Vedic Mathematics for the world....

[ashok mourya]

Vedic math was rediscovered from the ancient Indian scriptures between 1911 and 1918 by Sri Bharati Krishna Tirthaji (1884-1960), a scholar of Sanskrit, Mathematics, History and Philosophy. He studied these ancient texts for years, and after careful investigation was able to reconstruct a series of mathematical formulae called sutras

Bharati Krishna Tirthaji, who was also the former Shankaracharya (major religious leader) of Puri, India, delved into the ancient Vedic texts and established the techniques of this system in his pioneering work - Vedic Mathematics (1965), which is considered the starting point for all work on Vedic math. It is said that after Bharati Krishna's original 16 volumes of work expounding the Vedic system were lost, in his final years he wrote this single volume, which was published five years after his death.

Development of Vedic Math
Vedic math was immediately hailed as a new alternative system of mathematics, when a copy of the book reached London in the late 1960s. Some British mathematicians, including Kenneth Williams, Andrew Nicholas and Jeremy Pickles took interest in this new system. They extended the introductory material of Bharati Krishna's book, and delivered lectures on it in London. In 1981, this was collated into a book entitledIntroductory Lectures on Vedic Mathematics. A few successive trips to India by Andrew Nicholas between 1981 and 1987, renewed the interest on Vedic math, and scholars and teachers in India started taking it seriously.
The Growing Popularity of Vedic Math
Interest in Vedic maths is growing in the field of education where maths teachers are looking for a new and better approach to the subject. Even students at the Indian Institute of Technology (IIT) are said to be using this ancient technique for quick calculations. No wonder, a recent Convocation speech addressed to the students of IIT, Delhi, by Dr. Murli Manohar Joshi, Indian Minister for Science & Technology, stressed the significance of Vedic maths, while pointing out the important contributions of ancient Indian mathematicians, such as Aryabhatta, who laid the foundations of algebra, Baudhayan, the great geometer, and Medhatithi and Madhyatithi, the saint duo, who formulated the basic framework for numerals.

Vedic Maths in Schools
Quite a few years ago, St James' School, London, and other schools began to teach the Vedic system, with notable success. Today this remarkable system is taught in many schools and institutes in India and abroad, and even to MBA and economics students.
When in 1988, Maharishi Mahesh Yogi brought to light the marvels of Vedic maths, Maharishi Schools around the world incorporated it in their syllabi. At the school in Skelmersdale, Lancashire, UK, a full course called "The Cosmic Computer" was written and tested on 11 to 14 year old pupils, and later published in 1998. According to Mahesh Yogi, "The sutras of Vedic Mathematics are the software for the cosmic computer that runs this universe."

Since 1999, a Delhi-based forum called International Research Foundation for Vedic Mathematics and Indian Heritage, which promotes value-based education, has been organizing lectures on Vedic maths in various schools in Delhi, including Cambridge School, Amity International, DAV Public School, and Tagore International School.

Vedic Math Research
Researches are being undertaken in many areas, including the effects of learning Vedic maths on children. A great deal of research is also being done on how to develop more powerful and easy applications of the Vedic sutras in geometry, calculus, and computing. The Vedic Mathematics Research Group published three new books in 1984, the year of the centenary of the birth of Sri Bharati Krishna Tirthaji.
Plus Points
There are obviously many advantages of using a flexible, refined and efficient mental system like Vedic math. Pupils can come out of the confinement of the 'only one correct' way, and make their own methods under the Vedic system. Thus, it can induce creativity in intelligent pupils, while helping slow-learners grasp the basic concepts of mathematics. A wider use of Vedic math can undoubtedly generate interest in a subject that is generally dreaded by children.

Vedic Math essentially rests on the 16 Sutras or mathematical formulas as referred to in the Vedas. Sri Sathya Sai Veda Pratishtan has compiled these 16 Sutras and 13 sub-Sutras. The links below take you to the explanation, meaning and methods of application with examples for these Sutras.

