G unit a Sutras Now, in dealing with various texts which are to be found in the Vedic The ganita sutras, are also called the Sulba sutras “the easy mathematical. In hindi, Ganita means Mathematics, Sutra is a distinctive type of literally composition, Sulbha means easy, Veda (literally knowledge) are. Sutras of Vedic Mathematics list. This list of sutras is taken from the book Vedic Mathematics, which includes a full list of the sixteen Sutras in Sanskrit, but in.
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Ganita Sutras Ganita Sutras is a complete system in itself. These are Vedic aphorisms. These are 29 in number; 16 of them are designated as Sutras and other 13 as Upsutras. Credit goes to Swami Bharti Krisna Tirthaji Maharaj, a Shankracharya of Kanshipeeth to focus the attention of the present generation about potentialities of Sutras.
The information contained in the book titled “Vedic Mathematics” compiled by Prof. Agarwala, published from the manuscript papers of Swamiji make us known as how Swamiji had to devote many years to decode the working rules of these Sutras. From the demonstrations of the working rules of these Sutras in this book it has convinced many about the potentialities of the Sutras. Since then many scholars have further demonstrated about their potentialities to make the mathematics much easier and more effectively within the comprehensions of much larger population and also about their utility and academic values in many ways.
Kapoor has approached the organization format of this system on the whole and as individual Sutras. His approach and the results give us further insight of this wonderful system.
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The parallel text of the Sutras adopted in different scriptures is being searched. Kapoor points out Shatpath Brahman. Hereunder, the illustrative reference with working rule is indicated in reference to Ganita Sutra 1. The other Sutras may be taken up in due course of time.
Text in Roman script: Text avails three technical words which take us to the basics of the working domain of the Sutra. These three technical words take us to the three basic concepts: The first concept is the wholesome concept. Here it manifests in many ways and can be availed as a unit, unit entity, unit measure, the counting number 1, the close interval of unit length etc. It is the concept of a queue, a pair of entities of a queue of which one is previous as comparison to the second and the second automatically being subsequent to the first.
Therefore, the Sutra 1 has many applied values which would work out for us 1 counting, 2 arrangement of counting pebbles, 3 arrangement of beads along a thread, 4 the queue of points along with line etc. Parallel text and application of Sutra 1 in Shatpath Brahman: As many are the members of the family, so many are the utensils and there is one extra. Let there be a family F of members m1, m2, Let this family has a kitchen K with utensils u1, u2, For one-to-one association of family members of F with the utensils of K, the first member m1 is to be associated first, the first utensil of K i.
To each member of F is associated from K. The requirement is that after such association we should have one extra utensil in K. This is precisely the basics and formation of Ganita Sutra 1. The text of Upsutra 1 avails a pair of technical words: As such, 1 part as symmetrical to the whole, and 2 part as proportionate of the whole would be two distinct aspects of the same organisation.
Infinity is another word in which melt away all finiteness. In infinite domains or self-contained domains, the uniformity and patterns are other keywords in terms of which the concept of oneness can be approached as a symmetry and proportions. The applied values of Upsutra 1 would help us reach at unit interval as replica of infinite line, the universality of Yatha pinde tatha brahmande as in the body so in the universe and Yatha brahmande tatha binde as in the universe so in the body as well as the universality of the Upanishadic comprehensions as that even when full is taken out of full, there still remains full.
With this, when one would work Sutra 1 with double of a unit instead of a unit or with any multiple of a unit instead of a unit, one would see that the rule works.
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With this, the Sutra 1 coupled with Upsutra 1 makes the potentialities of Sutra 1 manyfold. Ten place value system is the source concept. Text avails four technical words which take us to the basics of the working domain of the Sutra.
Nine numerals and ten place value system are the two basic steps in terms of which the infinitely long line stands tamed. The counting pebbles technique requires infinite pebbles for coverage of infinitely suyras line.
Vedic seers comprehended ten place value system. From the method of expression tenth counting gajita as 10 as in two digit form, we can notice that here lies a shift from single digit expression for first 9 counts to the next multiple digit expression initiation for expression of tenth count onwards.
We also know that first 9 counts as well can be expressed in double digit forms as: Further, it also would be interesting to note that the double digit form for 1 as 01 provides us an expression for the tenth count as 10 sufras by having swapping of places for first and the second digit.
