Problem Set 4 Solutions
Math 4033, History of Mathematics
Spring 2007
Problems 4.5: 1, 4, 5; 5.3: 2, 3, 13, 14, 19; 5.4: 1, 2, 5
4.5.1 Verify the following statements of Archimedes. (We assume that mo
Problem Set 1 Solutions
Math 4033, History of Mathematics
Spring 2007
Problems 2.3: 4, 5, 20; 2.4: 1c, 2, 9; 2.5: 3, 11; 2.6: 7, 8
1
1
2.3.4 (a) Show that the product of 14 by 1 + 1 + 4 is equal to 1
Math 4033, History of Mathematics
Midterm Exam Solutions
March 8, 2007
1. (a) (20 points) Fill in the following table with the equivalent numbers from the various
number systems weve studied.
Egyptian
Math 303 Final Exam Solutions
May 12, 2008
1. (10 pts) Give conditions under which the following equation would be true a + (b c) = (a + b) (a + c). This is just a matter of solving the equation. a +
Math 303 Exam 2 Solutions
Apr 9, 2008
1. (10 pts) Eight times any triangular number, plus 1, is a square number. Show that this is true for the rst four triangular numbers. 1(1 + 1) 2 2(2 + 1) 8T2 + 1
Math 303 Exam 1 Solutions
Feb 27, 2008
1. (10 pts) Identify the largest number expressible in a simple grouping system which uses a base of 5 and 10 distinct symbols. Give your answer as a number in t
Math 105 History of Mathematics
Second Test Answers
Prof. D. Joyce, November, 2010
Scale.
85104 A. 7484 B. 5973 C. Median 79.
Problem 1.
B.
Here is the rst stage of the computation.
x3
1
Essay. [25] S
Math 105 History of Mathematics
First Test Answers
Prof. D. Joyce, October, 2010
Scale. 89101 A. 7888 B. 5877 C. Median 84.
arguments, and even in previously accepted statements. It can be used to nd
HISTORY OF MATH
HOMEWORK 7 SOLUTIONS
11.4,6,11
Exercise from Class: Prove the formula used to make Wallis rst table:
1
(1 x
q
) dx =
p+q
1
(1 x1/p )q1 dx,
1/p q
0
0
where p and q are positive integers
HISTORY OF MATH
HOMEWORK 6 SOLUTIONS
11.4,6,11
11.4. Find the equation of the locus of points P = (x, y ) whose squared distances to two given
points (a, 0) have a given sum m.
We have
[(x + a)2 + y 2
HISTORY OF MATH
HOMEWORK 5 SOLUTIONS
9.30, 32, 35, 37, 38
9.30. Use Cardanos formula to solve x3 = 6x + 6.
We have p = 2, q = 3, so q 2 + p3 = 1. The positive real solution is
x = [3 + 1]1/3 + [3 1]1/
HISTORY OF MATH
HOMEWORK 4 SOLUTIONS
7.3,6,13,15,18
7.3. For the equation x2 = bx + c: Halve the number of roots (b/2), multiply this by itself
(b/2)2 ). Add this to the number (b/2)2 + c), extract th
HISTORY OF MATH
HOMEWORK 3 SOLUTIONS
A. Using modern methods, prove Prop. 3 of Quadrature of the Parabola:
From two points Q, Q on the parabola, draw lines parallel to the tangent line to the vertex P
HISTORY OF MATH
HOMEWORK 2 SOLUTIONS
2.12,13,14,18
2.12 To apply to [construct on] a given straight line AB a rectangle equal to a given rectangle.
Lets also construct the diagram in the book, just fo
Library Assignment #2: Periodical Literature
Provide research summaries of ten papers on the history of mathematics (both words are crucial)
that you have looked up and read. One purpose for doing thi
Library Assignment #1: Your Mathematician
Your Mathematician is
0. Look up YM in our text. Read the relevant pages and take notes.
1. Look up YM in the Dictionary of Scientic Biography or the Biograph
History of Mathematics
Homework 5 Solutions
1. Multiply 8743 by 5692 prosthaphaeretically.
We use the formula
1
cos a cos b = (cos(a + b) + cos(a b),
2
where cos a = 0.8743 and cos b = 0.5692.
find th
History of Mathematics
Homework 4 Solutions
1. Solve the following problem of Abu Kamil: Suppose 10 is divided into two parts and the
product of one part by itself equals the product of the other part
History of Mathematics
Homework 3
Due Wednesday, October 6
1. Beginning, as did Archimedes, with a regular hexagon inscribed in a circle, use an
Archimedean recursion algorithm to nd either p12 and P1
History of Mathematics
Homework 2 Solutions
1. Write the number 0.0862 in Babylonian notation.
Note that
0.0862 = 5 601 + 10 602 + 19 603 + 12 604 ,
so that 0.0862 = 0; 5, 10, 19, 12.
2. Verify that i
History of Mathematics
Homework 1 Solutions
1. Express 2/103 as a sum of two unequal unit fractions, and write these in Egyptian
hieroglyphic notation.
Using the formula from the book, we have
2
1
1
=
Problem Set 7
Math 4033, History of Mathematics
Solutions
Problems: 8.1: 6, 9, 10; 8.2: 1, 7, 8, 10; 8.3: 1, 3; 8.4: 2, 8, 11
8.1.6 Use Napiers rods to multiply 458 by 79.
Solution: The relevant boxes
Problem Set 6
Math 4033, History of Mathematics
Solutions
Problems: 7.3: 1, 2, 3, 14; 7.4: 1, 4, either 5 or 6
7.3.1 Find all three roots of the following cubic equations. (Note: For these you are int
Problem Set 5
Math 4033, History of Mathematics
Solutions
Problems 5.5: 1, 4, 5, 6, 7, 14, 15; 6.2: 5, 7; 6.3: 2, 5
Plus do the following problems from the OSU High School Math Contest.
5.5.1 Solve th
Problem Set 3 Solutions
Math 4033, History of Mathematics
Spring 2007
Problems 4.2: 7, 9, 12; 4.3: 1b and d, 4, 9, 10b, 16c-d, 20, 24, 26; 4.4: 1, 7
4.2.7 Prove that if two opposite sides of a paralle
Problem Set 2 Solutions
Math 4033, History of Mathematics
Spring 2007
Problems 3.2: 7, 11, 12; 3.3: 2, 7, 8, 13, 17, 21; 3.4: 3, 7; 3.5: 5, 6
3.2.7 (4 points, (b) and (d) only) Prove the following ide