Mathematics emerged independently in China by the 11th century BC. The Chinese independently developed concepts like large and negative numbers, decimals, algebra, geometry, and trigonometry. Early Chinese mathematics before 254 BC is not well documented, though they focused on astronomy and practical tasks rather than formal systems. Ancient Chinese mathematicians advanced algorithm development and algebra, with significant developments in the 13th century. Elements of early Chinese mathematics correspond to modern branches like number theory and geometry. The Pythagorean theorem and Pascal's triangle existed in China before Pythagoras and Pascal.

3. •Mathematics
in
China
emerged
independently by the 11th
century BC.

4. • The Chinese independently
developed
very
large
and
negative
numbers, decimals, a place
value decimal system,
a
system,
algebra,
geometry,
and trigonometry.

5. • Knowledge
of
Chinese mathematics before
254 BC is somewhat
fragmentary, and even after
this date the manuscript
traditions are obscure.

6. • As in other early societies
the
focus
was
on astronomy in order to
perfect
the
agricultural calendar, and
other practical tasks, and not
on
establishing
formal
systems.

7. • Ancient
Chinese
mathematicians did not develop
an axiomatic approach, but
made advances in algorithm
development and algebra. The
achievement
of
Chinese
algebra reached its zenith in the
13th century, when Zhu
Shijie invented method of four
unknowns.

9. • Frequently, elements of the
mathematics
of
early
societies
correspond
to
rudimentary results found
later in branches of modern
mathematics
such
as
geometry or number theory.

10. • The Pythagorean theorem for
example, has been attested to
the time of the Duke of Zhou.
Knowledge
of
Pascal's
triangle has also been shown
to have existed in China
centuries before Pascal, such as
by Shen Kuo.

11. Early Chinese
Mathematics

12. • Simple mathematics on Oracle
bone script date back to
the Shang Dynasty (1600–
1050 BC). One of the oldest
surviving mathematical works
is the Yi Jing, which greatly
influenced written literature
during
the
Zhou
Dynasty (1050–256 BC).

13. Oracle Bone Script Decimal

14. Yi Jing or I Ching
•

15. • For mathematics, the book
included a sophisticated use
of hexagrams. Leibniz
pointed out, the I Ching
contained elements of binary
numbers.

16. • Since the Shang period, the
Chinese had already fully
developed a decimal system.
Since early times, Chinese
understood basic arithmetic
(which dominated far eastern
history), algebra, equations,
and negative numbers with
counting rods.

17. • Although the Chinese were
more focused on arithmetic and
advanced
algebra
for
astronomical uses, they were
also the first to develop
negative numbers, algebraic
geometry
(only
Chinese
geometry) and the usage of
decimals.

18. • Math was one of the Liù Yì (
六艺) or Six Arts, students
were required to master
during
the
Zhou
Dynasty (1122–256 BC).

19. • Learning them all perfectly
was required to be a perfect
gentleman, or in the Chinese
sense,
a
"Renaissance
Man". Six Arts have their
roots in the Confucian
philosophy.

20. • They
also have geometry
which is the oldest existent
mathematical work in China
which is written in the Mo
Jing.
• It is similar to the definitions
given by the Greeks; Euclid
and Plato.

21. The
Mathematics
In Different
Dynasties

22. Qin Mathematics
• Not much is known about Qin
dynasty
mathematics,
or
before, due to the burning of
books and burying of scholars.
• The Qin dynasty created a
standard system of weights.

23. Han Mathematics
• In the Han Dynasty, numbers were
developed into a place value decimal
system and used on a counting board
with
a
set
of
counting
rods called chousuan, consisted of
only nine symbols, a blank space on
the counting board stood for zero.

24. Suan shu shu
• an ancient Chinese text on
mathematics
approximately
seven thousand characters in
length
• written on 190 bamboo strips

25. The Nine Chapters
Mathematical Art
on
the
• is a Chinese mathematics book,
its oldest archaeological date
being 179 AD (traditionally dated
1000 BC)
• the author(s) are unknown, they
made a huge contribution in the
eastern world

26. • It
was one of the most
influential of all Chinese
mathematical books and it is
composed of some 246
problems.
• It also contains the popular
theory, Chou Pei.

27. Chou Pei

28. • Chou Pei is oldest existing
Chinese texts containing
formal
mathematical
theories
and
were
produced during the Han
period.

29. • The
Arithmetic Classic of the
Gnomon and the Circular Paths of
Heaven (Chou Pei Suan Ching)
is dated before the 3rd century B.C
and contains various modern
mathematical principles such as
working with fractions using a
common denominator, and proofs
of many geometrical theories

30. • The text contains an accurate
process of division for finding
out the square root of
numbers.
• In fact, the Chou Pei presents
the oldest known proof of the
right-angle triangle theory in
the hsuan-thu diagram.

31. • This theory, commonly known
as the "Pythagorean theorem"
shows that the sum of the
squares of the legs of a right
triangle is equal to the squares
of the hypotenuse or a2+ b2 =
c2.

33. • The Chou Pei was not an isolated
academic text shared only by a
few
ancient
Chinese
mathematicians. The principles
in the text were reflected in the
popular approach known as chichu, or "the piling up of squares"
which was a process of using
geometry to solve algebraic
problems.

34. Sample Problems In
Pythagorean Theorem
or Chou Pei

35. • Find the value of ‘x’ using Chou Pei or the
Pythagorean Theorem