Individual Research Project Section 5.8

Project 5.13

Prepare an exhibit on cryptography. Include devices or charts for writing and deciphering codes, coded messages, and illustrations of famous codes from history. For example, codes are found in literature in Before the Curtain Falls, by J. Rives … See the whole entry

Individual Research Project Section 5.7

Project 5.12

What is a Diophantine equation?

Reference
Warren J. Himmelberger, “Puzzle Problems and Diophantine Equations,”  The Mathematics Teacher, February 1973, 136-138, or a more complete reference, see any number theory textbook.… See the whole entry

Individual Research Project Section 5.6

Project 5.11

Symmetries of a Cube
Consider a cube labeled as shown below:

List all the possible symmetries of this cube. See Problem 60, Problem Set 5.6 to help you get started… See the whole entry

Individual Research Projects Section 5.5

Project 5.8

You may have seen a geoboard, which is simply a board with pegs. Two simple geoboards with the pegs labeled A, B, C, ….

Distance on a Geoboard

Suppose that the horizontal and vertical distance between the pegs … See the whole entry

Individual Research Projects Section 5.4

Project 5.6

Historical Quest
We mentioned that the Egyptians wrote their fractions as sums of unit fractions. Show that every positive fraction less than 1 can be written as a sum of unit fractions. Reference Bernhardt Wohlgemuth, “Egyptian Fractions,” … See the whole entry

Individual Research Projects Section 5.2

Project 5.1

In the text we tried some formulas that might have generated only primes, but, alas, they failed. Below are some other formulas. Show that these, too, do not generate only primes.
a. n2 + n + 41… See the whole entry