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

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Presentation transcript:

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

Table of Contents Introduction Pythagorean Triplets 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

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

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

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)

Formula 2 (a is even)

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!