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March 19th, 2010, 01:36 PM  #1 
Newbie Joined: Mar 2010 Posts: 5 Thanks: 0  So, I drew this, now I can't figure it out
Was screwing around with CAD, and drew this pattern, using just pentagons of the same size. As you can imagine, it's getting a bit tedious to continue increasing it's size, and now I'm trying to write a macro to do it for me automatically. After two days now of pulling my hair out trying to write the macro, I'm at a loss. I've added some color to the images to show what I want to do with it when it's done, but was wondering if anyone can give feedback, or perhaps point to a name/formula for achieving this pattern, as I'm sure it's been discovered before, but I can't seem to find it. Click a Thumbnail to enlarge 
April 1st, 2010, 12:10 PM  #2 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: So, I drew this, now I can't figure it out
Hello pletch, Maybe a bit late, but maybe I can help you. It seems that one can calculate some angles here. For a start: The pentagon you used is made of sides with angles of 108 degrees. May be found by \frac{180(a2)}{a} with a is number of angles. Here: 5. Furtheron the white star. The "spike" of the white star has an angle of 1802(18010=1802*72=36 degrees. Now we can calculate the angles of the diamondsuitschape. The angles around a point are added 360 degrees. The diamondsuitschape lies with 2 angles of a pentagon and 1 "spike" of a star. We've seen: angle of a pentagon is 108 degrees, a spike is 36 degrees. 3602*10836=108. Notice that opposite angles are equal in the diamondsuitshape. given a fourangle(is that the correct word?) is 360 degrees, and 2 angles are 108 degrees, the other 2 will be =72 degrees. Can you now calculate the angles of the purple shape? I'm not familiar with macro's to do it automatically, maybe someone else can help you on that one? Good luck Hoempa 
April 2nd, 2010, 03:38 AM  #3 
Newbie Joined: Mar 2010 Posts: 5 Thanks: 0  Re: So, I drew this, now I can't figure it out
Thank you Hoempa, Your reply really got me thinking about it a bit differently. So I ended up setting up the macro this way (note: this is far from the optimal method, I'm sure, but so far its the only way I've found, and for artistic purposes, it's close enough): Made an object consisting of 5 polygons objects all pentagons and grouped them together as a single object. (for some reason this is a bit more difficult to macro than to simply create it as an object) With each group of pentagons inscribed in a 1" circle, I found the distance from center to center of the circles to be 1.84927588 (why I have no idea, but for artistic purposes, it works) then took 360 / 5 = 72 so placed 5 objects at 0, 72, 144, 216, and 288 degrees with an offset of 1.84927588" from the first point (macro lets you pick a point by direction and offset) each of the 5 objects was inserted with a rotation of 180 degrees to flip them upside down from the first one. as they were inserted, each was named with it's angle and rotation (a or b for 0 or 180 degrees) so the objects were named 0b, 72b, 144b, etc. Some other technical thing, they are colored now in the images to show that they are locked, so that the macro does not try to reread ones that it's already copied. Then the macro reads the name of each, and copies it out it's angle + 36 degrees at the same offset of 1.84927588" as well as it's angle  36 degrees at the offset. (note: the angle and offset are from the center of the object from which the name was read) Each is inserted at a rotation of 0 to be upside down from the previous row. again each new object is saved with the name of it's angle and an indicator of it's rotation, so these are called 36a, 36a, 36a, 108a, 180a, etc. (thankfully duplicating names does not matter) same steps repeated again (colored objects are locked so that they don't get read and copied again (also note at this point there are duplicate objects placed over each other using this method).... Unfortunately, now I need to find a way to make it do this, which means not duplicating the pieces in the middle of each angle :/ ugh, so far so good, but this next step is giving me problems, and to make this scale out infinitely does not seem so doable yet. So far so good, but still some work left to do on it. And here are a couple interesting patterns that came up from failed attempts at creating the macro the first few times. 
April 2nd, 2010, 03:59 AM  #4 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: So, I drew this, now I can't figure it out
Hey, You're welcome. You calculated the distance between the centres of circels, maybe an exact number can help you. Are you familiar with sinus and tangens? The distance from center to center can be calculated by adding distance from centre to spike, distance through the diamondsuitshape, and again the distance from spike to centre. Assumed the sides of the pentagons are 1 Gives me in degrees: tan(54)+tan(72)+2sin(54). That is not the value you've found. I hope you were correct. Hoempa 
April 2nd, 2010, 04:14 AM  #5 
Newbie Joined: Mar 2010 Posts: 5 Thanks: 0  Re: So, I drew this, now I can't figure it out 
April 2nd, 2010, 04:19 AM  #6 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: So, I drew this, now I can't figure it out
Hey, You have found a nice solution there! Good luck, Hoempa 
April 2nd, 2010, 12:43 PM  #7 
Newbie Joined: Mar 2010 Posts: 5 Thanks: 0  Re: So, I drew this, now I can't figure it out
Thank you for your help, it really got me to look at it a bit differently, it's funny how you can do something one way by hand, and in order to easily reproduce it with the computer requires a completely different approach. Hard to believe there are so many different patterns that can be done with 1 shape creating so many others. 
April 2nd, 2010, 10:39 PM  #8 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: So, I drew this, now I can't figure it out
Have you ever tried this? Draw a square. All side of the square are sides of a triangle with all equal sizes (I don't know the words on that one), draw the 4 triangles in the square. Suggestion: try figures with more, for instance 6 angles, all samesize and sameangled (for 6 angles, all angles will be 120 degrees). Easy pattern, but I liked it. Hoempa 
April 5th, 2010, 01:25 AM  #9 
Newbie Joined: Mar 2010 Posts: 5 Thanks: 0  Re: So, I drew this, now I can't figure it out 

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