MATH 4109 Test 1
What was the only fraction used by the Egyptians besides unit fractions?
(2/3)
What number does the symbol L represent in the Roman numeral system?
50
What number did the Babylonians use as the base for their numeration system?
60
What number is the base for a sexagesimal numeration system?
60
What strategy did the Romans use to represent numbers that were multiples of 1000?
A bar was drawn over the necessary symbols.
What are the two tools that are allowed for use in solving the three famous problems of antiquity?
A compass and a straightedge
For the Egyptians, the multiplication of two numbers was accomplished by successively doubling one of the factors. After that was done, what operation was used?
Addition
Egypt is on which continent?
Africa
What was the Pythagorean doctrine?
All is number.
What modern mathematical concept explains Zeno's paradox of the tortoise and the hare?
Convergent infinite series
What was the Babylonian style of writing called?
Cuneiform
Which style of writing did the Babylonians use?
Cuneiform
What symbols did the ancient Mayans use to represent the numbers from 1 to 19?
Dots and horizontal bars
True or False: It is commonly accepted that mathematics originated with problems related to solving equations.
False
True or False: The Egyptians had a symbol for zero.
False
True/False: The Babylonian base twenty numeration system enabled them to calculate with fractions as readily as with integers and led to a highly developed algebra.
False
True/False: The mathematical activity of the Babylonian scribes originated in the everyday mathematical necessities handling an agrarian economy -- for example, measuring land and commodities..
False
True/False: There is no evidence that the Babylonians knew how to solve quadratic equations
False, There is evidence.
The method of false position is most similar to which problem-solving strategy?
Guess and Check (also know as trial and error)
According to our notes and discussion, which civilization employed a symbol for zero?
Mayan
Whose army uncovered the Rosetta Stone in 1799?
Napoleon
Which system employed a subtractive principle in which the symbol for a smaller number is placed in front of the symbol for a larger number?
Roman
Who is the first mathematician of whom we have any knowledge?
Thales
The Babylonians were great at arithmetic and left behind many arithmetic tables. Why did the table of reciprocals of numbers have gaps in it?
The Babylonians only understood terminating sexagesimal fractions so they left out the ones that were not terminating.
Most of our knowledge of early mathematics in Egypt comes from two papyri. One is known as the Moscow Papyrus. What is the other one called?
The Rhind Papyrus
The Babylonian empire grew out of ancient Mesopotamia around 2 rivers. What are those two rivers?
The Tigris and the Euphrates
According to Thales, what is true about an angle that is inscribed in a semicircle?
The angle is a right angle
What was the Pythagorean crisis?
The discovery of irrational numbers
Why is it difficult to determine the unique value of a Babylonian numeral?
The lack of a zero makes it difficult to determine the place values of the digits.
Why is it generally accepted that geometry originated in the ancient Egyptian empire?
The yearly floods of the Nile required that land had to be remeasured for tax purposes.
What was unique about the Egyptians' work with fractions?
Their refusal to deal with fractions that were not unit fractions or (2/3)
What was the most important rule that the Egyptians used when they wrote sums of unit fractions?
They could never use the same unit fraction twice.
The Plimpton 322 is an ancient Babylonian clay tablet. It provides evidence that the Babylonians knew about what mathematical idea or procedure?
They knew about the Pythagorean theorem.
The numbers, 1, 3, 6, 10, and 15, are examples of which type of numbers?
Triangular Numbers
One of the three problems of antiquity asks the solver to do what to a given angle?
Trisect the angle
True or False: Greek mathematics was more abstract than the mathematics of the Egyptian and Babylonian empires.
True
True/False: One feature of Babylonian mathematics is the lack of zero in its numeration system.
True
True/False: Thanks to the many clay tablets that have been found and translated, we know that Babylonian mathematics was more advanced than Egyptian mathematics.
True
To find the length of a diagonal of a given square, the Babylonians used an approximation of what irrational number?
sqrt(2)
If "x" is the length of the hypotenuse of a right triangle and "a" is the length of one of the legs, what is the length of the other leg of the triangle?
sqrt(x^2 - a^2)
