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Pythagorean Triplets

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

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Pythagorean Triplets

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  1. Pythagorean Triplets Done by 2i3: Jonathan NgOng Yan ZheGaw Ban Siang Chin Ming Fwu

  2. Table of Contents • Introduction • 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. What is it? • Based on the Pythagorean theorem • Common example - 3:4:5 triangle

  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!

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