Unit 3: Bharatvarsha - Land of Science, Math, Astronomy, & Astrology PDF

UNIT-3 BHARATVARSHA – LAND OF SCIENCE, MATHEMATICS, ASTRONOMY & ASTROLOGY Unit Content:Vedic Mathematics, Contribution of Ancient Indian Mathematicians, Scientists & thinkers to the modern age of Science, Mysteries of Astronomy and Astrology as per ancient Indian literature. Aim...

UNIT-3 BHARATVARSHA – LAND OF SCIENCE, MATHEMATICS, ASTRONOMY & ASTROLOGY Unit Content:Vedic Mathematics, Contribution of Ancient Indian Mathematicians, Scientists & thinkers to the modern age of Science, Mysteries of Astronomy and Astrology as per ancient Indian literature. Aim: To make students aware of the contribution of India to the disciplines like Mathematics & various Sciences. To let them know original source of all knowledge. To let them feel proud on richness of ancient Indian text, Vedas, Puranas& Upnishads etc. Expected Outcomes: After completing this unit, students will be aware ofthe contribution of Indian sages, Mathematicians & Scientists to the modern Scientific world, Unit content is sufficient to make students realize richness of Indian culture & heritage. Modern age is the age of Science & Technology & the world believes that the Modern age is really rich in advanced scientific knowledge & this is all because every information spreads rapidly and is well documented and safe so easily available to anyone anytime. But it is really surprising when we look back to our ancient literature i.e. our Vedas, Puranas& Upnishads which contain scientific theories in areas of Science, Mathematics, Arts, Astronomy, Astrology, Architecture and many more, which are far richer and superior as compared to modern Scientific theories, this literature also contain knowledge of super space technology that is beyond imagination of modern scientists. A good example may be seen in Indus valley civilization in architecture of the cities, closed drainage system, rain water management, flush toilets etc. Indian mythological stories are full of such miraculous things used in ancient time to which modern world assumes to be a boon from the west. Content here will help the students to know actual origin of many inventions and also mathematical formulae and many more important concepts thought to be originated from the modern world. We have earlier studied that Veda means knowledge or wisdom; it is derived from the word VID which means to know. Vedas were written in Sanskrit by sages in ancient India only. There are four Vedas: 1. Rig Veda- Knowledge of the Hymns of praise, to recite. 2. Samveda- Knowledge of Melodies, to chant. 3. Yajur Veda- Knowledge of sacrificial formulas, for rituals after death (Liturgy). 4. Atharva Veda- Knowledge of magic tricks, named after ‘Rishi Atharva’. 3.1 Ancient Mathematicians & their contribution to ‘Modern Mathematical Theories’ as per Vedas. Mathematics is an integrated part of life, if we notice around us so many numbers and formulae we use in our daily life like telling the time, calculating the duration, measuring the speed, sun rise, sunset, date, month, years, measuring units and many more. It is not a surprise that we have been in a practice of doing so since a time immemorial. Mathematics, Astronomy & astrology are not only closely related but seems to complement each other several times. Our ancestors had their own time clock for measurement of time and work accordingly. Many important mathematical formulae of Arithmetic, concept of square root & cube root, Geometry, Solid Geometry & Algebra have been invented and mentioned since ancient times which with time translated & rediscovered and brought to the world and world assumed these like something never felt before. In India, Mathematics has its roots in the Vedic literature which is nearly 4000 years old. Ruler or present day scale are believed being used by the Indus Valley Civilization prior to 1500 BCE. One such scale made up of ivory was found during excavation in Lothal, showing divisions on it with the smallest division measuring approximately 1.704 mm. Evidences show that people of Indus valley civilization were using weights to measure the things by quantity. A total of 558 weights were excavated from Mohenjodaro, Harappa, and Chanhu-Daro. Contribution of famous Ancient Indian Mathematicians to modern Mathematics: In words of Einstein: ‚Without Indians, no worthwhile scientific discovery could have been made‛. The credit to most of the inventions & discoveries has been given to the West although it was done far before that in India proofs of which are abundantly available in our Vedas & Upnishads & this is all because western countries well documented their research work while we could not preserve knowledge of our fore fathers. Some of such inventions are being discussed below as per the available ancient Indian text. Aryabhata: Born between 476-550 CE, was a great Indian Mathematician & Astronomer who really invented ‘0’, Zero. Though the concept of having nothing was known, but the concept of zero is it fully developed in India around the fifth century A.D. Before the invention of zero it was too difficult for the Mathematicians to perform the simplest arithmetic calculations. Zero, meaning the absence of any quantity. ‚The zero is widely seen as one of the greatest innovations in human history, is the cornerstone of modern mathematics and physics, plus the spin-off technology.