History of Math Final

Who wrote the first complete mathematical work by a woman that is in existence today?

Maria Agnesi

Who wrote the first surviving mathematical text by a woman?

Maria Agnesi

which of the following numeration systems had a symbol for zero

Mayan

What method did archimedes use to approximate the area of a circle

Method of exhaustion (using inscribed and circumscribed polygons in circles)

What did newton call his method of calculus

Method of fluxions

Which statistical method was formulated by Gauss while he was in prep school?

Method of least squares

on what meterial did egyptians write their documents?

Papyrus

What was the motto on Gauss's unofficial coat of arms?

Pauca sed matura

What did the picture-symbols in the egyptian numeration system represent?

Powers of ten

What are Mersenne primes?

Prime numbers that can be written in the form 2 ^(n) - 1

who believed that numbers is the substance of all things

Pythagoreans

which of the following triangle congruence theorems is equivalent to the proposition? "If two triangles have the two sides equal to two sides respectivley, and also have the base equal to the base, then they also have the angles equal which are contained by the equal straight lines.

Side Side Side Congruence Theorem

the number 5268 is equivalent to which of the following is sexagesimal notation?

1,27,48

What is the fourth triangle number

10

What does the fundamental theorem of arithmetic have to say about the number 144

144 cannot be written as a product of prime numbers; therefore it is a perfect number

using Hindu-Arabic notation, the numeral 3, 8, 14, 2 represents a mayan numeral. What is the value of the place in which 8 is positioned?

18*20 = 360

Use the splitting identity to write the fraction 2/13 as the sum if unit fractions

2/13 = 1/13 + 1/14 + 1/182

What is the base for a vigesimal numeration system

20

What is the hindu arabic numeral that is equivalent to the roman numeral MMDCXLIX

2649

what is the archimedean value of pi

3 1/7

A babylonian tablet found in 1936 shows the babylonias sometimes used a more accurate value of pi than 3 they determined the area of a circle by taking it as equal to 24/25 of 1/12 the square of the circles circumference. What calue of pie does this yeild?

3 1/8

Fill in the blank: 13,456 = 1 * 10,000 + 3 * 1,000 + ___ * 10 + 6 * 1

45

Solve the following problem from a babylonian tablet. "I summed the area and a fourth of my square side so that it was 0;45." Let x be the square side and represent the word problem algebraically. Which of the following quadratic equations represents this problem?

4x^2+x-3=0

The rhind papyrus contains a problem in which the reader is asked to perform a calculation. Here are the instructions in my own paraphrased form. "You shall subtract 1/9 of 9 from 9 to get a number. square that number. multiply the result by 10 add half of that number to itself what is the final result

960

Which mathematician was the daughter of the British poet, Lord Byron, and wrote about how to program Charles Babbage's Analytical Engine?

Ada Byron King

Use the egyptian doubling and adding method to find the product of 36 and 49. begin the method by doubling 1 and 4. Which numbers do we add together to get the product of 36 and 49?

Add the multiples of 49 that correspond to the powers of 2 that add up to 36.

what is the city in present day northern egypt that was the center for learning during the height of the greek civilization

Alexandria

Which of the following was the most famous of archimedes inventions

Archimedian Screw

Which two mathematicians (in addition to Gauss) finally rejected the Parallel Postulate creating Non-Euclidean Geometry?

Bolyai and Lobachevsky

What mathmetician wrote about negative numbers as "debts" and positive numbers as "fortunes"

Brahmagupta

Who is known as the Prince of Mathematicians?

Carl Friedrich Gauss

What are the three points that lie on an Euler line?

Centroid, Circumcenter, Orthocenter

Florence Nightingale's rose diagram was a variant of which of the following graphs?

Circle Graph

Where do we get most of our information about the babylonian mathematics

Clay Tablets

What are the only two tools that are allowed to trisect an angle accordign to the ancient "Rules"

Compass and straightedge

What information did Gauss add to our understanding of the fundamental theorem of algebra?

Complex solutions occur in conjugate pairs.

What was the babylonian style of writing called

Cuneiform

Who translated Newton's book, the Principia, into French?

Emilie du Chatelet

Which mathematician whose research was in modern algebra left Nazi Germany to teach at Bryn Mawr College in the United States?

Emmy Noether

What do we call two numbers that are equal to the sum of the proper divisors of the other number?

Friendly numbers

Which mathemetician is credited with first using the symbol / for the integral

Gottfried Wilhelm Leibniz

Working independently of Isaac Newton, what other mathematician developed the basics of calculus at just about the same time?

Gottfried Wilhelm Leibniz

Which mathematician was the highest ranking woman in the U.S. Navy when she died?

