Net of the Cone
Guideline for the Construction
* Take a slider
*Input a=PerpendicularLine((1,0,0),xOyPlane)
* Input c- Circle(a,(0,0,0))
*input A=Point(a)
*input B=Intersect(xAxis,a)
*input e=Cone (B,A,1)
* Trace the Point A in given line then make the cone
* Click the point e and go to in Algebra and click in Auxiliary object
*Rename point (d=e) and (b=d)
* input
- C=(yAxis,xAxis)
- I=Segment(C,A)
- r= Distance(B,C)
- =Angle(A,C,B)
- A'= Rotate (A,t ,yAxis)
- f=PerpendicularLine(A',xOyPlane)
- B'=Intersect(f,xOyPlane)
- =2r/Distance(B',C)
-C'=Rotate(C,/2,f)
-C'_1=Rotate(C,(-)/2,f)
-g=CircumCircularArc(C',C,C'_1)
-h=Distance(A',B')
-r'=Distance(B',C')
k=x(A')
=t
-i=Surface((k-v*r' cos(u*β/2))cos( ϕ )-(1-v)h* sin( ϕ),v*r' sin(u*β/2),(1-v)h* cos( ϕ)+(k-v*r' cos(u*β/2))sin( ϕ
),u,-1,1,v,0,1)
-j=Curve((k-r' cos(u β/2)) cos(ϕ),r' sin(u β/2), (k-r' cos(u β/2)) sin(ϕ),u,-1,1)
-D=((k-r' cos(β/2)) cos(ϕ), r' sin(β/2), (k-r' cos(β/2)) sin(ϕ))
- E=((k-r' cos((-β)/2)) cos(ϕ), r' sin((-β)/2), (k-r' cos((-β)/2)) sin(ϕ))
- F=(k cos(ϕ)-h sin(ϕ),0,h cos(ϕ)+k sin(ϕ))
- Segment(D,F)
- Segment(E,F)