Small challenge
06-11-2017, 09:58 PM (This post was last modified: 06-12-2017 08:12 AM by Pekis.)
Post: #17
 Pekis Member Posts: 103 Joined: Aug 2014
RE: Small challenge
Hello,

I just don't fully understand the figure in your cone challenge ...

Anyway, I wanted to give an epilogue to my challenge with a generalized formula with a isosceles triangle (with one base and two equal sides) instead of an equilateral one:

let c=Fraction of Outer circle radius left for the isosceles triangle
let p=1-c=Fraction of Outer circle radius for the figure inside the inner circle
let b=Base length of the isosceles triangle
let e=Fraction of the outer circle radius for base length => b=e*r
let d=Side length of the isosceles triangle
let a=Fraction of the outer circle radius for side length => d=a*r
let k=a/e=Ratio between Side and Base of the isosceles triangle

=> a=(sqrt(4*k²-p²)-p*sqrt(4*k²-1))/(2*k)
It's good looking ...

Arc length: r*2*arcsin(a/(2*k))
Arc height: r*sqrt(4-(a/k)²)/2
Arc Angle span: 2*arcsin(a/(2*k))
Arc Start angle: t+arcsin(a/(2*k))
Arc End angle: t-arcsin(a/(2*k))
And instead of the PI/6 angle in ACE, we now have Angle ACE=arcsin(1/(2*k))

For an equilateral triangle, k=1 and it leads to
a=((sqrt(4-p²)-p*sqrt(3))/2
(same as previous formula a=(sqrt(3)*(c-1)+sqrt((c+1)*(3-c)))/2))

Thanks
 « Next Oldest | Next Newest »

 Messages In This Thread Small challenge - Pekis - 06-06-2017, 08:05 AM RE: Small challenge - pier4r - 06-06-2017, 01:26 PM RE: Small challenge - Pekis - 06-07-2017, 09:53 AM RE: Small challenge - PedroLeiva - 06-07-2017, 11:35 AM RE: Small challenge - Pekis - 06-07-2017, 03:49 PM RE: Small challenge - PedroLeiva - 06-08-2017, 12:59 PM RE: Small challenge - Jim Horn - 06-07-2017, 04:25 PM RE: Small challenge - Pekis - 06-07-2017, 04:31 PM RE: Small challenge - SlideRule - 06-07-2017, 08:42 PM RE: Small challenge - Pekis - 06-07-2017, 09:54 PM RE: Small challenge - SlideRule - 06-07-2017, 10:53 PM RE: Small challenge - Pekis - 06-08-2017, 05:10 AM RE: Small challenge - SlideRule - 06-08-2017, 12:12 PM RE: Small challenge - Vtile - 06-09-2017, 01:14 PM RE: Small challenge - Csaba Tizedes - 06-11-2017, 10:59 AM RE: Small challenge - Pekis - 06-09-2017, 07:08 AM RE: Small challenge - Pekis - 06-11-2017 09:58 PM

User(s) browsing this thread: 1 Guest(s)