### Spirostars

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

### LOGO Challenge - the Humble Square

Look at how the pattern is built up - in that way you will know how to break the final pattern down into more manageable pieces.

### LOGO Challenge - the Logic of LOGO

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

# First Forward Into Logo 7: Angles of Polygons

##### Age 11 to 18 Challenge Level:

First Forward Into Logo
Previous: FF6

In FF6 you considered and hopefully explored the following procedures:

TO CIRCLE :CH
REPEAT 360 [ FD :CH RT 1]
END

TO CIRC :CH :ANG
REPEAT 360 [ FD :CH RT :ANG]
END

As a consequence different sized circles and some polygons may have resulted. Did any of you manage to draw a heptagon ($7$- sided)? A nonagon ($9$-sided)? A endecagon($11$- sided)? $13$-gon? Etc. etc....

Imagine walking around the outside of a pentagon....as you: go forward then turn, go forward then turn, go forward then turn, go forward then turn, ... finally go forward then turn. You should be back where you started... go on try it, convince yourself. In your journey you should have turned through $360^\circ$ .

Five times you turned through $72^\circ$ . N.B. $5 \times72 = 360$.

 Hence: For a pentagon - REPEAT 5 [ FD 45 RT 360/5] For a heptagon - REPEAT 7 [FD 45 RT 360/7] For a nonagon - REPEAT 9 [ FD 45 RT 360/9]

See the pattern?
So why not experiment?
Go on try:
TO POLY :N
REPEAT :N [FD 45 RT 360/:N]
END

Then try:
TO POLY :N :M
REPEAT :N [FD :M RT 360/:N]
END

Next: FF8