THE DAY THE MATH WORLD STOOD STILL

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.