Spirolaterals

Starting with a number sequence, like 12345, and using graph paper, move 1 unit right, 2 units down, 3 units left, 4 units up, 5 units right, 1 unit down, 2 units left, and so on, until you begin retracing the pattern, or until it's obvious that this will never happen.

Try some of these sequences:

124

125

225

235

123

1234

12345

123456

112

1122

11223

112233

Try some sequences of your own. Make some observations about the resulting patterns. How does the number of digits in the sequence affect the pattern? How does changing a digit in a sequence change the pattern? Can you predict anything about which sequences will repeat and which will spiral off into space?

 

 

Try doing the spirolateral for the 7 digits in your phone number. How would you handle a 0 in the sequence?

 

 

Try doing the spirolateral for your name (first, last, or middle). Use the following code to assign digits to the letters of your name:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

 

Bonus: Make a convincing argument that any spirolateral using a 3 digit sequence must repeat itself (Keep track of how far you go in each of the four directions right, down, left, and up. Where should you wind up if the pattern is to repeat itself?)