### Cylinder

Cylinder in Cartesian coordinates
g := (x,y) -> [cos(x), sin(x), y]:
a1:=0: a2:=Pi: b1:=0: b2:=Pi:
c1 := 1: c2 := 3:
Point := 2:
f1:= (t) -> t:
f2:= (t) -> 1:
Take away NormVector in the display

g := (x,y) -> [cos(x), sin(x), y]:
a1:=0: a2:=Pi: b1:=0: b2:=Pi:
c1 := 1: c2 := 3:
Point := 2:
f1:= (t) -> 1:
f2:= (t) -> t:

g := (x,y) -> [cos(x), sin(x), y]:
a1:=0: a2:=Pi: b1:=0: b2:=Pi:
c1 := 1: c2 := 3:
Point := 2:
f1:= (t) -> t:
f2:= (t) -> t:
Take away NormVector.

g := (x,y) -> [cos(x), sin(x), y]:
a1:=1.8: a2:=Pi: b1:=Pi: b2:=2*Pi-1:
c1 := 1.8: c2 := 2.2:
Point := 2:
f1:= (t) -> t:
f2:= (t) -> t^2:
Take away surf,Plane,SurfCurve,

g := (x,y) -> [cos(x), sin(x), y]:
a1:=1.8: a2:=2.2: b1:=3.8: b2:=4.2:
c1 := 1.8: c2 := 2.2:
Point := 2:
f1:= (t) -> t:
f2:= (t) -> t^2:
Take away Plane

### Sphere

Sphere latitude:
g := (x,y) -> [cos(x)*sin(y), sin(x)*sin(y), cos(y)]:
a1:=0: a2:=Pi: b1:=0: b2:=Pi:
c1 := 1: c2 := 3:
Point := 2:
f1:= (t) -> t:
f2:= (t) -> 1:

Sphere longitude:
g := (x,y) -> [cos(x)*sin(y), sin(x)*sin(y), cos(y)]:
a1:=0: a2:=Pi: b1:=0: b2:=Pi:
c1 := 1: c2 := 3:
Point := 2:
f1:= (t) -> 1:
f2:= (t) -> t:

### Cone

Make a 90 degree and 180 degree cone
Cone parameterization
g := (x,y) -> [(1-x)*cos(y), (1-x)*sin(y), x]:
a1:=0: a2:=3: b1:=0: b2:=1:
c1 := 0: c2 := 1:
Point := 1/2:
f1:= (t) -> 1/2:
f2:= (t) -> t:
latitude circle - discuss why it is not a geodesic using intrinsic arguments, including the lack of half-turn symmetry and the fact that it unfolds to circle.

g := (x,y) -> [x*cos(y), x*sin(y), x]:
a1:=0: a2:=3: b1:=0: b2:=3:
c1 := 0: c2 := 1:
Point := 1/2:
f1:= (t) -> 1/2:
f2:= (t) -> t:
latitude circle - discuss why it is not a geodesic using intrinsic arguments, including the lack of half-turn symmetry and the fact that it unfolds to circle.

Next change to:
f1:= (t) -> t:
f2:= (t) -> 1/2:

Then to:
b2:=Pi/2:
cc:=.8497104921: dd:=-.5553603670:
f1:= (t) -> cc*sec(t/sqrt(2)+dd):
f2:= (t) -> t:
Discuss where secant comes from and where cc and dd come from.