Grace Hopper

Who coined the phrase "de-bugging" when she discovered that a moth had gotten into one of the early computers and caused a short in the machine?

Grace Hopper

Eulers work on the konigsberg bridge problem laid the fondation for which branch of mathematics

Graph Theory

Euler gave several proofs of Heron's formula for the area of a triangle with side lengths a, b, and c: Area = Sqrt(s*(s-a)*(s-b)*(s-c)) what is s

Half the perimeter of the triangle

Many mathematicians made progress on the proof of the Fundamental Theorem of Algebra. What was Euler's contribution?

He proved the theorem for polynomial equations of degree less than or equal to 6.

With which physical disability was Euler afflicted in his later years?

He was blind.

Why is Leonhard Euler known as the most prolific mathematician?

He wrote a massive amount of material during his lifetime, much of which remained unpublished at his death.

What is the subject of the Prime Number Theorem?

How many prime numbers are there less than a given positive integer?

Who was the first prominent woman mathmetician

Hypatia

What is the difference between an arithmetic sequence and a geometric sequence?

In an arithmetic sequence, consecutive terms have a common difference. In geometric sequences, consecutive terms have a common ratio.

Who wrote the principia

Isaac Newton

What does the Fundamental Theorem of Algebra tell us about the equation x^4 + 3 = 4x?

It has at most 4 complex solutions.

when you are using the Euclidean algorithm to find the greatest common divisor of two numbers, how do you know which number is the greatest common divisor

It is the last non zero remainder rhat you get when you divide.

why is the rhind papyrus significant in the history of mathematics

It is the source of most of our knowledge of egyptian mathematics.

Why is euclids elements considered the most important mathematical text of all time.

It provided a model of an axiomatic system with definitions, axioms, and theorems.

Which mathematician was unable to obtain a professorship in her native country of Russia or in Germany but did obtain a position in Sweden?

Sofia Kovalevskaya

Which French mathematician corresponded with Carl Friedrich Gauss using the pseudonym, L. LeBlanc?

Sophie Germain

Which French mathematician intervened with the French army to guarantee Gauss's safety during the Napoleonic wars?

Sophie Germain

who is the earliest mathmetician of whom we have any knowledge?

Thales

How was the ancient Indian interpretation of the Pythagorean relationship different from that of the ancient greeks

The Indians applied the relationship to the side lengths and the diagonal of a rectangle.

What is the most significant contribution of Indian mathematics to the development of the history of mathematics

The base ten numeration system

What was the pythagorean crisis in mathematics

The discovery of irrational numbers.

In a given right triangle, we know that the equation x^2 = y^2 - z^2 is a relationship that is true for the sides of the triangle what is y?

The length of the hypotenuse

What is the method that was used in the rhind papyrus to solve linear equations

The method of false position

The babylonian tablet pictured below provides evidence that the babylonians knew about which mathematical idea or procedure?

The pythagorean theorem

According to Newton, what is fluxion

The speed at which the quantity changes

According to Euclid's Fifth Postulate, what is true if a transversal intersects two straight lines such that the sum of the measures of the interior angles on the same side is less than 180 degrees?

The two straight lines meet on the same sides as the interior angles

what was unique about the egyptians work with fractions

Their refusal to deal with fractions that were not unit fractions

Are there any odd perfect numbers?

This remains an unsolved problem.

What is Newtons third law of motion due to gravity

To every action there is an equal and opposite reaction

What purpose did the sieve of Eratosthenes serve

To identify prime numbers

What si zero divided by zero

Zero divided by zero is not defined because there are infinity numbers that you can multiply by zero and get zero as a product.

what is a postulate

a statement that is accepted as true without proof

Which of the following is known as Euler's identity?

e^(ix) = cos(x) + i * sin(x)

What is the restriction on the function f(x) in the fundamental theorem of calculus

f(x) must be continuous on [a, b]

How did newtons generalized binomial theorem improve on the expansion of (a+b)^n

n could be any rational numer

why did the greeks classify 6 as a perfect number

six is a perfect number because it is the sum of its proper factors: 6 = 1+2+3

Which number did Euler refer to as "neither nothing, nor greater than nothing, nor less than nothing"?

sqrt(-1)

Supposed a given right triangle has legs whose lengths are x and y and has a hypotenuse whose length is x+2 what expression is y equal to?

sqrt(4x+4)

Using Newtons method what is the formula for determining the nth term in a sequence of approximations to a solutions of a polynomial equation?

x<n = x<n-1 - (f(x<n-1))/(f'(x<n-1))

set up this problem using the babylonian z-Method.; "The difference of two numbers is 18 the product of two numbers is 15 what ware the two numbers?" What expression would you use to represent the two numbers?

z+9 and z-9