       Re: A question about a sphere

• To: mathgroup at smc.vnet.net
• Subject: [mg107057] Re: [mg107038] A question about a sphere
• From: "David Park" <djmpark at comcast.net>
• Date: Tue, 2 Feb 2010 03:24:12 -0500 (EST)
• References: <24744797.1265023377774.JavaMail.root@n11>

```Here is an easy solution using the Presentations package. First we
parametrize a sphere and then draw the sphere, the lines of latitude, and
the lines of longitude using the parametrization. (We could have just used
Sphere for the sphere.) I used 6 lines of longitude in honor of the
Babylonians.

Needs["Presentations`Master`"]

sphere[r_, \[Phi]_, \[Theta]_] :=
r {Cos[\[Phi]] Cos[\[Theta]], Cos[\[Phi]] Sin[\[Theta]], Sin[\[Phi]]}

Draw3DItems[
{(* Draw the sphere *)
Opacity[.5], Orange,
ParametricDraw3D[
sphere[1, \[Phi], \[Theta]], {\[Phi], -\[Pi]/2, \[Pi]/
2}, {\[Theta], 0, 2 \[Pi]},
Mesh -> None],
(* Draw 5 lines of latitude *)
Opacity, Black,
Table[ParametricDraw3D[
sphere[1, lat, \[Theta]], {\[Theta], 0,
2 \[Pi]}], {lat, {80 \[Degree], 40 \[Degree],
0, -40 \[Degree], -80 \[Degree]}}],
(* Draw lines of longitude *)
Table[ParametricDraw3D[
sphere[1, \[Phi], long], {\[Phi], -\[Pi]/2, \[Pi]/2}], {long, 0,
300 \[Degree], 60 \[Degree]}]},
NeutralLighting[0, .5, .1, 0 \[Degree], -30 \[Degree]],
NiceRotation,
Boxed -> False,
ImageSize -> 400]

NeutralLighting provides white lights with a little ambient light and
lowered to give a better rendering. NiceRotation prevents jumping of the
image if you rotate with the mouse.

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

From: Marwa Abd El-Wahaab [mailto:m.a.elwahaab at gmail.com]

Dear Sir,

I am a Mathematica 7 user.

I have a question :

I want to draw a sphere, then draw 5 circles on this sphere like
*latitudes*and draw 5 lines on this sphere like
*longitudes*.