1 / 16

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.

deiter
Download Presentation

Pythagorean Triplets

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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!

More Related