1.	Starting with 1,1, determine the next five Fibonacci numbers. 	

2.	Suppose a sequence begins 1, 4, and continues by adding the previous two numbers to determine the next number.  Determine the next five numbers in this sequence. 	

3.	Suppose a sequence begins 2, 1, and continues by adding the previous two numbers to determine the next number.  Determine the next five numbers in this sequence. 	

4.	Suppose a sequence begins 1, 4, and continues by adding the previous two numbers to determine the next number.  What do the quotients of consecutive numbers drift toward? 	

5.	Suppose a sequence begins 2, 1, and continues by adding the previous two numbers to determine the next number.  What do the quotients of consecutive numbers drift toward? 	

6.	Show that the difference between the golden mean f and its reciprocal is 1. 	

7.	How does the geometric mean of two numbers compare to their arithmetic mean? 	

8.	Construct a rectangle with area 1 whose ratio of dimensions is the golden mean. 	

9.	Draw a figure that has rotational symmetry but no reflectional symmetry.	

10.	Draw a figure that has reflectional symmetry but no rotational symmetry.	

11.	Draw a figure that has both reflectional and rotational symmetry.	

12.	Draw a strip pattern that has only translation and rotation symmetries.	

13.	Draw a strip pattern that has only translation and glide reflection symmetries.	

14.	Draw a strip pattern that has all possible symmetries.	

15.	Draw a wallpaper pattern that has only translation symmetries.	

16.	Draw a wallpaper pattern that has only translation and rotation symmetries.	

17.	Draw a wallpaper pattern that has only translation and reflection symmetries.	

18.	Draw a wallpaper pattern that has only translation and glide reflection symmetries.	

19.	Draw a wallpaper pattern that has translation, rotation, and reflection symmetries.	

20.	Identify the elements of the symmetry group of a square. 	

21.	Identify the elements of the symmetry group of a non-equilateral isosceles triangle. 	

22.	Why do imperfect patterns sometimes pose a challenge to the classification scheme? 	

23.	How do pattern classification schemes aid anthropologists? 	

24.	What are some of the isometries of a cube? 	

25.	What are the isometries of a circle? 	

26.	Draw a shape that has rotational symmetry but no reflection symmetry.	

27.	Draw a shape that has reflection symmetry but no rotational symmetry.	

28.	Draw a shape that has exactly five lines of reflection symmetry.	

29.	Draw a shape that has both reflection symmetry and rotational symmetry.	

30.	How many elements are in the symmetry group of the regular pentagon shown below?

31.	How does a fern leaf demonstrate a fractal structure?	

32.	How does the Sierpinski triangle illustrate an iterated function system?	

Answer Key

1.	1, 1, 2, 3, 5, 8, 13	
2.	1, 4, 5, 9, 14, 23, 37	
3.	2, 1, 3, 4, 7, 11, 18	
4.	The numbers drift toward the golden mean.	
5.	The numbers drift toward the golden mean.	
6.	Approximately 1.618 – (1/1.618) = 1.618 – 6.18 = 1	
7.	The geometric mean is less than or equal to arithmetic mean.	
8.	Length = 1/[Ö(golden mean)] Width = Ö(golden mean)	
9.	E.g., 

10.	E.g.,

11.	E.g.,

12.	E.g.,

13.	E.g.,

14.	E.g.,

15.	E.g., 
QQQ
QQQ
QQQ	
16.	E.g., 
 SSS
SSS
SSS	
17.	E.g., 

18.	E.g., 

19.	E.g., 
XXX
XXX
XXX	
20.	The identity, 1/4 turn, 1/2 turn, 3/4 turn, horizontal reflection, vertical reflection, left diagonal reflection, right diagonal reflection.	
21.	The identity, and vertical reflection.	
22.	It's hard to decide if the imperfections are intentional.	
23.	They describe patterns in a formal scheme.	
24.	There are rotations and reflections around lines through the center.	
25.	Rotation and reflection through plane through the center.	
26.	Answers may vary. One example is shown below.
	
27.	Answers may vary. One example is shown below.
	
28.	Answers may vary. One example is shown below.
	
29.	Answers may vary. One example is shown below.
	
30.	10	
31.	The fern leaf exhibits similarity at ever-finer scales.	
32.	Its construction is a sequence of elements defined recursively by applying a single rule over and over.