Scribd
Upload
48 views2 pages

Problem Egypt

This document contains exercises on Egyptian and Babylonian mathematics from a history of mathematics course. For Egyptian mathematics, students are asked to perform computations using Egyptian algorithms, solve equations using the method of false position, find volumes and areas, and explain issues with teaching mathematics via examples as in the Ahmes Papyrus. For Babylonian mathematics, exercises include converting between base 10 and sexagesimal, performing computations, approximating square roots, using tables and linear interpolation to solve equations, deriving an approximation of pi, and explaining issues with teaching using clay tablets and the sexagesimal system.

Uploaded by

Ines Barão
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
48 views2 pages

Problem Egypt

This document contains exercises on Egyptian and Babylonian mathematics from a history of mathematics course. For Egyptian mathematics, students are asked to perform computations using Egyptian algorithms, solve equations using the method of false position, find volumes and areas, and explain issues with teaching mathematics via examples as in the Ahmes Papyrus. For Babylonian mathematics, exercises include converting between base 10 and sexagesimal, performing computations, approximating square roots, using tables and linear interpolation to solve equations, deriving an approximation of pi, and explaining issues with teaching using clay tablets and the sexagesimal system.

Uploaded by

Ines Barão
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 2

Texas A&M University MATH 629

History of Mathematics

Exercises on Egyptian Mathematics.


1. Compute 623 255 using the Egyptian binary algorithm.
2. Compute 25 31 using the Egyptian binary algorithm.
3. Compute 7112 127 using the Egyptian binary algorithm.
4. Show that if n is a multiple of five, 2n can be broken into the sum of two unit
fractions, one of which is a third of 1n .
5. Solve x  12 x  16 using the mathod of false position. Be sure to express the
fractional answer al the Egyptians. (This is Proposition 16 of the Ahmes.)
6. Solve the following problem using the method of false position: If thrice a heep plus
a fourth more is 247, what is the heep?
7. Devise a method by which the Egyptians may have found the formula for the exact
volume of a pyramid? (Remember, the formula can be computed by calculus, but the
Egyptians did not have that tool.)
8. The amount of bread to be distributed to four persons, A, B, and C are in the
continued proportions 1 , 1 , 3 . If there are 1200 loaves of bread to be distributed,
2 4 5
how much does each get?
9. Solve the following problem using the method of false position: If thrice a heep plus
a fourth more is 247, what is the heep?
10. Using the Egyptian method find the area of a circle of diameter 11.
11. Pedagogy: Explain the issues of teaching mathematics by example, la the Ahmes
Papyrus. What aspect make teaching this way simpler? harder? What kind of
graduate is the result of such instruction? (For example. Are graduates capable? Are
graduates flexible?)
12. Complete the checklist for Egypt by filling in the scaled numbers and justifying by
essay answers the values you have given. You may cite comments or problems from
the text or lecture notes; you may also contribute your own observations.

Exercises on Babylonian Mathematics.


1. Convert the following numbers and computations into sexagesimal. Perform the
computations.
a. 125, 256, 3601, 45000
b. 12  37, 120 " 98, 3200  420
c. 23 12, 210 52
2. Determine 17 24 as a sexagesimal number.
3. Determine Modify the Babylonian root finding method (for 2 ) to find the square root of
any number. Use your method to approximate 3 . Begin with x 0  1.
4. Consider the table:
n n3  n2
1 2
2 12
3 36
4 80
5 150
6 252
Solve the following problems using this table and linear interpolation. Compare with the
exact values. (You can obtain the exact solutions, for example, by using Maple:
evalf(solve(x 3  x 2  a, x)). Here a  the right side.)
x 3  x 2  55 and x 3  x 2  250
5. Derive the approximate value of = as determined from the data at Susa.
6. Complete the checklist for Mesopotamia by filling in the scaled numbers and justifying by
essay answers the values you have given. You may cite comments or problems from the text
or lecture notes; you may also contribute your own observations.
7. Pedagogy: Explain the issues of teaching mathematics when clay tablets are used for written
communication. What difficulties do you perceive in teaching the sexagesimal system?
Using tables to solve nonlinear equations requires a working knowledge of interpolation.
Explain why interpolation is a naturally occurring task in everyday life, even today.

You might also like