Announcements:
January 16 through April 16, 2008
Mathematics became an essential part of literate culture in
England in the early modern period. This exhibition showcases
the means, serious and playful, by which readers learned, practiced, and
implemented mathematics in England, from the mid-sixteenth through the
eighteenth century. Drawing on the Beinecke Library's print and manuscript
collections of early modern English material, the exhibition includes
student exercise books, almanacs, textbooks, illustrations, account books,
poems, literature, and instruments made out of paper. [ca. 60 items]
http://www.library.yale.edu/beinecke/brblevents/brblexhibits.html
http://www.library.yale.edu/beinecke/images/The%20Reckoner's%20Art%20News%20Release.pdf
If you like the exhibit above, you may also want to
check out the following virtual exhibit at the Smithsonian Institution.
"Slates, Slide
Rules and Software: Teaching Math in America".
Homework Assignments (includes reading assignments)
Do the following reading.
On page 27 in the text, read problems 30 and 31, just to get a sense as to the level of algebraic sophistication of Babylonian mathematics. You are not responsible for doing these, and we are not going to do any problems this complicated.
In the course text, read the introduction to Chapter 2 and Section 2.1.1. As usual, don't worry about the technical details of the mathematics on this first reading.
Go to the following website:
The MacTutor History of Mathematics archive (University of St.
Andrews, Scotland)
http://www-groups.dcs.st-and.ac.uk/~history/ .
(There is also a link to the site on the course webpage.) When you get to the
website, click on History Topics and then Ancient Greek Mathematics.
This will get you to a list of topics on ancient Greek mathematics. I want
you to read the following article on this website:
"How do we know about Greek mathematics?"
It would be useful for you to print out this article, since we may refer
to it in class discussion. In addition, on the same website, look up and read
the biography of Thales. You may also want to read the
biography of Pythagoras, but I do not think that we will get to
him until Thursday (after the quiz).
For Thursday, February 28:
No new assignment.
For Tuesday, March 4:
In the text, read pages 30-36.
Go to the the MacTutor History of Mathematics
archive (University of St. Andrews, Scotland),
http://www-groups.dcs.st-and.ac.uk/~history/ . On that website,
look up and read the following:
The biography of Pythagoras.
Squaring the circle
Doubling the cube
The biography of Eudemus
The biography of Proclus
You can find the articles on Squaring the Circle and Doubling the Cube by first going to the MacTutor History of Mathematics archive; then click on History Topics Index, and then click on Ancient Greek Mathematics. At that point you should see links for the desired articles.
Read problems 1, 2, 3, and 4 on pages 62-63.
Do Email Assignment 4 and email me your answers by 8:00am on Tuesday, March 4.
For Thursday, March 6:
No new assignment.
For Tuesday, March 11:
In the text, read pages 34-43.
Go to the
MacTutor History of
Mathematics archive and read the biographies of Plato,
Aristotle, Eudoxus, and Euclid.
Do not worry about detail in these articles; just try to get a sense of the
main contributions of each of the people listed.
To see a dynamic version of our proof of the Pythagorean Theorem, go to
"Animations of
Two Classics".
Go to the following website
http://curvebank.calstatela.edu/hippias/hippias.htm and look at the
dynamic derivation of the quadratrix. Note that it is is the combination
of two motions, the sweeping of the radius of the circle and the horizontal
line moving downward. The quadratrix is generated by the intersection of
the circle and the line.
Do problem 6 on page 63.
There is no email assignment for March 11.
E-mail Assignments
E-Mail Assignment 1:
The answers to the following questions should be emailed to me by 8:00 am on Tuesday, February 5. In addition to the text, you may need to look at the handout containing the contents of the Rhind Papyrus and the Moscow Papyrus.
1. In addition to two versions of Egyptian, hieroglyphic and demotic, what was the third language on the Rosetta Stone?
2. The Rhind and Moscow papyri have problems involving the pesu of two "foods" made from grain. Name one of those two "foods". Note that both can be made from grain, but I do not want grain or the name of a specific type of grain as an answer.
3. To what does the Egyptian term "seked" refer?
The answers to the following questions should be emailed to me by 8:00 a.m. on Tuesday, February 12. You will need to do the assigned reading in the text.
1. What numbers are characterized by the author of our text as regular sexagesimal numbers?
2. What do the initials BM and YBC, respectively, mean when referring to the classification of a Babylonian tablet?
3. According to the author of our text, what component of a circle did the Babylonians generally consider the defining component of the circle, the radius, the diameter, the circumference, or the area?
Answers to the following questions should be emailed to me by 9:00am on Tuesday, February 19. The answers should be given in complete sentences. All of the answers can be found in Chapter 1 in the text.
1. Plimpton 322 is a tablet in the Plimpton Collection at Columbia University. In the text's discussion of Plimpton 322, which column in Table 1.1 does not actually appear on the tablet (actually, for which is there not an equivalent column on the tablet)? Your answer can be given in terms of the headings of the columns in Table 1.1 on page 18.
2. Although there are some tablets with different equivalent values, in most old Babylonian tablets involving circles, what numerical value was used to represent the ratio of the circumference to the diameter? (This numerical value represents the general Babylonian equivalent to π.)
3. What is a gnomon, in the context in which it is used in Chapter 1 of the text?
The answers to the following questions should be emailed to me by 8:00am on Tuesday, March 4. You will need to do the assigned readings in the text and the assigned readings from the MacTutor History of Mathematics website.
What is an lune?
What is a syllogism?
What Greek mathematician was the first major historian of mathematics?
Paper Assignments
Paper 1 -- Due Tuesday, January 29.
Paper 2 -- Due Tuesday, February 26 (originally February 21)
Paper 3 --
Some related websites
Page maintained by Ross Gingrich.
URL: http://www.southernct.edu/~gingrich/mat30001spring2008/index.html
Last revised: March 7, 2008