‛ Peter Gobets, secretary of the or the Zero Project. According to documented history, the irrationality of pi was proved in Europe only in 1761 by Lambert. The great Indian mathematician Aryabhata worked on the approximation of the value of pi, and concluded that is irrational and its value is approximately 3.1416. He did this in 499 Common Era at the age of 23.Notable works: Aryabhaṭiya, Arya-siddhanta Aryabhatta was the first to explain how the Lunar Eclipse and the Solar Eclipse happened. He told about rotation of Earth on its axis, reflection of light by moon, sinusoidal functions, solution of single variable quadratic equation, value of π correct to 4 decimal places & circumference of Earth to 99.8% accuracy. Brahmagupta was a highly accomplished Indian astronomer and mathematician born in 598 AD in Bhinmal, a state of Rajasthan. The most important contribution of Brahmagupta to mathematics was introducing the concept and computing methods of zero (0). His formulas are still used to solve mathematical problems, and his conceptual theories have been inspiring for modern physics. He is also known for Modern number system, Brahmagupta's theorem, Brahmagupta-Fibonacci identity, Brahmagupta's interpolation formula etc. Brahmagupta's is also known for his remarkable finding in geometry i.e. formula for cyclic quadrilaterals known as Brahmagupta's formula. at the age of 30 in 628 AD he wrote Brahmasphutasiddhanta which covers a good deal of work on mathematics, including algebra, geometry, trigonometry, and algorithmic. Bhaskara Also known as Bhaskaracharya, born in 1114. He was the one who acknowledged that any number divided by zero is infinity and that the sum of any number and infinity is also infinity.He authored the famous book ‚SiddhantaSiromani‛ was written by him is divided into four parts called Lilavati, Bijaganita, Grahagaṇita and Golādhyāya. These four parts deal with arithmetic, algebra, mathematics of the planets, and spheres respectively.He is known as the greatest mathematician of medieval India. Mahaviracharya Hewas a 9th-century Jain Mathematician possibly born in Karnataka. He established the terminology such as equilateral, and isosceles triangle; rhombus; circle and semicircle. He discovered algebraic identities like a3 = a (a + b) (a − b) + b2 (a − b) + b3. Mahāvīra's Gaṇita-sāra- saṅgraha gave systematic rules for expressing a fraction. MadhavaHe is considered as the founder of Kerala School of Astronomy & Mathematics. Madhava may have discovered the sine and cosine series about three hundred years before Newton. Madhava (circa 1340 – 1425 A.D.) was the first to describe infinity. His contributions include infinite-series expansions of circular and trigonometric functions and finite-series approximations. Power series expansions of trigonometric sine, cosine and tangent functions is also the work of Madhava. Pingala 290 BCE-270 BCE, Matrameru, binary numeral system, arithmetical triangle are some notable works of Pingala. He was an ancient Indian poet & Mathematician, author of ‘Pingala-sutra’ or Chandaḥśāstra which presents the first known description of binary number system. Pingala is sometimes also credited with the first use of Zero, as he used the ‘Sunya’ in Sanskrit. In Pingala's system, the numbers start from number one, and not zero. Varahamihira: Born: Between 505–587 CE, he was also called Varāha or Mihira, he was an astrologer-astronomer who lived in or around Ujjain in present-day Madhya Pradesh, India. Panchsidhantika, Brihat Samhita and many more text written by him giving invaluable information regarding mathematics & Astronomy, planetary motion, eclipses and rainfall etc. Mihira’s most famous astrological work is Hora Shastra or Brihadjathaka. Baudhayana Born around 800 BC, the theorem by Pythagoras was given in 570-500 BCE but it is mentioned in the BaudhayanaSulba-sutra of India, which was written between 800 and 400 BCE. Nevertheless, the theorem came to be credited to Pythagoras.Baudhayana was also known for approximation of the square root of 2 and the statement of a version of the Pythagorean Theorem 3.2Contribution of famous Ancient Indian Scientists to modern Science: Agastya Samhita written during era of God Ram sometimes more than 170,000 years ago by sage Agatsya, describes method to make dry electric cell with 1.138 volts and 23 mA and electroplating process, hydrogen balloons. The ancient text of Agastya Samhita describes the method of making electric battery, and that water can be split into oxygen and hydrogen. Modern battery cell resembles Agastya’s method of generating electricity. For generating electricity, Sage Agastya had used the following material: 1.One earthen pot 2.Copper plate 3.Copper sulphate 4.Wet saw dust 5.Zinc amalgam His text says:सस्ं थाप्यमृण्मयेपात्रेताम्रपत्रंससु स्ं कृ तम।