MAT 300
Spring 2004 E-mail Assignements
| EA1 | EA2 | EA3 | EA4 | EA5 | EA6 |
| EA7 | EA8 |
The answers to the following questions should be emailed to me by 5:00 pm on Monday, February 2.
a. When was the Rhind Mathematical Papyrus written (copied) and who was the scribe that copied it?
b. The Egyptians recorded their mathematics on papyrus. We write on paper. What medium did the Mesopotamians (Babylonians) of the Hammurapi era use for recording their writing and mathematics (i.e. what did they "write on")?
The answers to the following questions should be emailed to me by 7:00 pm on Monday, February 9. You will need to use your text and the handout with the contents of the Rhind Papyrus and the Moscow Papyrus. Again, these questions are short-answer questions.
In the Rhind Papyrus, the method of false position is used to solve what kind of equations?
What does the Egyptian term pesu refer to in the Rhind and Moscow papyri? You will need a phrase or sentence to answer this question.
The Rhind and Moscow papyri have problems involving the pesu of two "foods" made from grain. What are those two "foods"?
What does the Egyptian term seked refer to?
The answers to the following questions should be emailed to me by 2:00 pm on Tuesday, February17. The answers are all in the reading in the course text.
What numbers are characterized by the author of our text as regular sezagesimal numbers?
How did the Babylonians do the equivalent of our operation of division?
Give one way that the Babylonians would have found the area of a circle. While we might think in terms of formulas, the Babylonians would have thought in terms of procedures or processes.
Plimpton 322 is a tablet in the Plimpton Collection at Columbia University. In the text's discussion of Plimpton 322, which column does not actually appear on the tablet?
The answers to the following questions should be emailed to me by 6:00pm on Monday, February 23. You will need to do the assigned reading in the text and the assigned readings from the MacTutor History of Mathematics website.
Identify the modern country in which each of the following cities is located. There is a map on the insider back cover of your text that may prove useful. Also note that only one of the four cities would actually lie in modern Greece.
Athens
Crotona
Miletus
Syracuse
Many textbooks on the history of mathematics credit Thales with five theorems of elementary geometry: State one of these theorems.
How many titled works (books, articles, etc.) can we attribute to Pythagoras? Note that I am distinguishing between a work and a result. For example, the proof of the "Pythagorean theorem" is a result, but not a work.
Give two examples of (classes of) figurate numbers. Your answer should be the name of the class of numbers, not specific examples of that class. For example, if "odd numbers" were an acceptable answer (which it is not), I would want your answer to be "odd numbers", not an example of an odd number.
State the problem of "squaring the circle".
The answers to the following questions should be emailed to me by 5:30 pm on Thursday, March 4. You will need to do the assigned reading in the text and the assigned readings from the MacTutor History of Mathematics website.
What is a lune?
What statement was written above the door to Plato's Academy?
Eudoxus used the method of exhaustion to to prove that the volume of a cone is one-third the volume of the cylinder having the same base and height. However, another Greek mathematician is often credited with first stating that relationship, although not proving it. Who was that mathematician? Hint: It was not Antiphon.
What were the two "academic" institutions founded in Alexandria around 320 BCE by Ptolemy?
Euclid's most famous work was called The Elements. However, that was not his only work. Name one other work by Euclid.
The answers to the following questions should be emailed to me by 10:00 pm on Monday, March 8. These questions are based on already assigned reading, particularly the reading in the text and from the MacTutor website that were assigned for Thursday, March 4.
Euclid's Elements is a work broken into thirteen sections called books, and we call those sections Book I, Book II, Book III, ....., Book XIII. Which of these thirteen Books were on Number Theory?
What Greek mathematician was the first major historian of mathematics?
What work is our principal source of information about the early history of Greek geometry and who was the author? Note: The answers to #3 and #4 are NOT the same person.
One of the handouts in class on Thursday was a list of definitions from Book VII of Euclid's Elements. Note that Book VII is about numbers, not magnitudes. According to Euclid, what is the definition of a composite number? If you did not get a copy of the handout on Thursday, you can can find Euclid's Elements online at http://aleph0.clarku.edu/~djoyce/java/elements/elements.html . You then just need to find the Book VII definitions.
The answers to the following questions should be emailed to me 6:00 pm on Monday, March 15. These questions are based on Chapter 2 and Section 3.1 in the text and the new readings from the MacTutor website.
Euclid begins Book II of the Elements with a definition. State that definition.
Give an example of material in The Elements that is probably due to Theaetetus.
In which Book of the Elements does Euclid first discuss the similarity of figures?
The method of exhaustion was used to deal with what kinds of problems?
What was the contribution of Eratosthenes to the problem of doubling the cube?
What is a palimpsest ?
The answers to the following questions should be email to me by 12:00 pm (noon) on Tuesday, April 6. The questions are based on Chapter 3 in the text, the new readings from the MacTutor website, and a website to be referenced below.
There is a website related to the program on Archimedes that we saw in class. The site is http://www.pbs.org/wgbh/nova/archimedes/ . On that page is a link to another page called "Approximating Pi". Go to the "Approximating Pi" page. There you will find a link to an interactive diagram which can be used to approximate the circumference of a circle of diameter 1, using the perimeters of regular inscribed and circumscribed polygons. Using that page, find the perimeter of the inscribed hexagon (6 sides) and the perimeter of the circumscribed hexagon. Note that answers are given to four decimal places. If you have trouble running the interactive applet, there is a link there to a Non-interactive Version, that will allow you to do the assignment.
Using the website given in #1, find the perimeter of the inscribed polygon of 48 sides and the perimeter of the circumscribed polygon of 48 sides.
What combination of geometric shapes was inscribed on the gravestone of Archimedes and what result did that engraving represent? The result was one that Archimedes may have considered his most important.
What was the name of Apollonius' most important work?
Apollonius dealt with the focal properties of the ellipse and the hyperbola, but not the focal property of the parabola. That property was proven by Diocle. What is the focal property of the parabola?
Most Greek mathematicians/astronomers believed that the sun revolved around the earth. Apollonius had two models for this motion. One was called the eccenter (or eccentric) model. What was the other called?
In which of Ptolemy's works does his chord table appear?
Last updated: April 3, 2004