Group 3 Flashcards
1
Q
- used small bamboo rods arranged to represent numbers 1 to 9 which were placed in columns representing units, tens, hundreds, thousands, etc.
- decimal place value system
A
Ancient Chinese Number System
2
Q
the Ancient Chinese Number System dates back to at least the
A
2nd millennium BCE
3
Q
- similar to the counting board
- used beads sliding on wire
A
Abacus
4
Q
first Chinese abacus
A
suanpan
5
Q
first Chinese abacus dates back to about
A
2nd century BCE
6
Q
one of the first known examples of a magic square
A
Lo Shu Square
7
Q
Same sum in magic squares is called
A
magic constant
8
Q
magic constant of the Lo Shu Square
A
15
9
Q
Lo Shu Square dates back to
A
650 BCE
10
Q
legend of Emperor Yu’s discovery of the square on the back of a turtle is set as taking place in about
A
2800 BCE
11
Q
bigger magic squares culminated in the elaborate magic squares, circles, and triangles of who
A
Yang Hui (13th century)
12
Q
Yang Hui’s triangle is identical to the later
A
Pascal’s triangle
13
Q
- written over a period of time probably by a variety of authors
- became an important tool in the education of civil service
- covered hundreds of problems in practical areas such as trade, taxation, engineering, and payment of wages
A
Jiuzhang Suanshu or Nine Chapters on the Mathematical Art
14
Q
example of equation on the Nine Chapters on the mathematical art
A
deduction of an unknown number from other known information
15
Q
Who re-discover the sophisticated matrix-based method found in the Nine Chapters on the Mathematical Art
A
Carl Friedrich Gauss
16
Q
- First mathematician known to leave roots unevaluated giving more exact results
- Formulated an algorithm using a regular polygon with 192 sides which calculated the value of π as 3.14159
- Developed early forms of integral and differential calculus
- Among the greatest mathematicians in Ancient China
- produced a detailed commentary on the “Nine Chapters”
A
Liu Hui
17
Q
What did Liu Hui formulate
A
algorithm using a regular polygon with 192 sides which calculated the value of π as 3.14159
18
Q
What did Liu Hui develop
A
integral and differential calculus’ early forms
19
Q
To calculate the smallest value of the unknown number, it uses the remainders after dividing the unknown number by a succession of smaller numbers, such as 3, 5 and 7
A
Chinese Remainder Theorem
20
Q
who initially posed the Chinese Remainder Theorem
A
Sun Tzu (3rd century CE)
21
Q
Technique for solving problems in the Chinese Remainder Theorem is used in
A
- measure planetary movements (Chinese astronomers in 6th century CE)
- internet cryptography (today)
22
Q
When is the golden age of chinese mathematics
A
13th century CE
23
Q
- explored solutions to quadratic and even cubic equations using method of repeated approximations
- extended his technique to solve equations involving numbers up to the power of ten
- wrote “Shushu Jiuzhang” or “Mathematical Treatise in Nine Sections”
A
Qin Jiushao
24
Q
Qin Jiushao’s method of repeated approximations is very similar to the later devised by
A
Sir Isaac Newton (17th century)
25
Important study that Qin Jiushao wrote
"Shushu Jiuzhang" or "Mathematical Treatise in Nine Sections"
26
- invented by mathematics in India
- created between the 1st century to 4th centuries and later adopted in Arabic mathematics by the 9th century
Hindu-Arabic numeral system
27
before 1000 BCE in India
Vedic period
28
what was created in Vedic Period
arithmetic operations
29
text that lists several simple Pythagorean triples, as well as a statement of the simplified Pythagorean theorem for the sides of a square and for a rectangle
Sulba Sutras (or “Sulva Sutras”)
30
Sulba Sutras (or “Sulva Sutras”) when
8th century BCE
31
- early as the 3rd or 2nd century BCE
- recognized five different types of infinities: infinite in one direction, in two directions, in area, infinite everywhere, and perpetually infinite
Jain Mathematics
32
- 3rd century CE
- Indians refined and perfected the system, particularly the written representation of the numerals that is used across the world today
- sometimes considered one of the greatest intellectual innovations of all time
Decimal Place Value Number System
33
What was the first character used for the number zero
circle
34
Include zero as a number was credited to who
- Brahmagupta or possibly
- Bhaskara I
35
Golden Age of Indian Mathematics
- 5th - 12th century
- created fundamental advances in the theory of trigonometry
36
- produced categorical definitions of sine, cosine, versine, and inverse sine, and specified complete sine and versine tables
- wrote the Aryabhatiya which summarizes Hindu mathematics up to the 6th Century
Aryabhata
37
summarizes Hindu mathematics up to the 6th century
Aryabhatiya
38
- also called Bhaskaracharya
- Indian mathematician and astronomer who extended Brahmagupta's work on number systems
- made important contributions to many different areas of mathematics
Bhaskara II
39
Bhaskara II is credited with
explaining previously misunderstood operation of division by zero
40
- great 7th Century Indian mathematician and astronomer
- wrote some important works on both mathematics and astronomy
Brahmagupta
41
Brahmagupta is a great __ century Indian mathematician and astronomer
7th
42
Brahmagupta wrote some important works on both what
mathematics and astronomy
43
Most of Brahmagupta's works are composed in __ __, a common practice in Indian mathematics at the time
elliptic verse
44
What is Brahmagupta's most famous text
Brahmasphutasiddhanta
45
Brahmagupta explained how to find what
cube and cube root of integer
46
