digital album mathematicians (1)

FAMOUS MATHEMATICIANS AND THEIR CONTRIBUTIONS Anusree A S Mathematics 2021-23 Batch SNMTC,Moothakunnam

CONTENTS 1. ARYABHATTA 2. BHASKARACHARYA 3. BRAHMAGUPTA 4. RAMANUJAN 5. PYTHAGORAS 6.RENE DESCARTES 7. EUCLID

ARYABHATTA 476CE-576CE

ARYABHATTA Aryabhatta was born in Kusumapura (present-day Patna, India) which is a small town in Bihar, India. Born - 476 CE Died - 550 CE Era - Gupta era Main interests - Mathematics, Astronomy

WORKS Aryabhata is the author of several treatises on mathematics and astronomy some of which are lost. His major work, 'Aryabhatiya', a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modem times. The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spherical trigonometry, It also contains continued fractions, quadratic equations, sums-of- power series, and a table of sines.

CONTRIBUTIONS He discovered the positions of the 9 planets and found that these planets revolve around the sun. Calculated the value of pi=3.1416. Calculated the summation of series of squares and cubes, Determined the area of a triangle.

Table of sine for each 3.45 degrees Introduced Cosine Sum of first n integers, first n squares, and first n cubes. Believed earth rotated on-axis Believed Moon and Planets shine by reflected sunlight He explained how to find cube roots. His value for a year = 365 days and 6 hours ( > actual value by minutes)

BHASKARACHARYA 1114 AD-1185 AD

BHASKARACHARYA Bhaskaracharya was born in Vijjadavida in the Sahyadri mountain range, near the town of Patan in the Western Ghat region in present-day Khandesh in Maharashtra. Born - 1114 AD Died - 1185 AD Era - Shaka era Main interests -Algebra, Calculus, Arithmetic, Trigonometry,Astronomy

WORKS Siddantha Siromani (Grahaganitam and Goladhyaya -This text was by Bhaskara ,when he was 36 years Old( in 1 1.50CE) Lilavati Bijaganitam Karanakutuhalam -This text was composed by Bhaskara ,when he was 69 years old ( inl 18.3CE) Vasana Bhasya

CONTRIBUTIONS He introduced the idea that dividing a number by zero results in infinity. Differential calculus Cyclic Method to solve the algebraic expression. Contribution on permutation. Calculated the derivatives of trigonometric functions and formulae.

CONTRIBUTIONS In Lilavati, solutions of quadratic, cubic, and quartic indeterminate equations are explained. A proof of the Pythagorean theorem by calculating the same area in two different ways. Solving quadratic equations with more than one unknown, and found negative and irrational solutions.

Brahmagupta 598 CE-668 CE

BRAHMAGUPTA Brahmagupta lived in Bhillamāla in Gurjaradesa (modern Bhinmal in Rajasthan, India) during the reign of the Chavda dynasty ruler, Vyagrahamukha. Born - 598 CE Died - 668 CE He was the son of Jishnugupta and was a Hindu by religion, in particular, a Shaivite. Main interests -Mathematics,Astronomy

WORKS Brahmagupta composed the following treatises: Brahmasphutasiddhanta, composed in 628 CE. Khandakhadyaka, composed in 665 CE. Grahanarkajnana,(ascribed in one manuscript)

CONTRIBUTIONS Brahmagupta (AD 628) was the first Mathematician to provide the formula for the area of a cyclic quadrilateral. His contributions to geometry are significant. He is the first to discuss the method of finding a cyclic quadrilateral with rational sides. He introduced four different methods of multiplications namely, Gun Mantrika, Khanda, Bheda, Ista.

