Contribution Of Aryabhatta In Mathematics

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Contribution of aryabhatta in mathematics

Number notation

Numerical values

He made a notation system in which digits are denoted with the help of alphabet numerals e.g., 1 = ka, 2 = Kha, etc.

Aryabhatta assigned numerical values to the 33 consonants of the Indian alphabet to represent 1,2,3…25,30,40,50,60,70,80,90,100.

Notation system

 He invented a notation system consisting of alphabet numerals Digits were denoted by alphabet numerals. In this system devanagiri script contain varga letters (consonants) and avarga letters (vowels).1-25 are denoted by 1st 25 varga letters.

Place-value: Aryabhatta was familiar with the place-value system.

Square root & cube root

His calculations on square root and cube root would not have been possible without the knowledge of place values system and zero. He has given methods of extracting square root cube root along with their explanation.

Algebra

Integer solutions: Aryabhatta was the first one to explore integer solutions to the equations of the form by =ax+c and by =ax-c, where a,b,c are integers. He used kuttuka method to solve problems.

Indeterminate equations: He gave general solutions to linear indeterminate equations ax+by+c= 0 by the method of continued fraction.

Identities: He had dealt with identities like (a+b)2=a2+2ab+b2 and ab={(a+b)2-(a2-b2)}/2

Algebraic quantities: He has given the method of addition, subtraction, multiplication of simple and compound algebraic quantities.

Geometry

Discover the P  Value

The credit for discovering the exact values P may be ascribed to the celebrated mathematician Aryabhatta.

Rule: Add 4 to 100, multiply by 8, add 62000. The result is approximately the circumference of a circle of diameter twenty thousand. By this rule the relation of the circumference to diameter is given.

Trigonometry

Sine Table: Aryabhatta gave a table of sines for calculating the approximate values at intervals of 90/24 = 3 45’. This was done using the formula for sin (n+1)x –  sin nx in terms of sin nx and sin (n-1) x.

Versine: He introduced the versine (versin = 1-cosine) into trigonometry.

Aryabhatta was one of those ancient scholars of India who is hardly surpassed by any one else of his time in his treatise on Mathematics and Astronomy. In appreciation of his great contributions to mathematics and astronomy, the government of India named the first satellite sent into space on 19-4-1975 as aryabhatta, after him.

 

Contribution of Varaha mihira in mathematics

Varahamihira (505 – 587) was an Indian astrologer whose main work was a treatise on mathematical astronomy which summarised earlier astronomical treatises. He discovered a version of Pascal’s triangle and worked on magic squares. He was aware of gravity over a millennium before Isaac Newton.

Varahamihira worked as one of the Navaratnas for Chandragupta Vikramaditya. His book Pancasiddhantika (or Pancha-Siddhantika, The Five Astronomical Canons) dated 575 AD gives us information about older Indian texts which are now lost. The work is a treatise on mathematical astronomy and it summarises five earlier astronomical treatises, namely the Surya, Romaka, Paulisa, Vasistha and Paitamaha siddhantas.

Varahamihira is said to have origins from Eastern Iran from a sect known as Maga Brahmins.(Quote: Ramesh Chitor). In more ways than one, the Surya Siddhanta or Treatise on Sun hints that Mihira was from Iran as Iran was the only South Asian country following the practice of SUN worship. Varaha was a name coined by Vikramaditya- king of Ujjain. Mihira(meaning “friend” in Persian)accurately predicted death of Vikramidtya’s son during the 18th year. The entire army, intelligence and the king could not save this fatal incident. This will remain as the greatest astrological prediction ever made by Mihira. VarahaMihira’s painting can be found in the Indian Parliament alongside Aryabhatta.

Some important trigonometric results attributed to Varahamihira

 

 

 

 

 

 


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Mathematics is a branch of science that deals with the logic of shape, quantity, and arrangement. Math is all around us, in everything we do. It is the building block for everything in our daily lives, including mobile devices, computers, Software, architecture (ancient and modern), art, Money, engineering, and even Sports.

