Contributions of Indian to the world in Mathematics & Astronomy .

Indian Knowledge System Contributions of Indian to the world in Mathematics & Astronomy.

1. Contributions of Indian to the world in Mathematics & Astronomy . Dr.K.BHARATH, Associate Professor – MBA, School of Comm & Mgmt , Sanjivani University , Kopargaon Maharashtra

2. Introduction to Science and Technology in Ancient India Ancient India was a hub of scientific and technological innovation . Key fields of advancement: Mathematics, Astronomy, Medicine, Metallurgy, and Engineering . Contributions to global knowledge: Concepts like zero, decimal system, and early surgical techniques.

3. Key Scientific Achievements Mathematics: Invention of zero, development of the decimal system, and contributions to algebra and geometry . Astronomy : Aryabhata's work on the heliocentric theory, calculation of the Earth's circumference, and the concept of planetary motion . Medicine : Sushruta's advancements in surgery, including cataract surgery, and Charaka's contributions to Ayurveda.

4. Contributions of Aryabhata of I ndian to the world Introduction to Aryabhata: Aryabhata (476-550 CE) was a renowned Indian mathematician and astronomer. Authored the famous work " Aryabhatiya " at the age of 23. Key Mathematical Contributions: Decimal Number System: Introduced the concept of zero and the place-value system. Laid the foundation for the modern decimal system. Approximation of Pi (π): Calculated the value of Pi as 3.1416, remarkably close to the actual value. Emphasized the importance of Pi in geometry and trigonometry. Trigonometry: Developed the sine ( jya ) and cosine ( kojya ) functions. Provided tables of sines, which were later adopted in global mathematics.

5. Aryabhata's Contributions to Astronomy Heliocentric Theory : Proposed that the Earth rotates on its axis, explaining the apparent movement of stars . Suggested that the Moon and planets shine due to reflected sunlight . Eclipses: Provided a scientific explanation for solar and lunar eclipses . Explained that eclipses occur due to the shadows cast by the Earth and Moon Calendar and Timekeeping : Developed a calendar system based on the rotation of the Earth and the positions of the planets . Accurately calculated the length of the solar year as 365.358 days , close to the modern value . Legacy: Aryabhata's work influenced both Indian and Islamic scholars, and his ideas spread to Europe, shaping early modern astronomy .

6. Contributions of Brahmagupta of Indian to the World Introduction to Brahmagupta : Brahmagupta (598-668 CE) was a prominent Indian mathematician and astronomer . Known for his influential work, the Brahmasphutasiddhanta (The Opening of the Universe ). Key Mathematical Contributions : Zero as a Number : Brahmagupta was the first to define zero as a number and explained its mathematical operations. Introduced rules for addition, subtraction, and multiplication involving zero . Negative Numbers : Defined operations with negative numbers, including subtraction and addition with negative values . Quadratic Equations : Provided solutions to quadratic equations and laid the groundwork for the quadratic formula . Devised methods for solving indeterminate quadratic

7. Brahmagupta's Contributions to Astronomy and Geometry ASTRONOMY: Calculation of Planetary Positions : Developed methods to compute the positions and movements of planets . Eclipses: Calculated the occurrence of solar and lunar eclipses with high accuracy . Length of the Year : Determined the length of the sidereal year as 365.2588 days, remarkably close to modern measurements . GEOMETRY: Cyclic Quadrilaterals : Formulated the Brahmagupta’s Formula to calculate the area of cyclic quadrilaterals . Pythagorean Theorem : Extended the work of Pythagoras to prove the theorem and applied it to astronomy and geometry . Concept of Gravity : Suggested that the Earth attracts objects, an early notion of gravity, centuries before Newton Legacy: His work in both mathematics and astronomy influenced future scholars, cementing his place as one of the greatest mathematicians in history.

8. BHASKARACHARYA’S CONTRIBUTIONS TO MATHEMATICS Introduction to Bhaskaracharya :: Bhaskara II (1114-1185 CE), also known as Bhaskaracharya , was a leading Indian mathematician and astronomer . Famous for his comprehensive work " Siddhanta Shiromani" (Crown of Treatises). Key Mathematical Contributions:: Algebra : Authored " Bijaganita " (Algebra), which systematically explained algebraic concepts . Solved quadratic, cubic, and quartic equations . Concept of Infinity : Addressed division by zero, proposing that any number divided by zero results in infinity, a revolutionary idea for the time . Differential Calculus : Anticipated principles of calculus centuries before its formal development by Newton and Leibniz . Discussed the concept of instantaneous velocity and rates of change.

9. BHASKARACHARYA’S CONTRIBUTIONS TO ASTRONOMY AND TRIGONOMETRY Astronomy : Astronomical Calculations : Wrote the " Goladhyaya " (Sphere) chapter, focusing on the geometry of celestial bodies . Calculated the time for Earth’s rotation on its axis and its orbit around the Sun . Eclipses and Planetary Positions : Provided accurate calculations of solar and lunar eclipses and the positions of planets . Earth’s Circumference : Estimated the Earth's circumference with remarkable precision for his time.

10. BHASKARACHARYA’S CONTRIBUTIONS TO ASTRONOMY AND TRIGONOMETRY Trigonometry: Trigonometric Functions: Contributed to the development of sine and cosine functions in trigonometry. Created precise trigonometric tables that were later used globally. Applications in Astronomy: Applied trigonometric principles to solve astronomical problems and improve calendar systems.

11. BHASKARACHARYA’S CONTRIBUTIONS TO ASTRONOMY AND TRIGONOMETRY Legacy : Bhaskaracharya’s works were translated into several languages, spreading his ideas across the world . His contributions to algebra, calculus, and astronomy laid the foundation for future developments in both Eastern and Western science.