Sridhar Acharya was an Indian mathematician from the 10th century AD who wrote two influential treatises on mathematics covering topics like counting, fractions, equations, and mensuration. He introduced concepts like zero and was one of the first to provide a formula for solving quadratic equations. Shakuntala Devi was an Indian mental calculator who achieved fame in the 1980s for her extraordinary ability to perform complex mathematical calculations within seconds. She correctly multiplied two 13-digit numbers picked at random in 28 seconds, as verified by computers. Liu Hui was a 3rd century Chinese mathematician who made important contributions to geometry and calculations of pi in his commentaries on a famous Chinese mathematics book. He presented an algorithm

1. mathematicians
Indian and international

2. INDIAN

3. Sridhar Acharya

4. Sridhar Acharya
Sridhar Acharya (c. 870, India – c. 930 India) was an
Indian mathematician, Sanskrit pundit and
philosopher. He was born in Bhurishresti
(Bhurisristi or Bhurshut) village in South Radha (at
present Hughli) in the 10th Century AD. His father's
name was Baladev Acharya and mother's name
was Acchoka. His father was also a Sanskrit pundit.

5. His works (1)
• He was known for two treatises: Trisatika (sometimes
called the Patiganitasara) and the Patiganita. His
major work Patiganitasara was named Trisatika
because it was written in three hundred slokas. The
book discusses counting of numbers, measures,
natural number, multiplication, division, zero, squares,
cubes, fraction, rule of three, interest-calculation, joint
business or partnership and mensuration.

6. His works (2)
• He gave an exposition on zero. He has written, "If 0(zero) is added to any number,the sum is the
same number; If 0(zero) is subtracted from any number,the number remains unchanged; If 0(zero)
is multiplied by any number,the product is 0(zero)". He has said nothing about division of any
number by 0(zero).
• In the case of dividing a fraction he has found out the method of multiplying the fraction by the
reciprocal of the divisor.
• He wrote on practical applications of algebra separated algebra from arithmetic
• He was one of the first to give a formula for solving quadratic equations.
• He found the formula :-
• Ax^2+bx+c=0
• 4a^2x^2+4abx+4ac=0
(Multiply by 4a)

7. Shakuntala Devi

8. Shakuntala Devi
• Shakuntala Devi (November 4, 1929 – April 21, 2013) was an
Indian writer and mental calculator, popularly known as the
"human computer”. A child prodigy, her talents eventually
earned her a place in the 1982 edition of The Guinness Book of
World Records. As a writer, Devi wrote a number of books,
including novels and non-fiction texts about mathematics,
puzzles, and astrology. She also wrote what is considered the
first study of homosexuality in India; it treated homosexuality
in an understanding light and is considered pioneering.

9. Achievements
• In 1977, at Southern Methodist University, she was asked to give the 23rd root
of a 201-digit number; she answered in 50 seconds. Her answer—
546,372,891—was confirmed by calculations done at the U.S. Bureau of
Standards by the UNIVAC 1101 computer, for which a special program had to
be written to perform such a large calculation.
• On June 18, 1980, she demonstrated the multiplication of two 13-digit
numbers—7,686,369,774,870 × 2,465,099,745,779—picked at random by the
Computer Department of Imperial College, London. She correctly answered
18,947,668,177,995,426,462,773,730 in 28 seconds. This event is mentioned in
the 1982 Guinness Book of Records. Writer Steven Smith states that the result
is "so far superior to anything previously reported that it can only be described
as unbelievable".

10. INTERNATIONAL

11. Liu hui

12. Liu Hui
• Liu Hui (fl. 3rd century) was one of the greatest mathematicians of
ancient China. He lived in the state of Cao Wei during the Three Kingdoms
period of Chinese history. In 263, he edited and published a book with
solutions to mathematical problems presented in the famous Chinese
book of mathematics known as The Nine Chapters on the Mathematical
Art.
• He was a descendant of the Marquis of Zixiang of the Han dynasty,
corresponding to current Zixiang township of Shandong province. He
completed his commentary to the Nine Chapters in the year 263.
• He probably visited Luoyang, and measured the sun's shadow.

13. Mathematical work
• In his commentaries on the Nine Chapters, he presented:
• An algorithm for calculation of pi (π) in the comments to chapter 1. He calculated
pi to 3.141024 < pi < 3.142074 with a 192 (= 64 × 3) sided polygon. Archimedes
used a circumscribed 96-polygon to obtain the inequality pi <tfrac, and then
used an inscribed 96-gon to obtain the inequality tfrac < pi . Liu Hui used only
one inscribed 96-gon to obtain his π inequalily, and his results were a bit more
accurate than Archimedes'.[8] But he commented that 3.142074 was too large,
and picked the first three digits of π = 3.141024 ~3.14 and put it in fraction form pi
= tfrac{157}{50}. He later invented a quick method and obtained pi =3.1416,
which he checked with a 3072-gon(3072 = 512 × 6). Nine Chapters had used the
value 3 for π, but Zhang Heng (78-139 AD) had previously estimated pi to the
square root of 10.

14. • This smaller work outlined instructions on how to measure distances and heights
with "tall surveyor's poles and horizontal bars fixed at right angles to them the
following cases are considered in his work:
• The measurement of the height of an island opposed to its sea level and viewed
from the sea
• The height of a tree on a hill
• The size of a city wall viewed at a long distance
• The depth of a ravine (using hence-forward cross-bars)
• The height of a tower on a plain seen from a hill
• The breadth of a river-mouth seen from a distance on land
• The width of a valley seen from a cliff
• The depth of a transparent pool
• The width of a river as seen from a hill
• The size of a city seen from a mountain.

15. Liu Xin

16. Liu Xin
• Liu Xin (ca. 50 BC – AD 23), later changed name to Liu
Xiu courtesy name Zijun, was a Chinese astronomer,
historian, and editor during the Western Han Dynasty
(206 BC-AD 9) and Xin Dynasty (AD 9–23). He was the
son of Confucian scholar Liu Xiang (77–6 BC) and an
associate of other prominent thinkers such as the
philosopher Huan Tan (d. 28 AD). Liu founded the Old
Text school of Confucianism.

17. Calculation of pi (π)(1)
• For centuries before the reign of Wang Mang (r. 9–23) the Chinese
had used the value of 3 for their calculation of pi,[4] the ratio of a
circle's circumference to its diameter (now known to be
approximately equal to 3.14159). Between the years 1 and 5, while
working for the de facto head of state Wang Mang, Liu Xin was the
first to give a geometrical figure which implies a more accurate
value of pi at 3.1547, although the exact method he used to reach
this figure is unknown. However, the ancient record of Liu Xin's 'Jia
Liang Hu' standard is still preserved in Beijing, which Joseph
Needham quotes below with modern references for archaic units.

18. Calculation of pi (π)(2)
• The standardised chia liang hu (has) a square with each
side 1 chhih (foot) long, and outside it a circle. The distance
from each corner of the square to the circle (thiao phang) is
9 li 5 hao. The area of the circle (mu) is 162 (square) tshun
(inches), the depth 1 chhih (foot), and the volume (of the
whole) 1620 (cubic) tshun (inches).[6]
• Later mathematicians such as Zhang Heng (78–139) and
Liu Hui would improve Liu's calculation for pi.