1. Ekadhikina Purvena
   (Corollary: Anurupyena)
   Meaning: By one more than the previous one
2. Nikhilam Navatashcaramam Dashatah
   (Corollary: Sisyate Sesasamjnah)
   Meaning: All from 9 and the last from 10
3. Urdhva-Tiryagbyham
   (Corollary: Adyamadyenantyamantyena)
   Meaning: Vertically and crosswise
4. Paraavartya Yojayet
   (Corollary: Kevalaih Saptakam Gunyat)
   Meaning: Transpose and adjust
5. Shunyam Saamyasamuccaye
   (Corollary: Vestanam)
   Meaning: When the sum is the same that sum is zero
6. (Anurupye) Shunyamanyat
   (Corollary: Yavadunam Tavadunam)
   Meaning: If one is in ratio, the other is zero
7. Sankalana-vyavakalanabhyam
   (Corollary: Yavadunam Tavadunikritya Varga Yojayet)
   Meaning: By addition and by subtraction
8. Puranapuranabyham
   (Corollary: Antyayordashake'pi)
   Meaning: By the completion or non-completion
9. Chalana-Kalanabyham
   (Corollary: Antyayoreva)
   Meaning: Differences and Similarities
10. Yaavadunam
    (Corollary: Samuccayagunitah)
    Meaning: Whatever the extent of its deficiency
11. Vyashtisamanstih
    (Corollary: Lopanasthapanabhyam)
    Meaning: Part and Whole
12. Shesanyankena Charamena
    (Corollary: Vilokanam)
    Meaning: The remainders by the last digit
13. Sopaantyadvayamantyam
    (Corollary: Gunitasamuccayah Samuccayagunitah)
    Meaning: The ultimate and twice the penultimate
14. Ekanyunena Purvena
    (Corollary: Dhvajanka)
    Meaning: By one less than the previous one
15. Gunitasamuchyah
    (Corollary: Dwandwa Yoga)
    Meaning: The product of the sum is equal to the sum of the product
16. Gunakasamuchyah
    (Corollary: Adyam Antyam Madhyam)
    Meaning: The factors of the sum is equal to the sum of the factors

 

[ashok mourya]

Vedic Math Basics

• Terms and Operations
• Addition and Subtraction
• Multiplication
• Division
• Miscellaneous

 

[Ryuzaki]

Learnt it while in school,very useful

 

[ashok mourya]

Learnt it while in school,very useful

Time to educate the world friend.Hope we will succeed.

 

[Indian Patriot]

This is a slippery ground. It is good to feel proud about one's past but it is equally important to take note that the world had moved on. Egypt, Mesopotamia, Iran were all ancient civilisations. In fact Mesopotamia, Iraq, was said to be the cradle of civilisation. What is Iraq today?

Its time India ditched its Hindu obsession and Vedic romanticism. Embrace the present, prepare for the future. The past is not going to come back.

 

[ashok mourya]

This is a slippery ground. It is good to feel proud about one's past but it is equally important to take note that the world had moved on. Egypt, Mesopotamia, Iran were all ancient civilisations. In fact Mesopotamia, Iraq, was said to be the cradle of civilisation. What is Iraq today?

Its time India ditched its Hindu obsession and Vedic romanticism. Embrace the present, prepare for the future. The past is not going to come back.

The same techniques used in Vedic mathematics is being taught in US schools. Only thing is that they do not call it Vedic mathematics, they call it oriental mathematics. There is nothing wrong in teaching vedic mathematics as a paper like Algebra, Geometry in Indian schools and universities.
Indian mathematics - Wikipedia, the free encyclopedia

 

[Indian Patriot]

The same techniques used in Vedic mathematics is being taught in US schools. Only thing is that they do not call it Vedic mathematics, they call it oriental mathematics. There is nothing wrong in teaching vedic mathematics as a paper like Algebra, Geometry in Indian schools and universities.

Study mathematics, just remove vedic and other religious nostaligia. World knows India invented maths and the world also knows India has nothing to show in 21st century. Computers, modern electronics, internet, space tech everything was invented by people who know nothing about Hinduism or Vedic science.

India boasts of Pushpak Viman in Ramayan yet the same country cannot even manufacture an aeroplane propeller today. Is this something to feel proud?

