Great mathematicianBHASKARACHARAYA : Great mathematicianBHASKARACHARAYA By
Sylvia Selva Rani .A
CSE –II year CONTENT : CONTENT INTRODUCTION
TERMS FOR NUMBERS
CONCLUSION INTRODUCTION : INTRODUCTION Bhaskaracharaya is the most well known ancient Indian mathematician.
Bhaskaracharay was popularly known as Bhaskar II.
He was born in 1114 A . D. Bijapur, Karnataka.
He was the famous Indian mathematicians of the Vedic age
He wrote Siddhanta Shiromani when he was 36 years old.
He was also an astronomer FAMILY BACKGROUND : FAMILY BACKGROUND Bhaskara was born into a family belonging to the Brahmin community.
His father Mahesvara was as an astrologer.
His grandfather hold a hereditary post as a court scholar.
A school in 1207 for the study of Bhāskara's writings was setup by his grandson. SIDDHANTA SHIROMANI : SIDDHANTA SHIROMANI Siddhanta Shiromani is Sanskrit which contained four sections:
1) Lilavati (arithmetic)2) Bijaganita (algebra)3) Goladhyaya (sphere/globe)4) Grahaganita (mathematics of the planets) LILAVATI (ARITHMETIC) : LILAVATI (ARITHMETIC) Lilavati is divided into 13 chapters and covers many branches of mathematics.
More specifically the contents include:
Properties of zero.
Estimation of ∏.
Arithmetical terms, methods of multiplication and squaring.
Kuttaka(intermediate equation of Ist order). BIJAGANITA (ALGEBRA) : BIJAGANITA (ALGEBRA) Bijaganita ("Algebra") was a work in twelve chapters. It includes:
Square root(positive & negative root)
Simple equations with more than one unknown.
Quadratic equations with more than one unknown.
Rolle’s theorem – (if f(a) = f(b) = 0 then f '(x) = 0 for a < x< b ) GOLADHYAYA (SPHERE/GLOBE) : GOLADHYAYA (SPHERE/GLOBE) The second part contains thirteen chapters on the sphere. It covers topics such as:
study of the sphere.
Nature of the sphere
Calculating the area of the sphere. TRIGONOMETRY : TRIGONOMETRY The Siddhanta Shiromani (written in 1150) demonstrates Bhaskara's knowledge of trigonometry.
He was the first to give the formula:
Sin(A + B)=sinAcosB + cosAsinB
Sin(A - B)=sinAcosB – cosAsinB
A proof of the Pythagorean theorem by calculating the same area in two different ways and then canceling out terms to get a² + b² = c². PROOF OF THE PYTHAGOREAN THEOREM : PROOF OF THE PYTHAGOREAN THEOREM Slide 11: First let's find the area of the big square, A=c^2.
Area of the blue triangles = 4(1/2)ab
Area of the yellow square = (b-a)^2
Area of the big square = 4(1/2)ab + (b-a)^2= 2ab + b^2 - 2ab + a^2= b^2 + a^2 c^2 = a^2 + b^2,concluding the proof. TERMS FOR NUMBERS : TERMS FOR NUMBERS In English, cardinal numbers are only in multiples of 1000. They have terms such as thousand, million, billion, trillion, quadrillion etc.
eka(1) dasha(10), shata(100) sahastra(1000), ayuta(10,000) laksha(100,000), prayuta
(1,000,000=million) koti(10,000,000), ASTRONOMY : ASTRONOMY The Earth is not flat, it is in spherical in shape.
The north and south poles of the Earth experience six months of day and six months of night.
Bhaskaracharaya was the first to discover gravity, then Sir Isaac Newton gave the law of gravity. CONCLUSION : CONCLUSION He passed away in 1185 AD.
He was the first to find all the fundamentals of the mathematics.
He was the champion among mathematicians of ancient and medieval India .
His works fired the imagination of Persian and European scholars, who through research on his works earned fame and popularity.