Calculus, Kerala's gift to the world
600 years before Newton and Liebniz, the Kerala mathematicians discovered the Calculus, Calculus or Kalana is said to be Kerala's gift to Europe ! This truth was unearthed by Dr C J Joseph and Dr CK Raju, in their books, the Crest of the Peacock and the Cultural Foundations of Mathematics respectively !
KSAM was founded by Madhava and had illustrious mathematicians like Parameshwara, Neelakanta, Jyeshtadeva, Achyuta Pisharady and the poet Melpathur. When KSAM is combined with Astrology, it becomes KSAMA, the Kerala School of Astronomy, Maths and Astrology.
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In the realm of Astrology, Kerala's gift was the satellite Gulika. Horary Astrology was well developed by the Kerala astrologers.
Western astronomers do not admit this truth.
It was an Englishman, Charles Mathew Whish, who brought to the world the genius of Kerala mathematicians in his book "On the Hindu Quadrature of the Circle and the infinite series of the proportion of the circumference to the diameter exhibited in the four Sastras, the Tantra Sahgraham, Yucti Bhasha, Carana Padhati and Sadratnamala"
It is to be noted that the origin of sine and cos is India. Jya and Koti Jya were the terms used by the Indian mathematicians. The Arabs converted these terms as Jiba and Kojiba. It was wrongly translated into Latin as Sinus and Cosinus and became Sin and Cosine in English. Bhuja Jya means R Sin, Koti Jya means R Cos and Sparsha Jya means Tan x. The Indian inverse functions are Sparsha chapa for Arctan, Bhuja chapa for Arc Sine and Koti Chapa for Arc cos.
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Aryabhata's Sine Table was the first Sine Table in the History of Mathematics. The Sine Table of Madhava is similar. When a 360 degree Circle is divided by 4, we get quadrants of 90 degrees each. The Madhava Sine Table can be called the Table of R Sine Differences, as sine values are given for every 3 degree 45 minutes. There are 24 * 3.45 = 90 or 24 R Sines. These tables were used by Christopher Clavius, when he solved the mathematical problem vexing the Westerners ! The Westerners triumphed with the knowledge of Indian Maths and initiated the Gregorian Calendrical Reforms !
Tan Tables were also given to mathematical students. The term Jya for 5 degrees was used first by the mathematician, Brahmagupta and we have 6 Jyas of 5 degrees each to constitute a Zodiacal Sign. The Zodiac is made up of 72 Jyas ( 72*5 = 360 ) and a Quadrant is made up of 18 Jyas ( 18*5 = 90 ). Tan values are given for every 5 degrees but then Tan tables make the mathematical students lazy !
Since there were no computers in hoary times, cowrie shells were used to calculate planetary positions. Paral Sankhya was used. Veda Veda means 44, as there are four Vedas ! Netra Netra means 22, as there are two eyes !
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The genius of Puliyoor Purushotaman Namboothiri condensed the thousands of slokas of the 18 Siddhantas into 1000 odd slokas, called the Ganitha Nirnaya. It is one of the best books on Mathematical Astrology ever written. He was ably assisted by the Maths Professor, Prof Krishna Warrier.
In the Kerala system, 14 major perturbations of the Moon are highlighted and 14 trignometric corrections are done for the 14 lunar anomalies.
After computing the Chandra Madhyamam, the mean longitude of the Moon, after 14 trignometric corrections, the longitude is called Samskrutha Chandra Madhyamam, Samskruthendu.
Chathur dasebhyebhyo balanyabhibhyo
Neethva Thulasadi Vasa Dhanarnam
Krithva tad Indor Apaneeya Thungam
Thado Mridujya phala Samskruthendu
After the fourteen corrections trignometric, tthe longitude of Moon is derived, known as the Cultured Longitude.
( Ganitha Nirnaya )
Then the Parinathi Kriya or Parinathi Samskara, Reduction to the Ecliptic is done.