Keep education secular, ditch false pride. Only then can a country move forward.

 

[ashok mourya]

the

Study mathematics, just remove vedic and other religious nostaligia. World knows India invented maths and the world also knows India has nothing to show in 21st century. Computers, modern electronics, internet, space tech everything was invented by people who know nothing about Hinduism or Vedic science.

India boasts of Pushpak Viman in Ramayan yet the same country cannot even manufacture an aeroplane propeller today. Is this something to feel proud?

Keep education secular, ditch false pride. Only then can a country move forward.

Zero invented by Indian Hindus.So it is communal,we should not use it .But computer runs on 0 and 1.

 

[Indian Patriot]

the

Zero invented by Indian Hindus.So it is communal,we should not use it .But computer runs on 0 and 1.

Learn to read first. You feel proud that India invented zero, good. You will be shocked to know Egypt and Mesopotamia are OLDER civilisations than India.

You are obsessed with Vedic not Mathematics. Study maths and science, keep religion and fake nostalgia out of it. History is history, live in present.

 

[ashok mourya]

Learn to read first. You feel proud that India invented zero, good. You will be shocked to know Egypt and Mesopotamia are OLDER civilisations than India.

You are obsessed with Vedic not Mathematics. Study maths and science, keep religion and fake nostalgia out of it. History is history, live in present.

ISRO is also communal who says Ayabhatta discoverd gravity before Newton .

 

[Indian Patriot]

ISRO is also communal who says Ayabhatta discoverd gravity before Newton .

That one is true. If ancient India was so advanced why are Indians so behind in science and technology today? Why is there no single Indian designed and build aircraft flying in the sky?

 

[ashok mourya]

That one is true. If ancient India was so advanced why are Indians so behind in science and technology today? Why is there no single Indian designed and build aircraft flying in the sky?

Then what is the Chandrayan and Mangalyan.Are they flow by Pakistan?.

Motions of the solar system
Aryabhata correctly insisted that the earth rotates about its axis daily, and that the apparent movement of the stars is a relative motion caused by the rotation of the earth, contrary to the then-prevailing view, that the sky rotated. This is indicated in the first chapter of the Aryabhatiya, where he gives the number of rotations of the earth in a yuga,[24] and made more explicit in his gola chapter:[25]

In the same way that someone in a boat going forward sees an unmoving [object] going backward, so [someone] on the equator sees the unmoving stars going uniformly westward. The cause of rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at the equator, constantly pushed by the cosmic wind.

Aryabhata described a geocentric model of the solar system, in which the Sun and Moon are each carried by epicycles. They in turn revolve around the Earth. In this model, which is also found in the Paitāmahasiddhānta (c. CE 425), the motions of the planets are each governed by two epicycles, a smaller manda (slow) and a larger śīghra (fast). [26] The order of the planets in terms of distance from earth is taken as: the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms."[8]

The positions and periods of the planets was calculated relative to uniformly moving points. In the case of Mercury and Venus, they move around the Earth at the same mean speed as the Sun. In the case of Mars, Jupiter, and Saturn, they move around the Earth at specific speeds, representing each planet's motion through the zodiac. Most historians of astronomy consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.[27] Another element in Aryabhata's model, the śīghrocca, the basic planetary period in relation to the Sun, is seen by some historians as a sign of an underlying heliocentric model.[28]

Eclipses
Solar and lunar eclipses were scientifically explained by Aryabhata. He states that the Moon and planets shine by reflected sunlight. Instead of the prevailing cosmogony in which eclipses were caused by Rahu and Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in terms of shadows cast by and falling on Earth. Thus, the lunar eclipse occurs when the moon enters into the Earth's shadow (verse gola.37). He discusses at length the size and extent of the Earth's shadow (verses gola.38–48) and then provides the computation and the size of the eclipsed part during an eclipse. Later Indian astronomers improved on the calculations, but Aryabhata's methods provided the core. His computational paradigm was so accurate that 18th-century scientist Guillaume Le Gentil, during a visit to Pondicherry, India, found the Indian computations of the duration of the lunar eclipse of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.[8]

 

[Indian Patriot]

Then what is the Chandrayan and Mangalyan.Are they flow by Pakistan?.