् छादयेच्छछच्िग्रीवेनचादााच्भ: काष्ठापासं च्ु भ:॥ दस्तालोष्टोच्नधात्वय: पारदाछछाच्दतस्तत:।सयं ोगाज्जायतेतेजोच्मत्रावरुणसच्ं ितम॥् Which means, ‚Place a well-cleaned copper plate in an earthenware vessel. Cover it first by copper sulfate and then by moist sawdust. After that, put a mercury-amalgamated zinc sheet on top of the sawdust to avoid polarization. The contact will produce an energy known by the twin name of Mitra-Varuna. Water will be split by this current into Pranavayu and Udanavayu. A chain of one hundred jars is said to give a very effective force. (p. 422)‛ When a cell was prepared according to Agastya Samhita and measured, it gives open circuit voltage as 1.138 volts, and short circuit current as 23 mA. ऄनेनजलभंगोच्स्तप्राणोदानेषवु ायषु एु वम्शतानांकंु भानामसंयोगकायाकृतस्मृतः. if we use the power of 100 earthen pots on water, then water will change its form into life-giving oxygen and floating hydrogen. वायबु न्धकवस्त्रेणच्नबद्धोयनमस्तके उदानःस्वलघत्ु वेच्बभरत्यकाशयनकम।् If hydrogen is contained in an air tight cloth, it can be used in aerodynamics, i.e. it will fly in air. (Today’s Hydrogen Balloon) Acharya Kanad was born in 600 BC. Kanad was an ancient Indian scientist & Philosopher who founded ‘Vaisheshika’ one of the schools of Indian Philosophy. It is surprising but true that ‚atomic theory’ was formulated by sage Kanadbefor 2600 years which Dalton gave in 1808 just before 200 years. Kanad propounded that an atom is an eternal particle which cannot be further divided, not visible by naked eye. He gave the idea that matter consists of indivisible units called atoms which is the smallest particle that cannot be destroyed and retains in its original form under all situations. MaharshiKanad mentioned in ‘Vaisheshika’ that word Karma is related to motion & he explained 5 types of motions- 1. Upward Motion 2. Downward Motion 3. Motion due to release of tensile strength 4. Shearing motion  5. General Motion MaharshiKanad proposed laws of motion around 600 BC years ago while Newton proposed his laws in his book ‘PhilosophiaeNaturalis Principia Mathematica’ in 1687. वेगःच्नच्मत्तच्वशेषातकमाणोजायते | Translation : Change of motion is due to impressed force. Newton’s First law- An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force. वेगःच्नच्मत्तापेक्षातकमाणोजायतेच्नयतच्दकच्ियाप्रबन्धहेतु | Translation : Change of motion is proportional to the impressed force and is in the direction of the force. Newton’s Second Law states, ‚Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration‛. वेगःसंयोगच्वशेषच्वरोधी | Translation : Action and reaction are equal and opposite. Newton’s Third Law states that, ‚Every action has an equal & opposite reaction‛. When we talk about gravity, the first name that pops into our heart is Sir Isaac Newton. In school we all have been told the story of how Newton was inspired to formulate ‚The Universal Law of Gravitation‛ when an apple fell from a tree. The world believes that Newton was the first to discover the gravitational concepts. You will be surprised to known that Indians knew the Laws of Gravity hundreds of years before Newton. India’s contribution to the subject of gravity began with Varahamihira (505– 587 CE), a Hindu astronomer and mathematician who thought of the idea of gravity but did not give it a specific name or meaning. Varahamihira claimed that there should be a force which might be keeping bodies stuck to the earth, and also keeping heavenly bodies in their determined places. Crucible steel (200BC) Historians now know that by at least 200 BC (a conservative estimate) South India was producing high quality steel, using a method Europeans would later call the crucible technique. Wrought iron, charcoal, and glass were mixed together and heated until the iron melted and absorbed the carbon, forming high grade steel. Sayana, a vedic scholar from the 14th century once said, "With deep respect, I bow to the sun, who travels 2,202 yojanas in half a nimesha." A yojana is 9 miles; a nimesha is 16/75 of a second. Therefore, 2,202 yojanas x 9 miles x 75/8 nimeshas = 185,794 miles per second or 2,99,000 kilometers per second. That’s astonishingly close to the real ‘scientifically-proven’ 3,00,000 kilometers per second figure. It’s often believed that his source was none other than the Vedas. 