Individual Research Projects Section 8.2

Project 8.2 A 51-Star Flag

  Recently there has been talk of Puerto Rico becoming the 51st state. If that happens, we will need to have a flag with 51 stars. Design a flag with 51 stars discussing the pros and cons of various possibilities.

48 stars, 1912-1959
49 stars, 1959
50 stars, 1950-present

Project 8.3

Write a paper on Pythagorean triples (numbers a, b, and c that satisfy the Pythagorean theorem). For example, pick an odd positive integer; say 9.
Square it: 81.
Find consecutive integers that have the sum 81: 40 and 41.
You have generated a Pythagorean triple: 9, 40, 41

92 + 402 = 412

Project 8.4

Look at Project 8.3, and extend the idea of a Pythagorean triplet. A Pythagorean quartet are four numbers a, b, c and d so that

a2 + b2 + c2 = d2

Outline a method for finding Pythagorean quartets.

What do you think is meant by a Pythagorean pentad?