Section 10.1 Space Curves (Cool
Parameterizations!)
Some of the links listed below are .pdf files. Others use
DPGraph or Derive 5.
- Problem #28 using DPGraph. ((z = x*y, x^2 + y^2 = 4)) This
shows both surfaces.
- Problem #28 using DPGraph (space curve
intersection). (rectangular(2*cos(u),
2*sin(u), 4*cos(u)*sin(u))
- Parameterizing 3-D curves in DPGraph is somewhat tricky. We
must use the parameter u.
- I've also created an equivalent Derive5 file here for Problem #28 (Derive5).
- Problem #29 using DPGraph. ((z = r, z = 1 + y)) This
shows both surfaces.
- Problem #30 using DPGraph. ((y = x^2, z = 4*x^2 + y^2)) This
shows both surfaces.
- Problem #30 using DPGraph (space curve
intersection). (rectangular(u,
u^2, 4*u^2 + u^4)
- Problem #32 using DPGraph. Instead, I
created a solid! (y >= x^2
& z >= 0 & z <= 0.5*sqrt(16 - x^2 - 4*y^2))
- Here is the note page for Problem #32
using DPGraph. It talks about creating 3-D solids.
- Problem #32 using DPGraph (space curve
intersection). (rectangular(u,
u^2, 0.5*sqrt(16 - u^2 - 4*u^4))