Page 180 - Basic College Mathematics with Early Integers

GROUP ACTIVITY 157

Evaluate.

4 6
117. 1-122 118. 1-172

2
2
3
119. x - y for x = 21 and y =-19 120. 3x + 2x - y for x =-18 and y = 2868
x
b
121. 1xy + z2 for x = 2, y =-5, and z = 7 122. 51ab + 32 for a =-2, b = 3

Chapter 2 Group Activity

Magic Squares Exercises
Sections 2.2–2.4 1. Verify that what is shown in the Dürer engraving is, in
fact, a magic square. What is the common sum of the
A magic square is a set of numbers arranged in a square
columns, rows, and diagonals?
table so that the sum of the numbers in each column,
row, and diagonal is the same. For instance, in the magic 2. Negative numbers can also be used in magic squares.
square below, the sum of each column, row, and diagonal Complete the following magic square:
is 15. Notice that no number is used more than once in
the magic square.

2 9 4 -1

7 5 3 0 -4

6 1 8

3. Use the numbers -16, -12, -8, -4, 0, 4, 8, 12, and 16
The properties of magic squares have been known
to form a magic square:
for a very long time and once were thought to be good
luck charms. The ancient Egyptians and Greeks under-
stood their patterns. A magic square even made it into a
famous work of art. The engraving titled Melencolia I,
created by German artist Albrecht Dürer in 1514, fea-
tures the following four-by-four magic square on the
building behind the central figure.

16 3 2 13
5 10 11 8

9 6 7 12

4 15 14 1