Geometry

[kermit911]

I couldn't find a topic that pertained to this, so sry if it doesn't belong here.

Ok, I have a circle that is 24 feet in diameter. I would like to put a 12 pointed circle that is 26 feet in diameter around the 24 foot circle. I don't know what you call a 12 pointed circle, sry. Decagon maybe, no thats 10. what ever, you get the idea. Is there a formula for this?

Here is what I am tring to do. I would like to put land scaping ties around my pool. I already know that for 12 of them I need to cut them at a 15 degree angle, but I don't know how long I need to make them. Thanx all

[Space]

dodecagon

[Hamish]

get a pair of compasses and open them to 13.46 feet (you could use a peace of string.) Draw a 26f circle and chose a point on it. use the string/compass to find the next point and move round the circle like this. If you have measured correctly you should end up at the first point and a figure with 12 regular sides.

 

Good luck!

[finex]

First off the angle would need to be 30 degrees for 12 tiles, as 12 x 30 = 360 degrees.

 

When you say "How long", you need to clarify that. Do you mean how long will the outside edge be, or do you mean how long to make the two equal length sides?

 

If I understand it right, you effectively want to have 12 triangular shaped tiles. Only they won't actually be a complete triangle, as they won't reach the centre. It'll be more like a Dairylea triangle with the pointy bit cut off.

[NetSquirrel]

Hi, kermit.  I've been having difficulty picturing what measurement it is you're looking for, despite your accurate description.  If my diagram is of any use at all, could you explain / mark what information it is you need?  If you want to know what the outer length is of each side of the dodecagon, that is 6.97 feet, or approximately 6 feet 31/32 inches.

[kermit911]

That was perfect Net Squirrel.  Thank you all.  Is there a formula that you can use to find this?

[landie]

1. Get a length of cord 13 ft long (radius) and, with one end fixed at the centre of your circle scribe the circumference by pulling the cord (taut) around the pivot point. leave the pivot piont marked.

2. Using the cord start at a point where you wish your star to begin and measure with the cord pulled taut where it intersects with the circle (you will find that this is 1/6 of the circumference. Carry on around the circle until you return to your point of origin. You should now have six equal points. Find a point equally between two of the six (find the length of cord which meets in the middle when measured from both sides to give you this.

From the new point, again with 13 ft length of cord follow step 2. to give you a twelve pointed circle 26ft in diameter.

Do the same at 12 ft radius ti give you the inside star but offset by half a segment to split the markings equally.