First Forward into Logo 7: Angles of Polygons

4856 /www/nrich/html/content/id/4856/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><a href="https://nrich.maths.org/8045">First Forward Into Logo</a> Previous:<a href="http://nrich.maths.org/public/viewer.php?obj_id=4855&part="> FF6</a> 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. $5 \times72 = 360$. <table style="" border=""> <tbody> <tr> <td> <div>Hence:</div> <div>For a pentagon - REPEAT 5 [ FD 45 RT 360/5]</div> <div>For a heptagon - REPEAT 7 [FD 45 RT 360/7]</div> <div>For a nonagon - REPEAT 9 [ FD 45 RT 360/9]</div> </td> <td><mdo:image alt="polygons" height="337" src="logo8.gif" width="264"></mdo:image></td> </tr> </tbody> </table> 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:<a href="http://nrich.maths.org/public/viewer.php?obj_id=4859&part="> FF8</a> </mdoxml> 2 3 0 0 1 1 1 First Forward into Logo 7: Angles of Polygons More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables. 2D Geometry, Shape and Space Angle properties of shapes Using, Applying and Reasoning about Mathematics Practical Activity Information and Communications Technology Logo