Those are airliners for you? What is the price of a ticket in a Chandrayaan?

This stupid Hinduvta obsession over "past glory" is going to pull this country down. You fool, India was not the only ancient civilisation. Egypt, Mesopotamia etc. were also wonders of the world and had contributed to humanity immensely. They couldn.t cope up and became basket case today.Fools like you live in the past and refuse to accept present.

 

[nik141991]

Everything was discovered in india, now modi ji has come we will rediscover are lost ancient techniques of building inter galactic spaceship vimana & applied its mercury vortex technology to our tejas Mk 2

 

[ashok mourya]

Those are airliners for you? What is the price of a ticket in a Chandrayaan?

An aircraft is a machine that is able to fly by gaining support from the air, or, in general, the atmosphere of a planet. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines.

Egypt and Iraqi civilization failed because they converted to Islam and obeyed whats written in holy Quran and forget science.But Hindu India with its vedic math and science still the only surviving civilization and religion.

Everything was discovered in india, now modi ji has come we will rediscover are lost ancient techniques of building inter galactic spaceship vimana & applied its mercury vortex technology to our tejas Mk 2

Obsessed about your own nation.the math you learn all over the world today mostly invented in vedic India.
The Aryabhatiya presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries. The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara I (Bhashya, c. 600 CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya, (1465 CE).

Mathematics
Place value system and zero
The place-value system, first seen in the 3rd-century Bakhshali Manuscript, was clearly in place in his work. While he did not use a symbol for zero, the French mathematician Georges Ifrahargues that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten with null coefficients.[14]

However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic form.[15]

Approximation of π
Aryabhata worked on the approximation for pi (

), and may have come to the conclusion that

is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇāmayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ."Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached."

[16]
This implies that the ratio of the circumference to the diameter is ((4 + 100) × 8 + 62000)/20000 = 62832/20000 = 3.1416, which is accurate to five significant figures.

It is speculated that Aryabhata used the word āsanna (approaching), to mean that not only is this an approximation but that the value is incommensurable (or irrational). If this is correct, it is quite a sophisticated insight, because the irrationality of pi was proved in Europe only in 1761 by Lambert.[17]

After Aryabhatiya was translated into Arabic (c. 820 CE) this approximation was mentioned in Al-Khwarizmi's book on algebra.[8]

Trigonometry
In Ganitapada 6, Aryabhata gives the area of a triangle as

tribhujasya phalashariram samadalakoti bhujardhasamvargah
that translates to: "for a triangle, the result of a perpendicular with the half-side is the area."

Aryabhata discussed the concept of sine in his work by the name of ardha-jya, which literally means "half-chord". For simplicity, people started calling it jya. When Arabic writers translated his works from Sanskrit into Arabic, they referred it as jiba. However, in Arabic writings, vowels are omitted, and it was abbreviated as jb. Later writers substituted it with jaib, meaning "pocket" or "fold (in a garment)". (In Arabic, jiba is a meaningless word.) Later in the 12th century, when Gherardo of Cremona translated these writings from Arabic into Latin, he replaced the Arabicjaib with its Latin counterpart, sinus, which means "cove" or "bay"; thence comes the English word sine.[19]

Indeterminate equations
A problem of great interest to Indian mathematicians since ancient times has been to find integer solutions to Diophantine equations that have the form ax + by = c. (This problem was also studied in ancient Chinese mathematics, and its solution is usually referred to as the Chinese remainder theorem.) This is an example from Bhāskara's commentary on Aryabhatiya:

Find the number which gives 5 as the remainder when divided by 8, 4 as the remainder when divided by 9, and 1 as the remainder when divided by 7
That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that the smallest value for N is 85. In general, diophantine equations, such as this, can be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose more ancient parts might date to 800 BCE. Aryabhata's method of solving such problems, elaborated by Bhaskara in 621 CE, is called the kuṭṭaka (कुट्टक) method. Kuttaka means "pulverizing" or "breaking into small pieces", and the method involves a recursive algorithm for writing the original factors in smaller numbers. This algorithm became the standard method for solving first-order diophantine equations in Indian mathematics, and initially the whole subject of algebra was called kuṭṭaka-gaṇita or simplykuṭṭaka.

