1. Egypt
Egyptian mathematics

2. 1680 B.C. Egypt (“Middle Kingdom”) Civil War
Hyksos  “Rulers of Foreign Lands” invaded
Joseph (Coat of Many Colors) set against this background
Turning point for Egypt
Invasion

3. Located near major rivers Slave class for Manual Labor
Babylonian Math and Egyptian Math
Located near major rivers
Slave class for Manual Labor
Agriculture and Farming Motivated Math
Theocratic Society
Comparing

4. contrasting Babylonian Egyptian Constant Invasions by neighbors
Trade more prevalent
Tigris and Euphrates required more engineering
Math problems were more difficult
Remained Secluded and in peace
Semi-isolation didn’t require trade
Nile flood seasons required simple irrigation
More regular and welcome
Emphasis on Astronomy to predict seasons
contrasting

5. Egyptian Pyramids 2500 BC: Great Pyramid at Gizeh 13 Acres
2 million stone blocks
Each 2.5 tons
54 ton granite blocks – roof
Dragged 600 miles
Set 200 ft above ground
Right angles within 1/27000 of 90 degrees
Sides of equal length up to 1/14000

6. Astronomical instruments found in Great pyramids

7. Egyptians are believed to have the first base-10 system.
As early as 2700 BCE (probably earlier)
Numeration

8. Writing System Egyptians wrote on papyrus, leather, cloth, and stone.
Hieroglyphics
Lead to Tally System
Hieratic
Cursive form of hieroglyphics
Writing System

9. The Moscow Papyrus
Student text covering practical problems and the application of geometric formula
Older than the Rhind Papyrus

10. Rhind Papyrus: 1650 B.C. Written by A’h-mose
Found by Henry Rhind
Illustrates Egyptian Method of Multiplication
Math was taught by example
Applied arithmetic

11. Egyptian Method of Multiplication
Method of Doubling
All numbers can be written in base 2

12. Multiply (27)(19) using only Egyptian methods
27 1
54 2
108 4
216 8
19 =
(27)(19) =
Multiply (27)(19) using only Egyptian methods

13. Egyptian Division
Division worked using the same method in reverse. Called Halving
For example, let’s divide 1495 by 65.
Double 65 until we are about to pass 1495

14. Egyptian Division
Tick off the numbers on the right column that add to a number between
1495 and 1495 – 65.

15. Egyptian Division
What if the numbers didn’t add up perfectly

16. Egyptian Division
What if the numbers didn’t add up perfectly

17. 12 1
24 2
48 4
96 8
192 16
= 324
= 27
Your turn: Divide 324 by 12

18. Fractions Egyptians only allowed unit fractions:
Symbol for fraction was oval
Same symbol for mouth
Common used fractions – Horus –eye
2/3 and 3/4 were only exceptions

20. Egyptians are given credit for the earliest known formula for the area of a circle in terms of the diameter D:
Area of a Circle