The Vedic Mathematics and Lilavati 

Dr. Tejaswini Pradhan

Asst. Professor, Dept. of Mathematics,

Kalinga University, Naya Raipur, Chhattisgarh

The two distinct mathematical works are Lilavati and Vedic Mathematics. They use different applications of mathematical ideas and appear to function independently. Nevertheless, both of them were composed with the same Vedic tradition as their foundation. They are actually fairly similar to one another. They, for example, meet the requirements for any number’s square-root. The formulae follow the same mathematical rules even if they appear to follow different ones.

The understanding of mathematics and astronomy in the 12th century was greatly enhanced thanks to the renowned mathematician Bhaskara and his publications. The four parts of his primary work, Siddhnta Shiromani, are titled “Lilvat”, “Bjagaita”, “Grahagaita”, and “Goldhyya”. Math, algebra, planetary mathematics, and spheres are the four subject-organized sections, in that order.

In 1114 AD, or the 1036 Saka era, Bhaskara was born. He records his birthplace and the year he was 36 when he finished his most significant achievement in a charming Sanskrit phrase. That phrase is

                rasa-guna-purṇa-mahisama shaka-nrpa samaye bhavat mamotpattih 

                rasa-guṇa-varṣeṇa maya siddhanta-siromaṇi racitaḥ  ||

With examples utilizing monarchs and elephants, Lilavati provides a variety of number-crunching techniques, including multiplications, squares, and progressions, making them easier for the average person to understand and appreciate.

The thirteen chapters of the book cover a variety of topics, including definitions, mathematical words, interest computation, arithmetical and geometrical progressions, plane geometry, solid geometry, the shadow of the gnomon, the Kuaka technique for solving indeterminate equations, and combinations.

Bhaskara provides a rule to find the square of any number in arithmetic calculations. According to this rule, any other number is taken and added or subtracted to a given number, let’s say x, to determine its square, making the resulting numbers easy to multiply. The square of x is the resultant numbers product. The comparison between this method and the one presented by Bharati Krishna Tirtha in his book Vedic Mathematics is made in the following paragraphs.

From 1925 to 1960 AD, Bharati Krishna Tirtha served as the Govardhan Math’s Sankaracharya. First and foremost, he is remembered for being the creator and author of Vedic Mathematics. In March 1884, Swami Bharati Krishna Tirthaji was born. He received the honorific Saraswathi. Between 1911 and 1919, he took intense meditation retreats in the Shringeri forests, where he first became aware of the sutras that he later connected to Vedic mathematics. He reportedly laboured on the sutras for eight years, writing each of the sixteen volumes by hand into a school notebook and treating them all as a one unit.

The Mahasamadhi of Bharati Krisna Tirtha occurred on February 2, 1960. In 1965, a posthumous edition of his work was released. This book contains a rule for calculating the square of a given number. This rule uses 10 or 50 or 100 as the base numbers, and according to the Yavadunam or Yavadadhikam rule, It is simple to calculate the square of the needed number. In the sentences that follow, this is explored in relation to the rule of Bhaskara.

Lilavati’s method of squaring

In Lilavati, the method for squaring of numbers in based on 

Meaning: Multiply the supplied number by the given Ista (a number that makes you easier to use), add the square of the Ista, and so on.

If a is the number to be squared then an Ista integer, b, is selected in such a way that (a + b) and (a- b) are simple to multiply if an is the number to be squared. After that, the b^2 is added since, a^2= (a + b)(a – b) +b^2.

The following examples are used to illustrate the method:

Example 1. If we wish to get the square of 15, we can assume that an Ista is 3. In that case, the procedure will be as follows: 

subtract from the number, add the Ista, multiply by the number, and then add the square of the Ista.

〖(15-3)∙(15+3)+3〗^2=225=〖15〗^2.

If we take the Ista as 5, then the required square of 15 is, 

〖(15-5)∙(15+5)+5〗^2=225=〖15〗^2.

Squaring Method in Vedic Mathematics

Special case techniques and general techniques are the two categories of procedures used in Vedic mathematics. The quick and efficient special case procedures can only be used on specific number combinations, yet they are nonetheless effective. Here, we’ll look at one unique technique.

Tirthaji gives as a sub-sutra of the Nikhilam rule, That is in Sanskrit is,

Meaning: Reduce a deficiency or excess to the same degree, and also set up the square of the deficiency or excess, no matter its degree.

Example 2 Let’s calculate the square root of 97. In this case, the nearest power of ten is 100. Since there is a 3 (shortfall) between 100 and 97, we further remove 3 from 97 to get at 94 for the LHS. Since 32 is 9 it produces the RHS. The complete answer is 9409.

Example 3. 〖106〗^2=?

LHS: 106 + 6 = 112, RHS: 6^2=36. 11236 is the answer.