## 'First Forward Into Logo 7: Angles of Polygons' printed from http://nrich.maths.org/

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