Add Sin M
To Cultured Longitude
After the fourteen Reductions
Deduct the Node
Then reduce it to Ecliptic
Then we get
Luna's true longitude !
Vikshepa Vritheeya Gatho Vipatha
Thasmannayel Jyam Parinathyabhikhyam
Yugmau pada sarvam idam Vidheyam
Syal Kranti Vritteeya Ehaisha Chandra.
( Ganitha Nirnaya )
There are 400 K verses dealing with Kerala Astrology. About Astronomy, Maths and Astrology, Siddhanta, Samhita and Hora.
By Govind Kumar
The main books of KSAM
Parameswara's Rule by R C Dutta
Madhava of Sangramagrama by Journal of Kerala Studies
On the Quadrature of the Circle by C T Rajagopal
Medieval Kerala Mathematics - Archive of History of Science by C T Rajagopal
Laghu Bhaskareeya by Sankara Narayanan
Siddhanta Darpana by Neelakanta
Siddanta Deepika by Parameswara
Tantrasangraha by Neelakanta
Venvaroha by Madhava
Yukthi Bhasha by Jyeshta Deva
Jyothir Meemamsa by Neelakanta
Geometry of Sree Yantra by N C Bolton
Mayoora Shikha ( The Crest of the Peacock ) by Dr Joseph
The Cultural Foundtions of Mathematics by Dr C K Raju
Bharateeya Ganitha
Bharateeya Pari Sthithi
Bharateeya Rasa Tantra - all by Dr C Krishnan Namboothiri
Badha Deepika by Parameswara
Aryabhateeya Bhasya by Neelakanta Somayaji
Sphuta Nirnaya by Achyuta Pisharodi
Siddhanta Darpana by Neelakanta
Ganitha Adhyaya by Bhaskara
Ganith Nirnaya by Puliyoor
Gola Deepika by Parameswara
Drig Ganitha - By Parameswara
Grahana Nyaya Deepika by Parameswara
Kerala School of Hindu Astronomy by Prof K V Sarma
Geometry in Ancient and Medieval India by T A Saraswathy
On the Hindu Quadrature of the circle and the infinite series of the proportion of the circumference to the diameter exhibited in the four Sastras, the Tantra Sahgraham, Yucti Bhasha, Carana Padhati and Sadratnamala by C M Whish.
These books are based on the gems of Indian Astronomy, Astrology and Maths.
Siddhanta Samhitha Hora
Angira Siddhanta Bhrigu Samhita Parasara Hora
Paulasa Siddhanta Surya Samhita Surya Hora
Bhrigu Siddhanta Brahma Samhita Manu Hora
Vasishta Siddhanta Vyasa Samhita Kashyapa Hora
Chyavana Siddhanta Atri Samhita Narada Hora
Vyasa Siddhanta Pitamaha Samhita Garga Hora
Lomasa Siddhanta Vasishta Samhita Marichi Hora
Manu Siddhanta Chyavana Samhita Angira Hora
Atri Siddanta
Angira Samhita Lomasa Hora
Parasara Siddhanta Yavana Samhita Paulasa Hora
Kashyapa Siddhanta Paulasa Samhita Yavana Hora
Garga Siddhanta Parasara Samhita Pitamaha Hora
Narada Siddhanta Garga Samhita Vyasa Hora
Surya Siddhanta Kashyapa Samhita Vasishta Hora
Marichi Siddhanta Lomasa Samhita Atri Hora
Pitamaha Siddhanta Marichi Samhita Chyavana Hora
Yavana Siddhanta Manu Samhita Bhrigu Hora
Brahma Siddhanta Narada Samhita Brahma Hora
Astrologer G Kumar of Zodiac Computers brought out a Kerala Astrology Software in 1999, using KSAM algorithms. It is considered to be one of the most accurate softwares in the world. His website is www.eastrovedica.com and email info@eastrovedica.com Mobile is 93885 56053. Landline 91 0487 255 2851
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