1. Done by 2i3: Jonathan Ng Ong Yan Zhe Gaw Ban Siang Chin Ming Fwu
Pythagorean Triplets
Done by 2i3:
Jonathan Ng Ong Yan Zhe Gaw Ban Siang
Chin Ming Fwu

2. Table of Contents Introduction Pythagorean Triplets
Pythagoras & his theorem
Pythagorean Triplets
What is it?
Ways to generate triplets (formulas)
Uses and Applications
Pythagorean Quadruples

3. Introduction
We will start by telling you about a brief history about Pythagoras, and of course, the Pythagorean theorem.

4. The Man himself Pythagoras was born in Samos, a small Greek island.
Mathematician and Philosopher
Other than Math, he also did other things, namely:
Religion
Science
Music

5. Pythagorean Theorem Most notable mathematics discovery
Right-angled triangle
Sq. of hypotenuse (side opp. right angle)
Equals to
Sq. of Side A + Sq. of Side B

6. Pythagorean Triplets
We are covering the Pythagorean Triplets today. Have fun!

7. Set of Numbers fulfilling the formula
What is it?
Based on the Pythagorean theorem
Common example - 3:4:5 triangle
Pythagorean Triplet
Set of Numbers fulfilling the formula

8. Uses and Applications Tests and Exams Time is very limited.
Save time to find lengths of the sides immediately.

9. How to Create Triplets 2 ways to do so:
Memorise by heart
Use a formula
The triplets will also mostly follow the ratio 3:4:5, or any triangle similar to it.

10. Some Pythagorean Triplets
3:4:5 right triangle & all its similar triangles
6:8:10 triangle
9:12:15 triangle
5:12:13 right triangle & all its similar triangles
10:24:26 triangle
20:21:29 right triangle and all its similar triangles
40:42:58 triangle

11. Formula 1 Conditions: m > n > 0
Both m and n must be positive integers

12. Formula 2 (a is odd)

13. Formula 2 (a is even)

14. Formula 3 Most Complicated
Both u and v must not have any common factors.
U must be odd

15. Pythagorean Quadruples
Similar to Pythagorean Triplets
Set of 4 numbers which fulfill the following formula:
a2 + b2 + c2 = d2

16. Thank You!