Method of Inversion in Āryabhaṭīyam - Revision history

Ramamurthy: Headings modified

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	~~==Introduction==~~
	Inverse means the opposite effect of an action or a step. In Mathematics we have operations such as addition (+), subtraction (−), Multiplication (×), Division (÷) etc.The process in which the effect of one operation is inversed by another operation is termed as inverse operations.		Inverse means the opposite effect of an action or a step. In Mathematics we have operations such as addition (+), subtraction (−), Multiplication (×), Division (÷) etc.The process in which the effect of one operation is inversed by another operation is termed as inverse operations.

	==Verse==		==Verse==
	गुणकारा भागहरा भागहरास्ते भवन्ति गुणकाराः ।		गुणकारा भागहरा भागहरास्ते भवन्ति गुणकाराः ।

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	<references />		<references />
	[[Category:Mathematics in Āryabhaṭīyam]]		[[Category:Mathematics in Āryabhaṭīyam]]
			[[Category:General]]

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	<math>1 \times 7 + 2 \div 3 \times 5 - 1 \div 2 = 7</math>		<math>1 \times 7 + 2 \div 3 \times 5 - 1 \div 2 = 7</math>
	==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%B5%E0%A5%8D%E0%A4%AF%E0%A5%81%E0%A4%A4%E0%A5%8D%E0%A4%95%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A4%A3_%E0%A4%95%E0%A5%80_%E0%A4%B5%E0%A4%BF%E0%A4%A7%E0%A4%BF%27 आर्यभटीयम् में 'व्युत्क्रमण की विधि']		[[आर्यभटीयम् में 'व्युत्क्रमण की विधि']]
	==References==		==References==
	<references />		<references />
	[[Category:Mathematics in Āryabhaṭīyam]]		[[Category:Mathematics in Āryabhaṭīyam]]

Ramamurthy: New Page created

2023-07-31T08:05:48Z

New Page created

New page

==Introduction==
Inverse means the opposite effect of an action or a step. In Mathematics we have operations such as addition (+), subtraction (−), Multiplication (×), Division (÷) etc.The process in which the effect of one operation is inversed by another operation is termed as inverse operations.
==Verse==
गुणकारा भागहरा भागहरास्ते भवन्ति गुणकाराः ।

यः क्षेपः सोऽपचयोऽपचयः क्षेपश्च विपरीते ॥
==Translation==
In the method of inversion multipliers become divisors and divisors become multipliers, additive becomes subtractive and subtractive becomes additive<ref>{{Cite book|title=Āryabhaṭīyam (Gaṇitapādaḥ)|publisher=Samskrit Promotion Foundation|year=2023|location=Delhi|pages=107-109|language=Saṃskṛta}}</ref>.
===Example===
A number is multiplied by 2 , then increased by 1 , then divided by 5, then multiplied by 3, then diminished by 2, and then divided by 7 , the result (thus obtained) is 1. Say what is the initial number.
{| class="wikitable"
|+
!Steps
!Given Order
!
!Steps
!Reverse Order
!
|-
|'''1'''
|Multiplied by 2
| rowspan="6" |↓
|'''6'''
|Divided by 2
| rowspan="6" |↑
|-
|'''2'''
|Increased by 1
|'''5'''
|Subtracted by 1
|-
|'''3'''
|Divided by 5
|'''4'''
|Multiplied by 5
|-
|'''4'''
|Multiplied by 3
|'''3'''
|Divided by 3
|-
|'''5'''
|Diminished by 2
|'''2'''
|Increased by 2
|-
|'''6'''
|Divided by 7
|'''1'''
|Multiplied by 7
|}'''Result: 1'''

Starting from the last number 1, in the reverse order

<math>1 \times 7 + 2 \div 3 \times 5 - 1 \div 2 = 7</math>
==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%B5%E0%A5%8D%E0%A4%AF%E0%A5%81%E0%A4%A4%E0%A5%8D%E0%A4%95%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A4%A3_%E0%A4%95%E0%A5%80_%E0%A4%B5%E0%A4%BF%E0%A4%A7%E0%A4%BF%27 आर्यभटीयम् में 'व्युत्क्रमण की विधि']
==References==
<references />
[[Category:Mathematics in Āryabhaṭīyam]]