Mathematics
Jagadguru Swami Sri Bhārāti Kṛṣṇa Tirthaji Maharaja's book "Vedic Mathematics" opened the floodgates of similar literature, often derived from the Swami's 16 Sūtras themselves. His treatise is a regards speed and accuracy in basic mathematics. The Vedic Math ideal is a mental calculation and one-line notation.
The foundations of Vedic Mathematics were mentioned in the Vedas themselves and even in the Vedanta scriptures. These had lain unused for many millennia, till the Swami rediscovered them.
His book, Vedic Mathematics, comprises many algorithms. He revealed his source in the ancient Hindu Vedas. Some are intuitively reconstructed from the Atharva Veda and from Parisistas (appendix) of the Atharva Veda. "The Upaveda of Sthapatya (engineering) comprises all kinds of architectural and structural human endeavor and all visual arts (and mathematics)." His work seems to be a whole Parisistas (appendix) itself.
The ancient Sanskrit writers did not use numerals when writing big numbers but preferred to use the letters of the Sanskrit Devanāgarī alphabet. In the Vedic Sūtras the key word steps to solving many problems are given in a terse, decimal code of certain sets of rhyming syllables, within the verses of the Sūtra. The fact that the alphabetic code is in the natural order and can be immediately interpreted, is clear proof that the code language was resorted not for concealment but for greater ease in versification.
The Swami had written sixteen volumes on the Vedic Mathematics field explaining all the topics of mathematical study. Alas, many advanced formula were promised but not given in his first and only book. After his 1956 life's work manuscript on Vedic mathematics was lost in a fire at the home of a disciple, though he was going blind from cataracts, he re-wrote the manuscript in 1957 in six weeks. It was to be proofread and published in the USA but was sent back to India in 1960 after his death. In 1965, this manuscript was published by Motilal Banarsidass, Varanasi, India and reprinted four times in the 1970s.
His book, Vedic Mathematics, included sixteen terse formulas for mental mathematics. For arithmetic, we are given several algorithms for whole number multiplication and division, (flag or straight) division, fraction conversion to repeating decimal numbers, calculations with measures of mixed units, summation of a series, squares and square roots (duplex method), cubes and cube roots (with expressions for a digit schedule), and divisibility (by osculation).
He gives a poem in Anusub metre, couched in the alphabetic Code-Language that has three meanings, a hymn to Lord Srī Kṛṣṇa, a hymn in praise of the Lord Shri Shankara, and the third the value of pi/10 to 32 decimal places, pi/10 = 0.31415926535897932384626433832792... with a "self-contained master-key" for extending the evaluation to any number of decimal places.
Several tests and techniques for factoring and solving certain algebraic equations with integer roots for quadratic, cubic, biquadratic, pentic equations, systems of linear equations, and systems of quadratic equations are demonstrated. For fractional expressions, a separation algorithm and fraction merger algorithms are given. Other techniques handle certain patterns of some special case algebraic equations. Just an introduction to differential and integral calculus is given.
Geometric applications are reviewed for linear equations, analytic conics, the equation for the asymptotes, and the equation to the conjugate-hyperbola. Five simple geometric proofs for the Pythagorean theorem are given. A 5-line proof of Apollonius' theorem is given.
Advanced topics promised included the integral calculus (the center of gravity of hemispheres, conics), trigonometry, astronomy (spherical triangles, earth's daily rotation, earth's annual rotation about the sun and eclipses), and engineering (dynamics, statics, hydrostatics, pneumatics, applied mechanics).
In his final comments he asserted that the names for "Arabic numerals," "Pythagoras' Theorem," and "Cartesian" co-ordinates are historical misnomers.
Read more about this topic: Bharati Krishna Tirthaji
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