Egypt

Reading: 1.1

Summary:
In Section 1.1, the author writes about the Egyptians and gave some back ground information of their number system. The Egyptians preferred to deal with unit fractions and wrote more complicated fractions as sums of unit fractions; the only exception was 2/3. Unlike the present numbers, they had characters to represent the 1's, 10's, 100's etc. For instance to represent 27 they would use two 10's and seven 1's characters; arranging them from least to greatest value.

Egyptians had some helpful techniques to help them with math problems. One technique they was used for multiplying numbers. If they wanted to multiply two numbers, A and B, they would have two columns: the left column started with 1 and the right the smaller of A and B. They would then proceed to double each number until the left columns contain numbers that will add up to the other, A or B. Having chosen the the numbers that would be added they would also add the corresponding number in the right column. As a result, the right column will add to the product of A and B.

 To solve linear equations false position was used. The scribes would guess the answers to the variables and upon finding them incorrect would adjust their educated guess by a proportion, of the corrected answer and the incorrect answer the got. 

Q&A:
1) How do mathematicians know the mathematical procedures and knowledge used in ancient Egyptian?
         The scribes left clay tablets and papyrus that contained problems and the steps that were used to solve them.

2) Any particular text that made significant contribution to understanding how the ancient Egyptians did              math?
     The Rhind Mathematical Papyrus and Moscow Mathematical Papyrus made where two particular texts

3) Did the Egyptians have any other fields of mathematics did they work in?
       They did some geometry. Through a method they were able to find the area of a rectangle, triangle and trapezoid.

Unanswered Question:
1) How did the ancient Egyptians develop their various algorithms?

Evaluation of Reading: 
Interesting: 7
Quality: 5
Complexity: 6