Maths Problem

 From: flatdog 24 May 2011  (1 of 13)
 I cannot get my brain working this morning. I have a circle 3.3mm dia. and I need a circular array of 11 of them centred on 0 so that their edges are just touching. I could paste 11 around a circle but I cannot work out how to calculate the diameter of the circle. Can anyone put me out of my misery? Many thanks, Philip

 From: ycarry 24 May 2011  (2 of 13)
 4297.2 In reply to 4297.1 11*3.3mm/pi

 From: d^^b (DAVID) 24 May 2011  (3 of 13)
 Maybe you can draw a 11-polygon The lenght of his side would be the diam. of the circle.... (I think, but I'm not sure)

 From: YHWH_777 24 May 2011  (4 of 13)
 4297.4 In reply to 4297.1 I believe that the radius of your large circle (the one containing the other 11 smaller circles) should be about 11.554648868472 mm I got it as follows: the circumference of the large circle is equivalent to the diameters of the 11 smaller circles, or 11 * 3.3 mm = 36.3 mm the formula for circumference = (2 * pi * r) or (d * pi) plugging in the numbers: 36.3 mm = d * pi 36.3 mm = d * 3.14... d = 36.3 mm / 3.14... d = 11.554648868472 mm NOTE: Please note that this calculation will be off slightly, since the circumference of a circle is actually curved, whereas the calculations above use the diameters of the smaller circles which are straight. But it should be pretty close.

 From: flatdog 24 May 2011  (5 of 13)
 4297.5 In reply to 4297.2 Tks

 From: Michael Gibson 24 May 2011  (6 of 13)
 4297.6 In reply to 4297.1 Hi flatdog - you can solve it geometrically like this- Start by drawing an 11 sided polygon of any size, and then draw a circle from one vertex to a midpoint, so you will have this: This has the layout that you want, just the whole thing is not at the specific scale that you want. So you can fix that by scaling it to your target size. To do that, draw a second circle of the specific size that you want at the same center point as the first circle like this: Now select the 11-sided polygon and run the Transform > Scale command. For the scale origin pick the center of the 2 circles. For the first reference point, pick a point on the large circle. For the second reference point, pick a point on the small, end-sized circle. The 11-sided polygon will now be sized to what you want, you can do a circular array using the center point of the polygon as the array origin. - Michael Attachments:

 From: YHWH_777 24 May 2011  (7 of 13)
 4297.7 In reply to 4297.6 Using the following website: http://www.csgnetwork.com/righttricalc.html I was able to calculate a more accurate diameter of 11.7132362585179. Thanks for the brain teaser!

 From: flatdog 24 May 2011  (8 of 13)
 4297.8 In reply to 4297.6 Thank you all for your suggestions but Michael wins the (sadly notional) prize. I am glad it wasn't too straightforward - I feared that I might end up feeling a little sheepish. Philip Attachments:

 From: d^^b (DAVID) 24 May 2011  (9 of 13)
 4297.9 In reply to 4297.8 Me too! :-) Nice render. What software did you use for?

 From: Frenchy Pilou (PILOU) 24 May 2011  (10 of 13)
 Cool gem :) It's the more little prime number over 10 :D --- Pilou Is beautiful that please without concept! My Gallery