Grasshopper

algorithmic modeling for Rhino

A f** trigonometric problem.

I thought this would be easy to solve, but it's fucking me. Who can find a solution?


The problem is, within a circle of radius "R" package a number "C" of circles tangent to the larger circle and to its two neighbors. As in the image. All that is needed is to formulate "r".


Seems simple right? But today is not my day. :v

We can only use the parameters R and C. Are not allowed geometric solutions.


Thank you if you try.

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Permalink Reply by Daniel González Abalde on November 27, 2015 at 10:57am

Right. Only these two parameters. Thanks.

Permalink Reply by Laurent DELRIEU on November 27, 2015 at 11:22am

r/sin(pi/C)+r = R

so r = R (1+1/sin(pi/C))

Permalink Reply by Daniel González Abalde on November 27, 2015 at 11:49am

Oh man! Thank you so much! My mind is like a potato today trying to do basic math. u.u
Thank you Laurent and Alex :)

Permalink Reply by Laurent DELRIEU on November 27, 2015 at 12:26pm

You are welcome Daniel. 

Permalink Reply by Nik Willmore on November 28, 2015 at 5:35am

Math details, found via Google Images search of "radius of a circle of circles" for a relevant diagram:

http://math.stackexchange.com/questions/767475/1-big-circle-formed-...

http://www.had2know.com/academics/inner-circular-ring-radii-formula...

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