Geometry question

[sinforoso]

Half the length of the chord divided by the radius is the sine of half the subtended angle.............

But that's, like, words. I'm talking about, like, equations, and stuff, as the scientists would say.

 

[charlie b]

Distance = Radius * sqrt(2) / (1 + sqrt(3))

Equivalent to, and perhaps slightly more "elegant" in some circles... = 2r / (sqrt(2)+sqrt(6))

I presume these equations are intended to relate only to the specific question in this thread, in which the lights are separated by 30 degrees of angle. There is no variable for angle in either formula.

 

[Smart $]

I presume these equations are intended to relate only to the specific question in this thread, in which the lights are separated by 30 degrees of angle. There is no variable for angle in either formula.

Correct.

Formula is for side length of a dodecagon, where radius (r) refers to the circumradius, not the inradius.

 

[PetrosA]

Hello.
I have a situation where I have to lay out 12 hi heads in a shape of a circle.
Is it possible to come up with equation for me to know a distance between light fixture to the adjacent light fixture in straight line?
My field situation is that i need this dimension.
I would be able to come up with that when i was 12 years when i had geometry classes old but now can't figure it out having 1500$ worth of lasers. . its so funny.
thank you in advance for your input

I hope you're laying this out on the floor

 

[Besoeker]

But that's, like, words. I'm talking about, like, equations, and stuff, as the scientists would say.

The words describe the equation.

 

[sinforoso]

I have a strange sense of humor, even by engineer standards perhaps.