Small challenge

06112017, 09:58 PM
(This post was last modified: 06122017 08:12 AM by Pekis.)
Post: #17




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=1c=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*k²p²)p*sqrt(4*k²1))/(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: tarcsin(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(4p²)p*sqrt(3))/2 (same as previous formula a=(sqrt(3)*(c1)+sqrt((c+1)*(3c)))/2)) Thanks 

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Messages In This Thread 
Small challenge  Pekis  06062017, 08:05 AM
RE: Small challenge  pier4r  06062017, 01:26 PM
RE: Small challenge  Pekis  06072017, 09:53 AM
RE: Small challenge  PedroLeiva  06072017, 11:35 AM
RE: Small challenge  Pekis  06072017, 03:49 PM
RE: Small challenge  PedroLeiva  06082017, 12:59 PM
RE: Small challenge  Jim Horn  06072017, 04:25 PM
RE: Small challenge  Pekis  06072017, 04:31 PM
RE: Small challenge  SlideRule  06072017, 08:42 PM
RE: Small challenge  Pekis  06072017, 09:54 PM
RE: Small challenge  SlideRule  06072017, 10:53 PM
RE: Small challenge  Pekis  06082017, 05:10 AM
RE: Small challenge  SlideRule  06082017, 12:12 PM
RE: Small challenge  Vtile  06092017, 01:14 PM
RE: Small challenge  Csaba Tizedes  06112017, 10:59 AM
RE: Small challenge  Pekis  06092017, 07:08 AM
RE: Small challenge  Pekis  06112017 09:58 PM

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