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