The Rule Of Plato

By: Abigail van Haastrecht December 4, 2014

Intro

This project is about 2 rules ( the rule of Plato and the rule Pythagoras) and how they are alike and how they are different. I will be conducting ten sets of Pythagorean triples using each rule. Then I will be using that information to find properties of each formula so I can hopefully figure out why they work.

Rule Of Plato

1) 4 + 4 squared/ 4-1 (3) = 4 squared/ 4+1 (5)

2) 6 + 6 squared/ 4 -1 (8) = 6 squared/4+1 (10)

3) 8 + 8 squared/ 4-1 (15) = 8 squared/ 4+1 (17)

4) 10 + 10 squared/ 4-1 (9) = 10 squared/ 4+1 (11)

5) 12 + 12 squared/ 4-1 (11) = 12 squared/ 4+1 (13)

6) 14 + 14 squared/ 4-1 (13) = 14 squared/ 4+1 (15)

7) 16 + 16 squared/ 4-1 (15) = 16 squared/ 4+1 (17)

8) 18 + 18 squared/ 4-1 (17) = 18 squared/ 4+1 (19)

9) 20 + 20 squared/ 4-1 (19) = 20 squared/ 4+1 (21)

10) 22 + 22 squared/ 4-1 (21) = 22 squared/ 4+1 (23)

Rule Of Pythagoras

1) 3 + 3 squared/ 2-1 (2) = 3 squared/ 2+1 (4)

2) 5 + 5 squared/ 2-1 (4) = 5 squared/ 2+1 (6)

3) 7 + 7 squared/ 2-1 (6) = 7 squared/ 2+1 (8)

4) 9 + 9 squared/ 2-1 (8) = 9 squared/ 2+1 (10)

5) 11 + 11 squared/ 2-1 (10) = 11 squared/ 2+1 (12)

6) 13 + 13 squared/ 2-1 (12) = 13 squared/ 2+1 (14)

7) 15 + 15 squared/ 2-1 (14) = 15 squared/ 2+1 (16)

8) 17 + 17 squared/ 2-1 (16) = 17 squared/ 2+1 (18)

9) 19 + 19 squared/ 2-1 (18) = 19 squared/ 2+1 (20)

10) 21 + 21 squared/ 2-1 (20) = 21 squared/ 2+1 (22)

Analyze

Both methods are the same but one is odd numbers and the other is even. Also in one you divide by two and in the other you divide by four. In the Rule of Plato, it is with even numbers so one leg and the hypotenuse are both odd. In the Rule of Pythagoras, it is with even numbers so one leg and the hypotenuse are even. I also noticed that in both rules, the hypotenuse is repeated in the next problem as the second leg.

Hey! over here!

I made the drawing above in the Analyze section by the way! :)

why does it work?

I think it works in both theorems because; you square the number and then divide by two taking the answer back to the original number and then adding or subtracting one.

Summing up

I think that what my analysis is pointing to is that they are more different than alike but the idea is the same.