Further, the above interlink of 01 and 10 takes us to their link and inerlocking as reflection pair of numbers as much as that the formats beneath 01 and 10 get sutrras like image of an arrow through looking mirror gets interlocked with the arrow itself.
The placements of arrow, mirror, and the image of the arrow work out a di-monad format with mirror playing the role of joint of the di-monad. This as such is a big leap forward from the organisation format of Sutra 1. This had become possible with the transition stage of Upsutra 1. Therefore, Sutra 1, Upsutra 1 and Sutra 2 together make autras interesting dimensions to the mathematics. The above organisation of Sutra 1, Upsutra 1 and Sutra 2 takes us to a stage where the middle of interval, which otherwise had the privilege of uncountably infinite placements, gets tamed as a unique mirror placement to have half unit in front of the mirror as first half and its image through the mirror as the second half.
However, simultaneously, it makes the working very delicate as we shall be permitting the second half to remain dormant while structures sutas of the second half also shall be silently marking their presence. We cannot afford to ignore ganiha existence sugras the structures because of the second dormant half. If one is to see the type of difficulties ganiat which the mathematics when worked without taking care for the second dormant half, one ganitx simply to pose to oneself as to why from hypercircle-8 onwards the values start decreasing.
It simply happens as the linear order worked in terms of half-dimension helps us sequentially increase only uptil seventh step parallel to the possible seven geometries of 3-space of linear order. The organisation of pairing of two halves with the help of a mirror at the middle is unique organisation of many features, of which the most important is the feature of common remainder for both the halves while both halves are divided by a common divisor.
Though this property may appear to be obvious but in fact when the same is viewed in the context of uncountably infinite points being handled in terms of counting numbers, one would realise, how important this property of constant remainders emerges to be. This is precisely Upsutra 2. The source concept here gania the concept of equality of units, the pair of halves etc. The text as such is the definition of remainder: This Upsutra along with Upsutra 1 makes the mathematics of Upsutras a very interesting branch in itself.
This makes the external expansion of counts ganiga one to two, two to sutraz and so on parallel to the internal partitioning from wholesome one to a pair of parts, then to three parts, four parts and so on. The source concept is the partitioning parallel to reflection pairing of object and image. We may illustrate one of the working rules of this Sutra, which would help us to reach at its organisational format as well.
Autras us multiply 11 by We shall be getting the product equal to Let us have a close look at this number. The central digit of this number is 2. The three parts of the number would permit depiction as: Now, let us chase the multiplication the Sutra way: Therefore, when we shall be having 1 as start with position, as a next step under the rule of Sutra 1, we shall be reaching at ganitx Then the reflection image of 12 would give us 21 and we shall be obtaining The process can be extended.
The pair of above corners may be taken as representing the first number 11 and the pair of lower corners may be taken as second number Now, when we shall be multiplying the first digit of lower number 11 with the pair of digits of the above number 11 one by one, we shall be sutrax as is depicted above in terms of the arrows. The depiction is of two parts. The first part is Urdhva vertical and the second part is Tiryag crosswise. This as such, would help us comprehend as that geometric format of square is being divided into two triangles and only 1 out of two sytras is being utilised by the organisation format of Sutra 3.
Here it would be relevant to note that the triangle is the first close organisation of lines. The triangle as such is the printout of 3-space on 2-space.
The sum of all the three internal angles of a triangle isp. The sum of all the three external angles of a triangle is 2p. We can express p as 3—2 p. The sum of all the four internal angles of a quadrilateral is 2p.
We can express it as 4—2 p.
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In general, the printout of n-space on 2-space is n-polygon and the sum of the internal angles n-polygon is n—2 p. This in general can be seen as that the printouts of n-space in the role of dimension on 2-space is n-polygon. Therefore, the organisation format suttras Sutra 3 is that of a printout of 3-space in the role of dimension on 2-space format.
Like that, one can proceed to reach at the organisation formats of the entire range of the text of 16 Ganita Sutras and 13 Upsutras but the context and the space at hand sutrsa not permit sutrxs proceed ahead with it. However, the organisation formats achieved uptil this stage well indicate about the mathematics of linear order of Sutra 1, spatial order of Sutra 2 and of solid order of Sutra 3.