3.3Contribution of Ancient Indian literature to modern Astronomy & Astrology: Brahmagupta was a highly accomplished Indian astronomer and mathematician He significantly contributed to astronomy as calculating the lunar & solar eclipses and predicting the position and motion of the planets. Brahmagupta told that Earth is round and not flat, he further told that it looks flat because we can see only a little fraction of it at a timeHe also calculated the length of the solar year down to the second as 365 days, 5 minutes, and 19 seconds, which is equivalent on what scientists have measured. While history credits Copernicus for proposing heliocentric model of our solar system, it was Rig Veda that first notes the central placement of the SUN & other planets orbiting it in the Solar System. We were the First ones to acknowledge the existence of the solar system Rig Veda 1.164.13 ‚Sun moves in its orbit which itself is moving. Earth and other bodies move around sun due to force of attraction, because sun is heavier than them.‛ https://www.mensxp.com/special-features/today/28424-10-facts-that-prove- how-incredibly-advanced-ancient-indian-science Rig Veda 1.35.9 ‚The sun moves in its own orbit but holding earth and other heavenly bodies in a manner that they do not collide with each other through force of attraction.‛ Vedas Explained The Science Behind The Rather ‘Feared’ Eclipses https://news.abplive.com/science/last-solar-eclipse https://www.theguardian.com/science/2018/jul/25/bl ood-moon While the world feared the eclipses and associated all types of paranormal occurrences with the phenomenon, Vedas already had a very proper and scientific explanation. The below excerpt is also proof that they knew that the moon wasn’t self-illuminated. Rig Veda 5.40.5 ‚O Sun! When you are blocked by the one whom you gifted your own light (moon), then earth gets scared by sudden darkness.‛ In our Vedas &Puranas we find so many examples of large & almost accurate calculations like distance of Sun from earth which were later on proved to be correct using various scientific devices & theories. Tulsidas began writing the Ramcharitmanas in Ayodhya in VikramSamvat 1631 (1574 CE). In which he mentioned the distance between earth & the Sun with the help of one chaupee: "जगु सहस्त्रजोजनपरभानु. लील्योताच्हमधरु फलजानू." 1 yug = 12000 years 1 sahasra = 1000 1 yojan = 8 miles Yug * Sahasra * Yojan was the distance covered by hanuman ji to reach Sun. (12000 * 1000 * 8) miles 96000000 miles 1 mile = 1.6 kilometer 96000000* 1.6 96000000 mile = 153600000 kilometer So as per Tulsidas child Hanuman covered 153,600,000 kilometer distance from earth to Sun to eat Sun thinking it as a sweet fruit. First scientific effort to calculate distance between Sun & earth was made by Giovanni Cassini in 1672, after around 150 years when Tulsidas wrote it in RamcharitManas. In the period from 500 BCE to the beginning of the Christian era some texts were written on the subject of astrology. Nineteen famous sages composed their Siddhāntas (texts). Candra‐prajnapti, Sūrya‐prajnapti, and Jyotiṣakaraṇḍaka were written. The Sūryasiddhānta, the ancient text of Indian astrology, was composed around 200 BCE. Exercise Multiple Choice Type Questions Q.1. Which Mathematician is credited for the invention of ‘0’?? A. Pingla B. Brahmgupt C. Aryabhatt D. Bhaskara Q.2. Which of the following is not a part of ‚SiddhantaSiromani‛ written by Bhaskara? A. Lilavati B. Bijaganita C. Geometry D. Goladhyaya Q.3. Which of the following was a Jain Mathematician? A. Madhava B. Mahaviracharya C. Aristotle D. Baudhayana Q.4. In which of the following Religious Text distance of Sun from the Earth is mentioned? A. RamcharitManas B. Mahabharat C. Bhagvad Gita D. Harsh charitra Q.5. Which sage used Earthen pots to produce electricity? A. Sage Vishvamitra B. Sage Durvasa C. Sage Agastya D. Sage Kanad Q. 6. Who was the first person in the world to converse about the atom? A. Sage Vishvamitra B. Sage Durvasa C. Sage Agastya D. Sage Kanad Q.7. Which law was described by Sage Kanad as ‚ A. Newton’s First law B. Newton’s Law of Gravitation C. Newton’s Second law D. Newton’s Third law Q.8. As per which Veda ‚Sun never sets or rise, it is Earth which rotates‛? A. Rigveda B. Samveda C. Yajurveda D. Atharva Veda Q.9. What is ‘Asva’ in ‚SaptAsvaRuda‛ as per vedic terminology? A. 7 colors B. 7 horses C. 7 recipes D. 7 wonders Q.10. ‘KrishiParashram’ a book on agriculture & weeds was written by whom? A. Sage Kanad B. Sage Durvasa C. Sage Agastya D. Sage Parashar Q.11. Sankhya Shastra is related to which of the following? A. Mathematics B. Numerology C. Mathematics D. Algebra Q.12. Who authored ‘Panchsiddhant’ a book on astronomy? A. Bhaskara B. Brahmdutt C. Varahamihir D. Vikramaditya Q.13. Vaimanik Shastra is the Science of-----------. A. Aircrafts B. Ships C. Missiles D. Boats Q.14. People of which civilization are supposed to be the first to develop a system of uniform weights & measures? A. Mesopotamia B. Egypt C. Indus valley  D. Greece Q.15. What number is denoted with ‘Sahastra’? A. 100 B. 10 C. 1 D. 1000 1. C 6. D 11. B 2. C 7. D 12. C 3. B 8. B 13. A 4. A 9. A 14. C 5. C 10. D 15. D