Transcendence

Consisting of 16 basic aphorisms or Sutras, Vedic Mathematics is a system of Maths which prevailed in ancient India. Composed by Bharati Krishna Thirtha, these 16 sutras help one to do faster maths. The first aphorism is this "Whatever the extent of its deficiency, lessen it still further to that very extent; and also set up the square (of that deficiency)" When computing the square of 9, as the nearest power of 10 is 9, let us take 10 as our base. As 9 is 1 less than 10, we can decrease it by the deficiency = 9-1 =8. This is the leftmost digit On the right hand put deficiency^2, which is 1^2. Hence the square of nine is 81. For numbers above 10, instead of looking at the deficit we look at the surplus. For example: 11^2 = (11+1)*10+1^2 = 121 12^2 = (12+2)*10+2^2 = 144 14^2 = ( 14+4)*10+4^2 = 196 25^2 = ((25+5)*2)*10+5^2 = 625 35^2= ((35+5)*3)*10+5^2 = 1225

Consisting of 16 basic aphorisms or Sutras, Vedic Mathematics is a system of Maths which prevailed in ancient India. Composed by Bharati Krishna Thirtha, these 16 sutras help one to do faster maths. The first aphorism is this "Whatever the extent of its deficiency, lessen it still further to that very extent; and also set up the square (of that deficiency)" When computing the square of 9, as the nearest power of 10 is 9, let us take 10 as our base. As 9 is 1 less than 10, we can decrease it by the deficiency = 9-1 =8. This is the leftmost digit On the right hand put deficiency^2, which is 1^2. Hence the square of nine is 81. For numbers above 10, instead of looking at the deficit we look at the surplus. For example: 11^2 = (11+1)*10+1^2 = 121 12^2 = (12+2)*10+2^2 = 144 14^2 = ( 14+4)*10+4^2 = 196 25^2 = ((25+5)*2)*10+5^2 = 625 35^2= ((35+5)*3)*10+5^2 = 1225

In India, mathematics is related to Philosophy. We can find mathematical concepts like Zero ( Shoonyavada ), One ( Advaitavada ) and Infinity (Poornavada ) in Philosophia Indica. The Sine Tables of Aryabhata and Madhava, which gives correct sine values or values of 24 R Sines, at intervals of 3 degrees 45 minutes and the trignometric tables of Brahmagupta, which gives correct sine and tan values for every 5 degrees influenced Christopher Clavius, who headed the Gregorian Calender Reforms of 1582. These correct trignometric tables solved the problem of the three Ls, ( Longitude, Latitude and Loxodromes ) for the Europeans, who were looking for solutions to their navigational problem ! It is said that Matteo Ricci was sent to India for this purpose and the Europeans triumphed with Indian knowledge ! The Western mathematicians have indeed lauded Indian Maths & Astronomy. Here are some quotations from maths geniuses about the long forgotten Indian Maths ! In his famou

In India, mathematics is related to Philosophy. We can find mathematical concepts like Zero ( Shoonyavada ), One ( Advaitavada ) and Infinity (Poornavada ) in Philosophia Indica. The Sine Tables of Aryabhata and Madhava, which gives correct sine values or values of 24 R Sines, at intervals of 3 degrees 45 minutes and the trignometric tables of Brahmagupta, which gives correct sine and tan values for every 5 degrees influenced Christopher Clavius, who headed the Gregorian Calender Reforms of 1582. These correct trignometric tables solved the problem of the three Ls, ( Longitude, Latitude and Loxodromes ) for the Europeans, who were looking for solutions to their navigational problem ! It is said that Matteo Ricci was sent to India for this purpose and the Europeans triumphed with Indian knowledge ! The Western mathematicians have indeed lauded Indian Maths & Astronomy. Here are some quotations from maths geniuses about the long forgotten Indian Maths ! In his famou

By means of the same argument, the circumference can be computed in another way too. That is as (follows): The first result should by the square root of the square of the diameter multiplied by twelve. From then on, the result should be divided by three (in) each successive (case). When these are divided in order by the odd numbers, beginning with 1, and when one has subtracted the (even) results from the sum of the odd, (that) should be the circumference. ( Yukti deepika commentary ) This quoted text specifies another formula for the computation of the circumference c of a circle having diameter d. This is as follows. c = SQRT(12 d^2 - SQRT(12 d^2/3.3 + sqrt(12 d^2)/3^2.5 - sqrt(12d^2)/3^3.7 +....... As c = Pi d , this equation can be rewritten as Pi = Sqrt(12( 1 - 1/3.3 + 1/3^2.5 -1/3^3.7 +...... This is obtained by substituting z = Pi/ 6 in the power series expansion for arctan (z). Pi/4 = 1 - 1/3 +1/5 -1/7+..... This is Madhava's formula for Pi, and this was disco

By means of the same argument, the circumference can be computed in another way too. That is as (follows): The first result should by the square root of the square of the diameter multiplied by twelve. From then on, the result should be divided by three (in) each successive (case). When these are divided in order by the odd numbers, beginning with 1, and when one has subtracted the (even) results from the sum of the odd, (that) should be the circumference. ( Yukti deepika commentary ) This quoted text specifies another formula for the computation of the circumference c of a circle having diameter d. This is as follows. c = SQRT(12 d^2 - SQRT(12 d^2/3.3 + sqrt(12 d^2)/3^2.5 - sqrt(12d^2)/3^3.7 +....... As c = Pi d , this equation can be rewritten as Pi = Sqrt(12( 1 - 1/3.3 + 1/3^2.5 -1/3^3.7 +...... This is obtained by substituting z = Pi/ 6 in the power series expansion for arctan (z). Pi/4 = 1 - 1/3 +1/5 -1/7+..... This is Madhava's formula for Pi, and this was disco

By means of the same argument, the circumference can be computed in another way too. That is as (follows): The first result should by the square root of the square of the diameter multiplied by twelve. From then on, the result should be divided by three (in) each successive (case). When these are divided in order by the odd numbers, beginning with 1, and when one has subtracted the (even) results from the sum of the odd, (that) should be the circumference. ( Yukti deepika commentary ) This quoted text specifies another formula for the computation of the circumference c of a circle having diameter d. This is as follows. c = SQRT(12 d^2 - SQRT(12 d^2/3.3 + sqrt(12 d^2)/3^2.5 - sqrt(12d^2)/3^3.7 +....... As c = Pi d , this equation can be rewritten as Pi = Sqrt(12( 1 - 1/3.3 + 1/3^2.5 -1/3^3.7 +...... This is obtained by substituting z = Pi/ 6 in the power series expansion for arctan (z). Pi/4 = 1 - 1/3 +1/5 -1/7+..... This is Madhava's formula for Pi, and this was disco