1 / 6

THE DAY THE MATH WORLD STOOD STILL

THE DAY THE MATH WORLD STOOD STILL. Or Euclid Saves Pythagoras. How did Euclid prove the Pythagorean Theorem. In Euclid’s time, Arabic numerals were unknown to the Greek world. Greeks knew geometry by shapes or units not numbers. So how did Euclid prove a 2 + b 2 = c 2 ?.

lel
Download Presentation

THE DAY THE MATH WORLD STOOD STILL

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. THE DAY THE MATH WORLD STOOD STILL Or Euclid Saves Pythagoras

  2. How did Euclid prove the Pythagorean Theorem • In Euclid’s time, Arabic numerals were unknown to the Greek world. • Greeks knew geometry by shapes or units not numbers. • So how did Euclid prove a2 + b2 = c2?

  3. Euclid’s Drawing First, he began with a right triangle.

  4. Euclid’s Drawing, Part II Next, he drew squares of the same size as the sides of the triangle.

  5. E F A D G C B K I H J Euclid’s Next Steps • Then, he drew a perpendicular line from HI to A. • And another line from A to H and from C to G. • Area of rectangle BHJK = 2 area of triangle ABH. • Area of square ABGF = 2 area of triangle CBG. • Angle ABH = angle ABC + angle CBH. • Angle CBG = angle ABC + angle ABG. • Since angle ABG = angle CBH, then angle CBG = angle ABH. Also, BH = CB and AB = AB. • Then, area of rectangle BHJK = 2 area of triangle ABH = 2 area of triangle CBG = area of rectangle ABFG.

  6. Euclid’s Conclusion • Do the same to the other square. • Then, square ABFG + square ACDE = square CBHI. • This is Euclid’s proof of the Pythagorean Theorem. Q.E.D.

More Related