Homework Guidelines

• The problems in the list below come from our textbook.
• Homework is due by 11:59PM on the due date on the Schedule.
• Turn in your homework via Canvas under the Assignments link.
• Complete solutions are posted in advance in Canvas under the Assignments link.
• Homework will be graded on completion and effort. You should get 100% on your homework!

Assigned Homework Problems

• HW 1

Section 1.2 Problems 1a,2a,3a,3d,4,5d,6c,7c,9a,10a,11a,12e,13a

Section 1.3 Problems 1af,2b,3,4b,5,6af,9,13af,15b,17abceg

• HW 2

Section 2.3 Problems 1c,2ad,3a,6,10,19,20 (For problems 19 and 20, complete the entire problem using Egyptian arithmetic and without modern algebraic notation or arithmetic.)

Section 2.4 Problems 1c,2,6,9

Section 2.5 Problems 1,4,6ac,9,11 (Work problem 4 two ways: as a modern human and as a Babylonian (ie use the hint).)

• HW 3

Section 2.6 Problems 1,2,4,7, Problem A

Section 3.2 Problems 1,4,7abc,8

Section 3.3 Problems 5,15,17,21,23

Section 3.4 Problems 4, 8

Section 3.5 Problems 2, 3

Construction Problems A,B,C,D

  A: Square a triangle.

  B: Double a circle.

  C: Bisect an angle.

  D: Trisect a line segment.

• HW 4

Section 4.2 Problems 2,3,6,8,12,Problem A (below)

Problem A Show that the figure on page 160 does construct the solution to ax=bc.

Note that for problems 2,3,6,and 8, you can use the hints in the book. You can also go to the online copy of Euclid’s elements and translate his argument into your own words. (link here.)

Section 4.3 Problems B-F below.

Problem B Read Prop 7 of Book II of Euclid’s Elements. If AB=x,AC=c, and CB=b in the diagram, write the algebraic equality described in Proposition 7. Then show algebraically that this proposition is true. Note the hardest part of this problem is understanding what Proposition 7 is saying.

Problem C Repeat the directions for Problem B but for Prop 9. Assume AC=c, AD=a, DB=b, and CD=d.

Problem D Read Euclid’s proof of the infinitude of primes (here and describe how his proof is different from a modern proof.)

Problem E Find two open problems in mathematics concerning prime numbers.

Problem F Use the Euclidean Algorithm to find the greatest common divisor of 12012 and 1430.

• HW 5

Section 4.4 Problem 4, Problem A below.

Problem A Suppose you wake up on a new planet with a different sun but the same planet-sun orientation as on earth. Suppose two people place a 1-meter-long stick and measure its shadow on the same day. At location X, the stick has no shadow but at location Y the stick has a shadow of length 0.1 m. If Y is 500 km north of X, find the radius of this new planet using Eratosthenes’ method.

Section 4.5 Problems 2,4,5,11

Section 5.3 Problems 13, 16, 17, Problems A-C below

Problem A Return to Diophantus’ Problem 8 of Book II (discussed on page 220 of our text).

• (i) What solution will you get if instead of setting 16-x^2=(2x-4)^2, you set 16-x^2=(mx-4)^2.
• (ii) Find a rational solution to the equation x^2+y^2=16 that Diophantus’ strategy will never construct.

Problem B Go to the translation of Diophantus’ Arithmetica here and read Proposition 27 from Book I.

• (i) Rewrite the problem in modern notation.
• (ii) Write out Diophantus’ solution in modern notation.

Problem C Go to the translation of Diophantus’ Arithmetica here and read Proposition 14 from Book III.

• (i) Rewrite the problem in modern notation.
• (ii) Write out Diophantus’ solution in modern notation.