Algebra
In Aryabhatiya, Aryabhata provided elegant results for the summation of series of squares and cubes:

and

(see squared triangular number)
Astronomy
Aryabhata's system of astronomy was called the audAyaka system, in which days are reckoned from uday, dawn at lanka or "equator". Some of his later writings on astronomy, which apparently proposed a second model (or ardha-rAtrikA, midnight) are lost but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, he seems to ascribe the apparent motions of the heavens to the Earth's rotation. He may have believed that the planet's orbits as elliptical rather than circular.

Motions of the solar system
Aryabhata correctly insisted that the earth rotates about its axis daily, and that the apparent movement of the stars is a relative motion caused by the rotation of the earth, contrary to the then-prevailing view, that the sky rotated. This is indicated in the first chapter of the Aryabhatiya, where he gives the number of rotations of the earth in a yuga, and made more explicit in his gola chapter:

In the same way that someone in a boat going forward sees an unmoving [object] going backward, so [someone] on the equator sees the unmoving stars going uniformly westward. The cause of rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at the equator, constantly pushed by the cosmic wind.

Aryabhata described a geocentric model of the solar system, in which the Sun and Moon are each carried by epicycles. They in turn revolve around the Earth. In this model, which is also found in the Paitāmahasiddhānta (c. CE 425), the motions of the planets are each governed by two epicycles, a smaller manda (slow) and a larger śīghra (fast). The order of the planets in terms of distance from earth is taken as: the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms."

The positions and periods of the planets was calculated relative to uniformly moving points. In the case of Mercury and Venus, they move around the Earth at the same mean speed as the Sun. In the case of Mars, Jupiter, and Saturn, they move around the Earth at specific speeds, representing each planet's motion through the zodiac. Most historians of astronomy consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy. Another element in Aryabhata's model, the śīghrocca, the basic planetary period in relation to the Sun, is seen by some historians as a sign of an underlying heliocentric model.

Eclipses
Solar and lunar eclipses were scientifically explained by Aryabhata. He states that the Moon and planets shine by reflected sunlight. Instead of the prevailing cosmogony in which eclipses were caused by Rahu and Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in terms of shadows cast by and falling on Earth. Thus, the lunar eclipse occurs when the moon enters into the Earth's shadow (verse gola.37). He discusses at length the size and extent of the Earth's shadow (verses gola.38–48) and then provides the computation and the size of the eclipsed part during an eclipse. Later Indian astronomers improved on the calculations, but Aryabhata's methods provided the core. His computational paradigm was so accurate that 18th-century scientist Guillaume Le Gentil, during a visit to Pondicherry, India, found the Indian computations of the duration of the lunar eclipse of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.

Sidereal periods
Considered in modern English units of time, Aryabhata calculated the sidereal rotation (the rotation of the earth referencing the fixed stars) as 23 hours, 56 minutes, and 4.1 seconds; the modern value is 23:56:4.091. Similarly, his value for the length of the sidereal year at 365 days, 6 hours, 12 minutes, and 30 seconds (365.25858 days) is an error of 3 minutes and 20 seconds over the length of a year (365.25636 days).

Heliocentrism
As mentioned, Aryabhata advocated an astronomical model in which the Earth turns on its own axis. His model also gave corrections (the śīgra anomaly) for the speeds of the planets in the sky in terms of the mean speed of the sun. Thus, it has been suggested that Aryabhata's calculations were based on an underlying heliocentric model, in which the planets orbit the Sun, though this has been rebutted. It has also been suggested that aspects of Aryabhata's system may have been derived from an earlier, likely pre-Ptolemaic Greek, heliocentric model of which Indian astronomers were unaware, though the evidence is scant. The general consensus is that a synodic anomaly (depending on the position of the sun) does not imply a physically heliocentric orbit (such corrections being also present in late Babylonian astronomical texts), and that Aryabhata's system was not explicitly heliocentric.