1. Pythagorean Triples – Part 2 Slideshow 39, Mathematics Mr. Richard Sasaki, Room 307

2. ObjectivesObjectives Learn another proof for Euclid’s formulae to calculate triples Check the points that we should have learned from the given project (relationships & rules with triples) Learn and use some laws in triples Introduce triangular numbers

3. Euclid’s Formulae We know all about Euclid’s formulae for generating triples now…

4. Rules and Patterns for Triples Triples always consist of three positive integers where they are either… All even numbers (always non-primitive) Two odd numbers and an even number Some properties for primitive triples include…

5. Rules and Patterns for Triples Example The test is passed as 144 is a square number.

6. Rules and Patterns for Triples So how do we calculate them? Example

7. Rules and Patterns for Triples

8. AnswersAnswers None have a factor of 4 or 3 Works but gives the wrong solution

9. Triangular Numbers You learned about these in the Winter Homework. They follow the list… What do these numbers have to do with Pythagorean triples?

10. Triangular Numbers If you checked the grading sheet (as advised), you would have seen… 45 36 12345678910 3645 282115 10 6 31 0 This produces the triangle numbers!

11. Triangular Numbers

12. AnswersAnswers