Mathematics is a vast subject, and there are many different branches of mathematics. Some of the most important branches of mathematics include:

Mathematics is a very important subject, and it is used in many different fields. Some of the most common fields where mathematics is used include:

Mathematics is a very important subject, and it is used in many different fields. If you are interested in Learning more about mathematics, there are many Resources available online and in libraries. You can also take math classes at a local community college or university.

Zero

Zero is a number that represents the absence of quantity. It is the only number that cannot be divided by any other number. Zero is also the only number that, when added to any other number, leaves the other number unchanged.

The concept of zero was first developed in India in the 6th century AD. It was introduced to the Western world by the Arabs in the 10th century AD. Zero is now used in all branches of mathematics and science.

Place value system

A place value system is a system of representing numbers using digits and place values. The place value of a digit is determined by its position in the number. The place value of a digit is the product of the digit and the value of the place it occupies.

The place value system is the most common system of representing numbers in the world. It is used in all branches of mathematics and science.

Decimal system

The decimal system is a system of counting and number representation that uses the number 10 as a base. The decimal system is the most common system of counting and number representation in the world. It is used in all branches of mathematics and science.

The decimal system is based on the idea of place value. Each digit in a decimal number has a place value that is determined by its position in the number. The place value of a digit is the product of the digit and the value of the place it occupies.

The decimal system is a very efficient system of counting and number representation. It is easy to learn and use. It is also very versatile and can be used to represent a wide range of numbers.

Trigonometry

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. Trigonometry is used in many different fields, including engineering, surveying, and navigation.

The basic trigonometric functions are sine, cosine, and tangent. The sine of an angle is the ratio of the opposite side of the triangle to the hypotenuse. The cosine of an angle is the ratio of the adjacent side of the triangle to the hypotenuse. The tangent of an angle is the ratio of the opposite side of the triangle to the adjacent side.

Trigonometry is a very important branch of mathematics. It is used in many different fields, including engineering, surveying, and navigation.

Algebra

Algebra is a branch of mathematics that deals with the study of mathematical symbols and how they are used to represent numbers, quantities, and operations. Algebra is used in many different fields, including science, engineering, and finance.

The basic concepts of algebra include variables, equations, and functions. Variables are symbols that represent unknown quantities. Equations are statements that show the Equality

Aryabhata was an Indian mathematician, astronomer, and physicist who lived in the 5th century CE. He is considered one of the greatest mathematicians of all time, and his work had a profound impact on the development of mathematics and astronomy in India and the Islamic world.

Some of Aryabhata’s most important contributions to mathematics include:

Aryabhata’s work had a profound impact on the development of mathematics and astronomy in India and the Islamic world. His work was translated into Arabic and studied by Islamic mathematicians, who built on his work and made further advances in mathematics. Aryabhata’s work also influenced the development of mathematics in Europe, where it was translated into Latin and studied by European mathematicians.

Here are some frequently asked questions about Aryabhata:

  1. Aryabhata was born in which of the following places?
    (A) Patna, India
    (B) Srinagar, India
    (C) Ujjain, India
    (D) Taxila, Pakistan

  2. Aryabhata is best known for his work in which of the following fields?
    (A) Mathematics
    (B) Astronomy
    (C) Medicine
    (D) Astrology

  3. Aryabhata is credited with developing the concept of zero. True or False?

  4. Aryabhata’s work on the decimal system was groundbreaking. True or False?

  5. Aryabhata’s work on trigonometry was also highly influential. True or False?

  6. Aryabhata’s work on astronomy was also highly influential. True or False?

  7. Aryabhata’s work on mathematics and astronomy had a profound impact on the development of science in India. True or False?

  8. Aryabhata’s work was translated into Arabic and Latin, and it had a significant impact on the development of science in the Islamic world and Europe. True or False?

  9. Aryabhata is considered to be one of the greatest mathematicians and astronomers of all time. True or False?

  10. Aryabhata’s work is still studied by mathematicians and astronomers today. True or False?

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