Small challenge
|
06-07-2017, 03:49 PM
(This post was last modified: 06-07-2017 04:11 PM by Pekis.)
Post: #5
|
|||
|
|||
RE: Small challenge
(06-07-2017 11:35 AM)PedroLeiva Wrote:(06-07-2017 09:53 AM)Pekis Wrote: Hello,Can you provide a numerial exaple to test?. TYVM, Pedro Hello, Here is a numerical example: cex=0 (Outer Circle centered at (0,0)) cey=0 r=5 (Outer circle Radius) c=0.2 (Fraction of Outer circle radius left for the triangle) a=(sqrt(3)*(c-1)+sqrt((c+1)*(3-c)))/2=0.223694816 d=a*r=1.11847408 (Side length of equilateral triangle) t=40° (0.6981317008 rad) (Angle at B) Ax=cex+r*(1-c)*cos(t)=3.064177772 Ay=cey+r*(1-c)*sin(t)=2.571150439 Cx=Ax+d*sin(PI/3-t)=3.446718437 Cy=Ay+d*cos(PI/3-t)=3.622172279 Dx=Ax+d*cos(t-PI/6)=4.165659718 Dy=Ay+d*sin(t-PI/6))=2.765371425 Bx=cex+r*cos(t)=3.830222216 By=cey+r*sin(t)=3.213938048 Ex=cex+(r*(1-c)+d*cos(PI/6))*cos(t)=3.806189078 Ey=cey+(r*(1-c)+d*cos(PI/6))*sin(t)=3.193771851 Distance OA=sqrt((Ax-cex)^2+(Ay-cey)^2)=4 OK Distance OA=4=r*(1-c) Distance AE=sqrt((Ax-Ex)^2+(Ay-Ey)^2)=0.9686269669 Distance EB=sqrt((Ex-Bx)^2+(Ey-By)^2)=0.03137303338 OK Distance AB=Distance AE+Distance EB=1=r*c Distance AC=sqrt((Ax-Cx)^2+(Ay-Cy)^2)=1.11847408 Distance CD=sqrt((Cx-Dx)^2+(Cy-Dy)^2)=1.11847408 Distance DA=sqrt((Dx-Ax)^2+(Dy-Ay)^2)=1.11847408 OK Distance AC=Distance CD=Distance DA=d => Equilateral CQFD |
|||
« 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)