Pythagorean Triplets

Pythagorean TripletsDone by 2i3:Jonathan NgOng Yan ZheGaw Ban SiangChin Ming Fwu

Table of Contents Introduction

Pythagoras & his theorem Pythagorean Triplets

What is it? Ways to generate triplets (formulas) Uses and Applications

Pythagorean Quadruples

Introduction

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

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

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

222 cba

Pythagorean Triplets

We are covering the Pythagorean Triplets today. Have fun!

What is it? Based on the Pythagorean theorem

Common example - 3:4:5 triangle

222 cba

Pythagorean Triplet

Set of Numbers

fulfilling the formula

Uses and Applications Tests and Exams

Time is very limited. Save time to find lengths of the sides

immediately.

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.

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

Formula 1

Conditions: m > n > 0 Both m and n must be positive integers

Formula 2 (a is odd)

3a2)1( 2

ab 1bc

Formula 2 (a is even)

12

2

ab 2bc

Formula 3

Most Complicated Both u and v must not have any

common factors. U must be odd

Pythagorean Quadruples Similar to Pythagorean Triplets Set of 4 numbers which fulfill the

following formula: a2 + b2 + c2 = d2

Thank You!