
ञो
Template:IPA
ञौ
Template:IPA
 
Five retroflex plosives                      
Template:IAST - 11  
Template:IAST
टि
Template:IAST
टु
Template:IAST
टृ
Template:IAST
टॢ
Template:IAST
टे
Template:IAST
टै
Template:IAST
टो
Template:IAST
टौ
Template:IAST
 
Template:IAST - 12  
Template:IAST
ठि
Template:IAST
ठु
Template:IAST
ठृ
Template:IAST
ठॢ
Template:IAST
ठे
Template:IAST
ठै
Template:IAST
ठो
Template:IAST
ठौ
Template:IAST
 
Template:IAST - 13  
Template:IAST
डि
Template:IAST
डु
Template:IAST
डृ
Template:IAST
डॢ
Template:IAST
डे
Template:IAST
डै
Template:IAST
डो
Template:IAST
डौ
Template:IAST
 
Template:IAST - 14  
Template:IAST
ढि
Template:IAST
ढु
Template:IAST
ढृ
Template:IAST
ढॢ
Template:IAST
ढे
Template:IAST
ढै
Template:IAST
ढो
Template:IAST
ढौ
Template:IAST
 
Template:IAST - 15  
Template:IAST
णि
Template:IAST
णु
Template:IAST
णृ
Template:IAST
णॢ
Template:IAST
णे
Template:IAST
णै
Template:IAST
णो
Template:IAST
णौ
Template:IAST
 
Five dental plosives                      
Template:IPA - 16  
Template:IPA
ति
Template:IPA
तु
Template:IPA
तृ
Template:IAST
तॢ
Template:IAST
ते
Template:IPA
तै
Template:IPA
तो
Template:IPA
तौ
Template:IPA
 
Template:IPA - 17  
Template:IPA
थि
Template:IPA
थु
Template:IPA
थृ
Template:IAST
थॢ
Template:IAST
थे
Template:IPA
थै
Template:IPA
थो
Template:IPA
थौ
Template:IPA
 
Template:IPA - 18  
Template:IPA
दि
Template:IPA
दु
Template:IPA
दृ
Template:IAST
दॢ
Template:IAST
दे
Template:IPA
दै
Template:IPA
दो
Template:IPA
दौ
Template:IPA
 
Template:IPA - 19  
Template:IPA
धि
Template:IPA
धु
Template:IPA
धृ
Template:IAST
धॢ
Template:IAST
धे
Template:IPA
धै
Template:IPA
धो
Template:IPA
धौ
Template:IPA
 
Template:IPA - 20  
Template:IPA
नि
Template:IPA
नु
Template:IPA
नृ
Template:IAST
नॢ
Template:IAST
ने
Template:IPA
नै
Template:IPA
नो
Template:IPA
नौ
Template:IPA
 
Five labial plosives                      
Template:IPA - 21  
Template:IPA
पि
Template:IPA
पु
Template:IPA
पृ
Template:IAST
पॢ
Template:IAST
पे
Template:IPA
पै
Template:IPA
पो
Template:IPA
पौ
Template:IPA
 
Template:IPA - 22  
Template:IPA
फि
Template:IPA
फु
Template:IPA
फृ
Template:IAST
फॢ
Template:IAST
फे
Template:IPA
फै
Template:IPA
फो
Template:IPA
फौ
Template:IPA
 
Template:IPA - 23  
Template:IPA
बि
Template:IPA
बु
Template:IPA
बृ
Template:IAST
बॢ
Template:IAST
बे
Template:IPA
बै
Template:IPA
बो
Template:IPA
बौ
Template:IPA
 
Template:IPA - 24  
Template:IPA
भि
Template:IPA
भु
Template:IPA
भृ
Template:IAST
भॢ
Template:IAST
भे
Template:IPA
भै
Template:IPA
भो
Template:IPA
भौ
Template:IPA
 
Template:IPA - 25  
Template:IPA
मि
Template:IPA
मु
Template:IPA
मृ
Template:IAST
मॢ
Template:IAST
मे
Template:IPA
मै
Template:IPA
मो
Template:IPA
मौ
Template:IPA
 
Four approximants or trill                      
Template:IPA - 30  
Template:IPA
यि
Template:IPA
यु
Template:IPA
यृ
Template:IAST
यॢ
Template:IAST
ये
Template:IPA
यै
Template:IPA
यो
Template:IPA
यौ
Template:IPA
 
Template:IPA - 40  
Template:IPA
रि
Template:IPA
रु
Template:IPA
रृ
Template:IAST
रॢ
Template:IAST
रे
Template:IPA
रै
Template:IPA
रो
Template:IPA
रौ
Template:IPA
 
Template:IPA - 50  
Template:IPA
लि
Template:IPA
लु
Template:IPA
लृ
Template:IAST
लॢ
Template:IAST
ले
Template:IPA
लै
Template:IPA
लो
Template:IPA
लौ
Template:IPA
 
Template:IPA - 60  
Template:IPA
वि
Template:IPA
वु
Template:IPA
वृ
Template:IAST
वॢ
Template:IAST
वे
Template:IPA
वै
Template:IPA
वो
Template:IPA
वौ
Template:IPA
 
Three coronal fricatives                      
Template:IPA - 70  
Template:IPA
शि
Template:IPA
शु
Template:IPA
शृ
Template:IAST
शॢ
Template:IAST
शे
Template:IPA
शै
Template:IPA
शो
Template:IPA
शौ
Template:IPA
 
Template:IAST - 80  
Template:IAST
षि
Template:IAST
षु
Template:IAST
षृ
Template:IAST
षॢ
Template:IAST
षे
Template:IAST
षै
Template:IAST
षो
Template:IAST
षौ
Template:IAST
 
Template:IPA - 90  
Template:IPA
सि
Template:IPA
सु
Template:IPA
सृ
Template:IAST
सॢ
Template:IAST
से
Template:IPA
सै
Template:IPA
सो
Template:IPA
सौ
Template:IPA
 
One glottal fricative                      
Template:IPA - 100  
Template:IPA
हि
Template:IPA
हु
Template:IPA
हृ
Template:IAST
हॢ
Template:IAST
हे
Template:IPA
है
Template:IPA
हो
Template:IPA
हौ
Template:IPA
 
                           

See also[]

  • Bhutasamkhya system
  • Katapayadi system

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
  • Template:Cite journal
  • Template:Cite jstor

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