Re: PROBLEM - A moving point on the surface of an expanding sphere.

On 21 Jan, 21:30, Gib Bogle <bo...@xxxxxxxxxxxxxxxxxxxxxxxx> wrote:
Golden Boar wrote:
If we have a sphere of radius r, with 2 poles, north and south, and a
point which travels over the surface of the sphere from the north pole
to the south pole, then the distance travelled by the point is simply
pi.r.

It takes the point 1 second to travel this distance, and the radius of
the sphere increases by 1 every second.

How do I calculate the distance travelled by the point over the
expanding surface of the sphere, from the north pole to the south
pole?

Also does anyone know of any programs I could use to plot the path of
the point?

At some point t along the path, determine the incremental movement in
the x, y and z directions (i.e. dx, dy, dz) that occurs over a small
time interval dt.  Then the increment to the path length, ds, you can
find from dx,dy,dz.  You then need to integrate ds/dt over the whole
time interval.

You could plot distance from the axis vs distance along the axis in Excel.

I don't really want to use the above technique as I havn't established
directions for y or z, at this point.

More info:
I have defined the unit line as the set of all points between 2
specified points, which has a value of 1.

The sphere is a unit sphere which I have defined as the set of all
unit lines which share a common point of origin.

An axis through the sphere is defined as a line between 2 points on
the surface which are directly opposite each other.

So basically, I need to do this with just the above info, so, only 1
dimension, no use of angles, no use of pi, no parallels, no
perpendiculars, no squares, no triangles, etc.

Is this possible?
.

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