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I have 3 column vectors:

phi contains the number of radians from the North Pole

theta contains the number of radians from the Greenwich meridian

D contains number data corresponding to the point (phi,theta) on the sphere.

 

How do I plot:

a) a contour plot on the surface of the sphere where each point at (phi, theta) has a corresponding data value D?

b) a plot where the height above the surface at (phi, theta) is some linear function of D such as radius*D*constant?

In a webinar on July 10, 2013, I solved the related rate problem:

Helium is pumped into a spherical balloon at the constant rate of 25 cu ft per min.
At what rate is the surface area of the balloon increasing at the moment when its radius is 8 ft?

A question in the Q&A at the end of the Webinar asked if it were possible to have an animation illustrate the expanding sphere and the rate of change in the surface area thereof. 

I have a list L. In geom3d, I want to write all tangent of plane of the spherefrom L. But I don't know. I only write one point . I tried 

> restart:

with(geom3d):

L:=[[-5, -5, 8], [-5, -1, 10], [-5, 3, 10], [-5, 7, 8], [-5, 8, -5], [-5, 8, 7], [-5, 10, -1], [-5, 10, 3], [-1, -5, 10], [-1, 7, 10], [-1, 10, -5], [-1, 10, 7...

restart;with(geom3d):

point(M,1,2,1):

plane(P,x+y-3=0,[x,y,z]):

plane(Q,2*x-2*y+z-1=0,[x,y,z]):

line(d,[1+2*t,1-t,t],t):

n:=NormalVector(P):

line(Delta,[M,n],t):

Eq:=Equation(Delta):

intersection(N,d,P):

coordinates(N):

Please write for me a code for the following problem.

Let (S): x^2 + y^2 + z^2 -2*x +2*z + 1 = 0 be a sphere and M(1, 2, -1), N(3, 1, -1) be two points. Find the coordinates of the point K lies on the sphere (S) such that the triangle KHN has minimum area. 

Thank you very much.

Equation of a sphere (6)...

February 16 2012 toandhsp 215

Write the equation of the sphere passing through the point B(-1,-1,0) and tangent to the line x = t + 1, y = 2*t + 1, z = -t + 2 at the point A(1, 3, 2) so that its radius obtain minimum value.

This is my code.

> restart:with(geom3d):

point(B,-1,-1,0):

point(A,1,3,2):

a:=[t+1,2*t+3,-t+2]:

line(Delta,a,t):

dsegment(AB,[A,B]):

Equation of a sphere (5)...

February 16 2012 toandhsp 215

Problem 1. Write the equation of the sphere passing through three points A(2, 3, -2), B(-2, 3, 4), C(0, -1, 2) and  tangent to the plane (P): x+5*y+z-33=0.

This is my code

> restart:with(geom3d):

point(A,2,3,-2):

point(B,-2,3,4):

point(C,0,-1,2):

plane(P,x+5*y+z-33=0,[x,y,z]):

point(T,x,y,z):

Write the equation of the sphere has its centre at C(1, 2, 3) and cut the  straight line

Delta: x = t+1, y = t-1, z = -t at the points A and B so that the triangle ABC is a equilateral triangle.

This is my code.

Equation of a sphere (3)...

February 15 2012 toandhsp 215

Problem. Write the equation of the sphere passing through the three points

A(-1, 2, 1), B(-3, 4, -5), C(1, 2, -3) and its centre 

1) lies in  the plane (P): 2*x + 3*y -z = 0;
2)lies on the sphere (x-3)^2 + (y+1/3)^2 + (z-1)^2=1.
 
This is my code
1) 

restart;with(geom3d):

point(A,-1,2,1):

point(B,3,-4,5):

Equation of a sphere (2)...

February 14 2012 toandhsp 215

Let A(1,-2,3), B(-1,0,1) be two points and (P): x+y+z+4=0 be a plane. Write the equation of the sphere has center lies on the line AB, radius of sphere equal to AB/6 and sphere tangent to the plane (P).

This is my code.

> restart:with(geom3d):

point(A,1,-2,3):

point(B,-1,0,1):

line(AB,[A,B],t):

eq:=Equation(AB):

point(M,op(eq)):

Please help me  write a code for the following problem:

Write the equation of the plane which passes through the points A(-1, 3, -6) and B(2, 2, -10) and tangent to the sphere

(x-1)^2 + (y + 1)^2 + (z - 7)^2 = 9.

Thank you very much.

Hello, can you help me? I need to draw a simple model of solar system (9 planets around the sun). I tried to draw planets with

> a[1] := animate(implicitplot3d,

                            [

                    ...

I currently need to cut a sphere into equal parts becuase I am carrying out an investigation for a school assignment. However, I do not know how I can cut the sphere into pieces in Maple, which I have been told it needs to be done through code. I will need to know how I can cut it so I can carry out my investigation by cutting it into different number of pieces. For example, cutting a sphere into half, so one piece would be a hemisphere.

 

Also, I will...

When I use the differential geometry package and setup a spherecial metric with greek letters using the palette it protects the variables displaying the actual greek symbol but it protects the basis elements (vectors and forms)  using the spelled versions i.e. dphi, dtheta.  In all subsequent calculations for other tensors like connection and curvature it displays the spelled names dphi dtheta whereas i would like to have the actual greek synbols displayed which it does in for example sin(φ...

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