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16 principles of vedic mathematics

Vedic Mathematics is an old system of mathematics to make it simple, easier and logical. It is basically rests on 16 Sutras with their own corollary or sub sutras and these sutras are used as the technique for solving the problems. They are Ekadhikena Purvena, Nikhilam Navatashcaramam Dashatah, Urdhva-Tiryagbyham, Paravartya Yojayet, Shunyam Saamyasamuccaye, (Anurupye) Shunyamanyat, Sankalana -Vyavakalanabhyam, Puranapuranabhyam, Chalana-Kalanabhyam, Yaavadunam, Vyashtisamanstih, Shesanyankena Charamena, Ekanyunena Purvena, Sopaantyadvaya Mantyam, Gunitasamuchyah and Gunakasamuchyah.


Ekadhikena Purvena ( एकाधिकेन पूर्वेन )

  Anurupyena is the sub sutra of this sutra. Ekadhikena Purvena means that "By one more than one before". It is used for finding squares of the numbers. When we add one to the prime numbers ending with nine such as 9,19,29,39,.......it is very difficult to divide. This method of Ekadhikena Purvena is used as a solution for that difficulty. 


Nikhilam Navatashcaramam Dashatah ( निखिलं नवतश्चारमं दशतः )

  Sisyate Sesasamjnah is the sub sutra of Nikhilam Navatashcaramam Dashatah. It means "Last from ten and rest of from nine". Basically, it designates that we can subtract the last digit from 10, and the rest of the numbers from the left side can subtract from nine. But the numbers must be less than or more than the base of 100, 1000...This method makes subtraction easy.


Urdhva-Tiryagbyham ( ऊर्ध्व​-टिर्यग्ब्य्हम् )

  Sub sutra of this technique is Adyamadyenantyamantyena. It means "Vertically and crosswise". This technique is used in the case of multiplication and division of any two numbers in vertically and crosswise.


Paravartya Yojayet ( परावर्त्य योजयेत् )

  Kevalaih Saptakam Gunyat is the sub sutra of Paravartya sutra. It means Transpose and adjusts. This technique is related to the Chinese remainder theorem and Horner's rule of synthetic division. This method helps to make division easier when the division is closer and slightly higher than the power of ten. 


Shunyam Saamyasamuccaye ( शून्यं साम्यसमुच्चये )

  The sub sutra of shunyam saamyasamuccaye is Vestanam. It means that "when the sum is the same and that sum is zero".All terms are equated to "0" and it is the common factor of this technique.


(Anurupye) Shunyamanyat (आनुरुप्ये) ष्हुन्यमन्यत्

  The sub sutra of this technique is Yavadunam Tavadunam. It means"If one is the ratio, then the other is zero". That means this technique is used when the numbers are not closer to the power of 10 and closer to each other. It makes the multiplication easier.


Sankalana -Vyavakalanabhyam ( संकलन व्यवकलनाभ्यां )

  Yavadunam Tavadunikritya Varga Yojayet is the sub sutra of Sankalana-Vyavakalanabhyam. It means"By Addition and Subtraction". This method is used by the additions and subtractions of  the equations. By adding and subtracting, it brings x+y and x-y forms.


Puranapuranabhyam (पूरणापूरणाभ्यां )

  The sub sutra of Puranapuranabhyam is Antyayordashake'pi. It means "By the completion or non-completion". In order to solve the quadratic equations, we can use the technique of puranapurananhyam.


Yavadunam ( यावदूनं )

  The sub sutra or corollary of Yavadunam is Samuccayagunitah. It means "By the deficiency". It is used to using numbers that are near to the power of ten as 13, 104, 1012.etc..and near to the multiple of a power of ten such as 42, 507, 2008 etc...


Vyashtisamanstih

  Lopanasthapanabhyam is the sub sutra of this technique. the meaning of Vyashtisamanstih is "Part and Whole". By using paravartya sutra, this method solves polynomial equations to find its factors.


Shesanyankena Charamena ( शेषाण्यईन चरमेण )

  Vilokanam is the sub sutra or corollary of Shesanyankena Charamena. It means "The remainders by the last digit". It is used to convert fraction as a decimal in all decimal places.


Sopaanlyadvaya Mantyam ( सोपान्ल्यदयमन्त्यं )

  Gunitasamuccayah Samuccayagunitah is the corollary of this technique. It means "The ultimate and twice the penultimate of multiplication".


Ekanyunena Purvena ( एकन्यूनेन पूर्वेन )

  The corollary of this technique is Dhvajanka. It means "By one less than the previous one". When the multiplier includes nines completely, this technique is used in the case of multiplication.


Gunitasamuchyah ( गुणितसमुच्चयः )

  Dwandwa Yoga is the corollary or sub sutra of Gunitasamuchyah. It means "the product of the sum is equal to the sum of the product".


Gunakasamuchyah ( गुणकसमुच्चयः )

  The sub sutra of this method is Adyam Antyam Madhyam. It means "the factors of the sum is equal to the sum of the factors".

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