HISTORY OF MATH (INDIA)

• Where is India located?

  India is located in South Asia.
• What is the land area of India?

  About 3.28 million square kilometers.
• What does the term 'Ganita' refer to in ancient Indian mathematics?


  'Ganita' refers to the 'Science of Calculations'.
• In what context was mathematics primarily studied in ancient India?

  In the context of numerical computation and geometric measurement.
• How was Indian mathematics utilized in society?

  It was used by common people in their daily activities and profession.
• When does the history of Indian mathematics begin?

  During the Vedic period, around 1500 BCE.
• What is one of the earliest contributions to mathematics from the Vedic period?

  The 'Śulbasūtras'.
• What do the 'Śulbasūtras' contain?

  Rules for geometric constructions and methods for transforming shapes.
• Who is believed to be the inventor of the concept of zero?

  Brahmagupta.
• What operations involving zero did Brahmagupta explain?

  How zero could be used in addition, subtraction, and multiplication.
• What is the Hindu-Arabic numeral system?


  The number system that uses digits from 0 to 9.
• When was the Hindu-Arabic numeral system developed?

  Around the 6th century CE.
• What is one of the most important contributions of the Hindu-Arabic numeral system?

  The use of zero as a number and a placeholder.
• What does the "0" in the number "105" signify?

  It shows there are no tens, separating the hundreds and ones places.
• What trigonometric functions did Indian mathematicians define?

  They defined the sine function, cosine, and versine.
• What is the Sanskrit word for sine?

  "Jya".
• How did Indian mathematicians influence modern trigonometry?

  They developed formulas and relationships of sine and cosine.
• What systematic methods did Indian mathematicians provide for algebra?

  Methods for solving linear and quadratic equations.
• What equation form did Indian mathematicians introduce methods for solving?

  Equations of the form \( ax + by = c \).
• Who is known as the father of Indian Mathematics?

  Aryabhata.
• What areas did Aryabhata work in?

  Square and cube roots, geometrical problems, and quadratic equations.
• What approximation for the value of \( \pi \) did Aryabhata provide?


  \( \pi \approx 3.1416 \).
• What did Aryabhata indicate about \( \pi \)?

  That \( \pi \) is an irrational number.
• How did Aryabhata calculate the length of the sidereal day?

  As 23 hours, 56 minutes, and 4.1 seconds.
• What is a sidereal day?

  The time it takes for the Earth to complete one revolution about its axis with respect to the fixed stars.
• How does a solar day differ from a sidereal day?

  A solar day lasts 24 hours, while a sidereal day is slightly shorter.
• Who introduced the rules for operations of negative numbers?

  Brahmagupta.
• What rule did Brahmagupta state about the product of two negative numbers?

  That the product of two negative numbers is a positive number.
• What was Brahmagupta's focus in his works?

  Astronomical calculations, such as planetary positions and eclipses.
• What is Brahmagupta's Formula used for?

  Calculating the area of a cyclic quadrilateral.
• Who was Bhaskara I?

  An Indian mathematician who lived in the 7th century.
• What is Bhaskara I best known for?

  His commentaries on Aryabhata's work.
• What formula did Bhaskara I suggest for calculating sine?


  \( \sin x = \frac{16x(p - x)}{5p^2 - 4x(p - x)} \).
• Who was Bhaskara II, also known as Bhaskaracharya?

  A 12th century Indian polymath, mathematician, astronomer, and engineer.
• What influential works did Bhaskara II author?

  “Lilavati”, “Bijaganita”, and “Siddhanta Shiromani”.
• What proof did Bhaskara II provide related to the Pythagorean theorem?

  He calculated the same area in two different ways and cancelled out terms.
• Who was Varahamihira?


  An influential Indian mathematician, astronomer, and astrologer from the Gupta period.
• What methods did Varahamihira provide?

  Methods for calculating planetary positions and predicting eclipses.
• What mathematical discovery is Varahamihira known for?

  Discovering the 4x4 magic square.