CONTRIBUTIONS He explained the method of inversion for the first time. He gave the method of squaring and cubing. His works on arithmetic include integer fractions, progressions, barter, simple interest, the mensuration of plane figures and problems on volumes.

ramanujan 1887-1920

SRINIVASA RAMANUJAN Ramanujan was born into a Tamil Brahmin Iyengar family in Erode, Madras Presidency (now Tamil Nadu, India). Born - 22 December 1887 Died - 26 April 1920 (aged 32) Education - Government Arts College (no degree), Pachaiyappa's College (no degree)Trinity College, Cambridge (Bachelor of Arts by Research, 1916)

WORKS Recorded his work in 4 notebooks of looseleaf paper Results were written without derivation. Mathematician Bruce C. Berndt says that Ramanujan was able to make the proofs but chose not to. Might have worked on slate Or maybe influenced by G.S Carr's book which stated results without proofs Mathematicians such as Hardy, G.N. Watson, B.M. Wilson and Bruce Berndt created papers from his work

CONTRIBUTIONS Ramanujan’s contributions stretch across mathematics fields, including complex analysis, number theory, infinite series, and continued fractions. 1729 is known as the Ramanujan number. It is the sum of the cubes of two numbers 10 and 9. This is the smallest number that can be expressed in two different ways as it is the sum of two cubes.

CONTRIBUTIONS Ramanujan’s other notable contributions include hypergeometric series, the Riemann series, the elliptic integrals, the theory of divergent series, and the functional equations of the zeta function. •December 22, being the birthday of Srinivasa Ramanujan has been declared as the “National Mathematics Day” to be celebrated every year.

pythagoras 570 BC- 495 BC

PYTHAGORAS Pythagoras was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. Born - 570 BC Died - 495 BC Era- Pre-Socratic philosophy Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on the island of Samos.

WORKS Although Pythagoras is most famous today for his alleged mathematical discoveries, classical historians dispute whether he himself ever actually made any significant contributions to the field. He founded a philosophical and religious school in Croton. His followers were commonly referred to as Pythagoreans. He made important developments in music and astronomy. He was an accomplished musician playing the lyre. He was the head of the society with an inner circle of followers known as \"mathematikoi\". They were taught by Pythagoras himself and obeyed strict rules.

CONTRIBUTIONS Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that \"in a right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the two other sides\". His other contributions include Pythagorean tuning, the five regular solids, the Theory of Proportions, the sphericity of the Earth, and the identity of the morning and evening stars as the planet Venus.

CONTRIBUTIONS He identified the properties of numbers such as odd, even, perfect. His discoveries laid the foundation for all the subsequent developments in geometry. Pythagoras is credited with having devised the tetractys, an important sacred symbol in later Pythagoreanism.

rene descartes 1596- 1650

RENE DESCARTES René Descartes was born in La Haye en Touraine, Province of Touraine (now Descartes, Indre-et- Loire), France. Born - 31 March 1596 Died - 11 February 1650 (aged 53) He was a French philosopher, mathematician, and scientist who invented analytic geometry. He is known as the Father of Modern Mathematics. He was also the Founder of Modern Philosophy.

WORKS He is famous for having made an important connection between geometry and algebra, which allowed for the solving of geometrical problems by way of algebraic equations. His famous works include Meditationes de Prima Philosophia. He claimed that education except mathematics gave him little of substance; only mathematics had given him certain knowledge. He was the first major figure in the philosophical movement known as Rationalism ( a method of understanding the world based on the use of reason).

CONTRIBUTIONS His greatest contribution was developing analytical geometry, which is applying algebra to geometry. He established a coordinate plane system, which he developed to visualize and locate exact points. He introduced methodological skepticism (doubted everything but wants certainty in life).

CONTRIBUTIONS Many of his contributions to mathematics are: Cartesian coordinate system Cartesian product Fibred category Cartesian Defect (geometry) Descartes' rule of signs Descartes' theorem Analytic geometry Pullback Theorem

EUCLID 325 BC–265 BC

EUCLID Euclid sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the \"founder of geometry\" or the \"father of geometry\". Born - 325 BC Died - 265 BC •He was the first mathematician who initiated a new way of thinking about the study of geometry.

WORKS The Elements is a mathematical treatise consisting of 13 books attributed to Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century. In addition to the Elements, at least five works of Euclid have survived to the present day. They follow the same logical structure as Elements, with definitions and proved propositions.

CONTRIBUTIONS One of the most notable influences of Euclid on modern mathematics is the discussion of the parallel postulate. In Book I, Euclid lists five postulates, the fifth of which stipulates If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.

CONTRIBUTIONS Euclidean Geometry states that the sum of the angles of a triangle is 180˚. Formulated a method to find out HCF. Gave proof that prime numbers are infinite. First, who proved √2 as a transcendental number.

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