Brahmagupta gave rules facilitating the computation of what
squares and square roots
47
Brahmagupta gave rules for dealing with what
five types of combinations of fractions
48
Brahmagupta gave the sum of what
squares and cubes of the first natural numbers
49
Brahmagupta established the basic mathematical rules for __ _ __
dealing with zero
50
Brahmagupta's different view of numbers allowed him to realize what
there could be such a thing as a negative number
51
Brahmagupta established __ as a good practical approximation of π (3.141593)
√10 (3.162277)
52
Brahmagupta area of a cyclic quadrilateral
Brahmagupta’s formula
53
Brahmagupta’s celebrated theorem on the diagonals of a cyclic quadrilateral
Brahmagupta's Theorem
54
- sometimes called the greatest mathematician astronomer of medieval India - source for several infinite series expansions
- happy to play around with infinity, particularly the infinite series when most previous cultures are rather nervous about the concept of infinity
Madhava
55
Madhava is sometimes called as
greatest mathematician astronomer of medieval India
56
Madhava is a source for several
infinite series expansions
57
What did Madhava by successively adding and substracting different odd number fractions to infinity
could home in on an exact formula for π
58
- Made significant contributions towards mathematics during the 8th Century onwards
- Were able to draw on and fuse together the mathematical Development of both Greek and Indian
Islamic Mathematics
59
Islamic mathematics made significant contributions toward what century
8th century onwards
60
Islamic mathematics were able to draw on and fuse together the development of both what
Greek and Indian mathematics
61
Islamic mathematics made use of __ __ __ to decorate their buildings, raising mathematics to the form of an art
complex geometric patterns
62
What was set up in Baghdad around 810
House of Wisdom
63
Where was the House of Wisdom set up
Baghdad
64
When was the House of Wisdom in Baghdad set up
around 810
65
Why did Islamic mathematics stagnate
stifling influence of Turkish Ottoman Empire from 14th - 15th century onwards
66
- One of the directors of the house of wisdom in the early 9th century
- Oversaw the translation of the major Greek and Indian mathematical and astronomy works into Arabic
- word “algorithm” is derived from the Latinization of his name, and the word "algebra" is derived from the Latinization of "al-jabr"
- Most important contribution to mathematics was his strong advocacy of the Hindu numerical system
Muhammad al-Khwarizmi
67
Where is the word algorithm derived from
Latinization of Muhammad al-Khwarizmi
68
Where is the word algebra derived from
Latinization of "al-jabr"
69
What is Muhammad al-Khwarizmi most important contribution to mathematics
strong advocacy of the Hindu numerical system
70
- considered the foundational text of modern algebra
- Muhammad al-Khwarizmi's book
The Compendious Book on Calculation by Completion and Balancing
71
- alternative to long multiplication for numbers
- later introduced to Europe by Fibonacci
lattice method
72
Muhammad al-Khwarizmi developed the first what
first quadrant
73
- introduced the theory of algebraic calculus
- used mathematical induction to prove the binomial theorem
- a 10th Century Persian mathematician
- worked to extend algebra still further
Muhammad Al-Karaji
74
- Generalized Indian methods for extracting square and cube roots to include fourth, fifth and higher roots in the early 12th Century
- carried out a systematic analysis of cubic problems
- Usually credited with identifying the foundations of algebraic geometry
Omar Khayyam
75
Omar Khayyam generalized Indian methods for extracting what
square and cube roots to include 4th, 5th and higher roots
76
Omar Khayyam carried out a systematic analysis of what
cubic problems
77
Omar Khayyam is usually credited with identifying what
foundations of algebraic geometry
78
- first to treat trigonometry as a separate mathematical discipline, distinct from astronomy
- gave the first extensive exposition of spherical trigonometry
- one of major contributions were the formulation of the famous law of sines for plane triangles
Nasir Al- Din Al-Tusi
79
Nasir Al- Din Al-Tusi gave the first extensive exposition of what
spherical trigonometry
80
What is Nasir Al- Din Al-Tusi one major contribution
formulation of famous law of sines for plane triangles
81
pioneer in the field of trigonometry
Nasir Al- Din Al-Tusi
82
developed a general formula by which amicable numbers could be derived
9th Century
Arab Thabit ibn Qurra
83
wrote the earliest surviving texts showing the positional use of Arabic numerals, and particularly the use of decimals instead of fractions
10th Century Arab
Abul Hasan al-Uqlidisi
84
continued Archimedes' investigations of areas and volumes, as well as on tangents of a circle
10th Century Arab geometer
Ibrahim ibn Sinan
85
established the beginnings of the link between algebra and geometry, and devised what is now known as "Alhazen's problem"
11th Century Persian
Ibn al-Haytham
86
Ibn al-Haytham devised what is now known as
Alhazen's problem
87
- applied the theory of conic sections to solve optical problems
- pursued work in number theory such as on amicable numbers, factorization and combinatorial methods
13th Century Persian
Kamal al-Din al-Farisi
88
- works included topics such as computing square roots and the theory of continued fractions
- discovery of the first new pair of amicable numbers since ancient times
- first use of algebraic notation since Brahmagupta
13th Century Moroccan
Ibn al-Banna al-Marrakushi
