1What is the primary feature of the numeration system in ancient India?
It was a place value system.
2Under what circumstances did the ancient Indians use the Pythagorean Theorem?
The theorem is used to find the length of the diagonals of squares and rectangles.
3Which empire transmitted the Indian numeration system to the west?
Islamic empire
4How was geometry used in the religious text, the Vedas?
Geometry was used to construct altars.
5How were the methods for adding and multiplying in the reading, Methods of Computing, different from the methods that we use today?
-The Indian methods worked from bottom to top.
- The Indian methods worked from left to right.
6How did the writing materials of the ancient Indians affect the development of their algorithms for computing?
The small writing space required the ability to erase a digit as soon as it was no longer needed.
7What was the most famous and important invention of Indian mathematicians?
Base ten numeration system
8What are the Vedas?
Religious texts
9What prompted the ancient Indians to invent their numeration system?
We do not know.
10Which branch of science was most closely related to the Aryans of ancient India?
Astronomy
11How was ancient Chinese mathematics different from ancient Greek mathematics?
The Chinese mathematics did not have a proof-based axiomatic development.
12Which set of numbers was used on the counting boards of the ancient Chinese?
Integers -- both postive and negative
13We have used the word "gnomon" in several places during this course, particularly during the module on ancient Chinese mathematics. What letter of the alphabet is a gnomon shaped like?
L
14What strategy did the Chinese use on their counting boards to avoid confusion between consecutive places?
Alternating the orientation of the rods
15The method that Liu Hui used to approximate the value of π was similar to the method used by which Greek mathematician?
Archimedes
16Why did Chinese mathematics develop independently of Western cultural influence for so long?
The geography of China isolated the region from the rest of the world.
17True or False: The Chinese numeration system that required the use of a counting board and rods was not a positional system.
False
18Why is the book Nine Chapters on the Mathematical Art significant in the history of mathematics?
It is central to Chinese mathematical activity for hundreds of years.
19The Nine Chapters on the Mathematical Art was central to the development of mathematics in which country?
China
20Chinese Square Root Algorithm: If a, b, and c are the digits (respectively) of the square root of x, then which of the following is equal to square root of x ?
100a+10b+c
21The mathematician, al-Khwarizmi, used a symbol for zero in his book about numeration. True or false
True
22In what area did the mathematician, Al-Uqlidisi, make his contributions?
Decimal fractions
23During the period of the Islamic Empire, negative numbers were acceptable solutions of quadratic equations. True or False
False
24What was the FIRST "translation movement?"
The movement to translate the world's knowledge into Arabic.
25Which city was the academic and intellectual center of the Islamic Empire and the home to the House of Wisdom?
Baghdad
26Which mathematician/poet used geometric methods to solve cubic equations?
Omar Khayyam
27What was the significance of The Book on Addition and Subtraction?
It explained the use of the Hindu decimal system of numerals.
28To what did "al-Jabr" and "al-Muqabala" refer in the title of al-Khwarizmi's book?
The operations used during the Islamic Empire to solve equations.
29In what branch of mathematics were the most important contributions of the Islamic mathematicians?
Algebra
30The Islamic mathematician, al-Khwarizmi, made his most significant contributions to which topic in mathematics?
Solving equations
31A Chinese text from the eleventh century provides evidence that they knew about what mathematical idea that is usually associated with a 17th century French mathematician?
Pascal's triangle
32What was the source of most of the mathematics in Fibonacci's work?
The procedures and concepts of tenth-century Islamic mathematics.
33Who was the greatest European mathematician of the 11th and 12th centuries?
Leonardo of of Pisa
34What is the most famous problem in Liber Abaci?
The rabbit problem
35In medieval Europe, which institution filled the educational void?
The Christian church
36What is the 6th number in the Fibonacci sequence? Be careful about this one. I am asking about the Fibonacci sequence as we know it today -- not the way that Fibonacci presented it in his book.
8
37Which equation defines the golden ratio, b/a?
b/a=(a+b)
38What is zero divided by a negative number?
Zero
39The Mathematical Classic of Master Sun is an important work from which country or empire?
China
40How did the educational system in medieval India facilitate the transmission of mathematical knowledge from one generation to the next?
The education system was family-based, and families would pass their libraries and traditions down to the next generation.
41Which mathematician used the letters at the end of the alphabet to represent unknown quantities and the letters at the beginning of the alphabet to represent known quantities or constants?
Rene Descartes
42Which book is considered the first book devoted entirely to algebra?
Arithmetica
43What is "syncopated" algebra?
Shorthand way of writing algebraic expressions using abbreviations
44What were the primary contents of the book, Ars Magna?
The solution of cubic and quartic equations.
45Who is the father of English cryptography?
John Wallis
46Bombelli wrote "It was a wild thought in the judgment of many; and I too for a long time was of the same opinion." Bombelli was referring to what set of numbers?
Imaginary numbers
47What strategy did Girolamo Cardano use to solve cubic equations?
With a particular substitution, he transformed the cubic equation into a quadratic equation which he did know how to solve.
48In which area did Girolamo Cardano make the most significant contributions?
Algebra
49In which stage of algebraic development did Diophantus make contributions?
Syncopated
50Who is sometimes called the "father of algebra?"
Diophantus
51Why did John Napier invent logarithms?
To make computation with large numbers less tedious.
52Who wrote the mathematical text, Almagest?
Ptolemy
53For what operation did John Napier use Napier's bones (or Napier's rods)?
Multiplication
54According to Kepler's First Law, what is the shape of planetary orbits around the sun?
Ellipse
55Besides mathematics and astronomy, in which other branch of science did Ptolemy make significant contributions?
Geography
56What is the base in common logarithms?
10
57The Ptolemaic model of the universe is a heliocentric model. True or False
False
58What is the heavenly body that is at the center of the Copernican model of the universe?
The sun
59According to one of the principles in the Copernican model, what is at the center of the moon's orbit?
The earth
60What is a chord of a circle?
A line segment that intersects a circle in two points.
61Who is the Indian mathematician who introduced negative numbers and the rules for computing with them?
Brahmagupta
62What was Viete's contribution to the development of the modern symbolism of algebra?
He used letters to represent unknown quantities