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.
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
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
Outline a method for finding Pythagorean quartets.
What do you think is meant by a Pythagorean pentad?