Announcements

 

 

Current Assignment(s), to be handed in:

 

 

For Wednesday, January 20. p. 51/52 : 1, 2, 3.

Math majors: Describe “Fibonacci’s Method” [p. 45] and the technique of “false position;” do 12, 13, 16, 19.

There will be a short quiz on Thursday, January 21. It will cover some history topics (nothing obscure or tricky) from the readings, and a few problems using the Egyptian method of doubling.

 

For Thursday, January 28: You should be up to date on the homework relating to the Babylonians. There will be a quiz on Thursday on this material. It will be similar to the one last week: a bit of history a discussion of arithmetic, and a few problems involving multiplication and division in sexagesimal.

 

For Monday, February 1: From syllabus: Egyptian Geometry, Thales.

Math Majors: Hand in a write-up of the geometric solutions to the quadratic equations x2 + px = q  and x2 - px = q. Compare what you get to the solution obtained using the quadratic formula (always choosing the positive or biggest root: the “+” instead of “ ±”). You may work together, but you have to hand in your own write up!

 

For Wednesday, February 10: From syllabus: Eudoxos. Get a compass for the Construction Assignment.

 

Quiz on Thursday: Learn the statement and proof of the Pythagorean Theorem from our webpage (we went over it in class as well). You do not have to memorize the diagrams:  they will be supplied on the quiz. The quiz will cover Egyptian geometry, Thales, and the Pythagorians from the readings. Know about triangular numbers also.

Math Majors: Hand in: p. 105, exercises 1 (give an algebraic proof using Tn = n(n+1)/2) , 6, 7a,b

The Construction Assignment will be due on Thursday, February 25.

For Thursday, February 18: Assignments through Alexandria and Euclid

Math Majors, for Monday:  Hand in 6 problems of your choice from the ones assigned to math majors.

MIDTERM

For Thursday, March 25: Material from syllabus on Arab mathematics (pp. 240 – 254)

For Monday, March 29: Do p. 233, # 13, 14, 15

For Monday, March 29: Material from the syllabus on Chinese mathematics (pp. 254 – 256  , 260 – 265)

 

 

 

For Wednesday, April 7: Read pp. 271 – 276 (Decline) and pp. 279 285, 289 – 294 (Fibonacci) – see syllabus for questions on these readings.

 

For Monday, April 12: p. 287: Do as many of 1, 2, 3, 4, 8 as you can. Do the Fibonacci part of the “Fibonacci-Newton” assignment from our homepage (or go directly to http://www.math.neu.edu/~bridger/U201/FibNewton/FibNewton.htm ).

 

 

 

 

 

 

 

 

 

 

From last year – disregard for now:

 

For Wednesday, April 1. (You should also be up-to-date on the readings, which means through “The Renaissance.”

Math majors for elective credit: In addition to the above, estimate π using an inscribed polygon of at least 192 sides (as discussed in class). Use a spreadsheet if you possibly can, and submit a printout.

 

For Monday, February 23. pp. 172—176 and pp. 185—194. Prepare discussion of questions in the syllabus.

Math majors for elective credit: do p. 170 #1,2,3,4, p. 184 #6,10.

 

For Wednesday, Feb. 11. Read about the Library and Museum of Alexandria, pp. 143—149. Think about answers to the questions posed in the syllabus. Work on the Construction Assignment, which is due on Thursday.

 

For Monday, Feb. 9. Read pp. 136—138 (Plato’s Academy). Learn a proof of the Pythagorean Theorem and the irrationality of  √2. (See website for sample proofs of these facts.)

Start work on the Construction Assignment from the Website. (Due on Thursday, Feb. 12.

 

For Wednesday, Feb 4. Read pp. 112-113,  117-119. Think about √2 and the implications of its “irrationality.”

 

For Monday, Feb 2. Read pp. 85—99 and pp. 107—109. (Math majors read pp 92—104 as well.)

Do p. 105 # 1 (illustrate with t4 = the tetractys instead of t2) and #4 (Math majors: do #3, 6, and 7 as well).

Also, for math majors:

  Look at squares with side (D – D/N), N = 1, 2, 3,…,13 say. Which one best approximates the area of the circle of diameter D? (A spreadsheet is a good tool.) Read p. 55 (bottom) in Burton. What do you think of his explanation for the Egyptian circle area formula? Compute the area of the pseudo-octagon in the book, and show that it doesn’t even have area equal to (D – D/9)2. (Note that the little triangles all have area 1/18 the area of the square since they are similar to a big triangle formed by drawing a diagonal—this is because similar triangles have areas in proportion to the squares of their corresponding sides.)

 

For Thursday, Jan. 22.  p. 29: #1b,e; #2c; #3, 4. (Math majors: add #6a, 12.)

 

For Monday, Jan. 12.  pp. 51—52: #2, 3a.  (Math majors: also do # 12 and 13 as well.)

                                      Read: pp. 20—27 (Babylonia) and think about the questions in the syllabus.