geometric challenge

Bob Jefferson · Post by **Bob Jefferson** » 10 Aug 2010, 20:59

I'm trying to draw a single panel of an eight-panelled beach ball that is six units in diameter. My maths is a bit ropey but would I be right in saying that, taking pi to be 3.14, it would be 9.42 long and 2.355 at its widest point?

Does anyone have the means of drawing such a shape and if so could they post it here please. There is a point to all this - honest!

Bazza · Post by **Bazza** » 11 Aug 2010, 10:47

> I'm trying to draw a single panel of an eight-panelled beach ball that is six
> units in diameter. My maths is a bit ropey but would I be right in saying
> that, taking pi to be 3.14, it would be 9.42 long and 2.355 at its widest
> point?

> Does anyone have the means of drawing such a shape and if so could
> they post it here please. There is a point to all this - honest!

My maths is good, but I'm not sure I understand the problem...

You have 8 panels, yeah? And you want to draw a beach ball on these 8 panels? Are the panels arranged 2x4? Or 1x8? What's a "unit"?

rmolehusband · Post by **rmolehusband** » 11 Aug 2010, 15:40

I think your calculations are correct

The circumference of the ball is pi * the diameter = 6pi.
The long axis of the segment will be half the diameter = 3pi = 9.42
The short axis will 1/8th of the diameter = 6pi / 8 = 2.36

That said, remember that such a panel as part of a ball (in 3 dimensions) has each edge of the panel is the same length as the long axis, so it's not possible to draw this accurately in two dimensions. That's why when you make a ball out of eight flat 2D segments you don't get a perfect sphere.

Assuming a 2d segment is good enough, you can either stick with your calculation (3pi) for the long axis in which case the edge length will be a bit longer or you can use the 3pi value for the edge length in which case the long axis will be a little shorter. There is only one circle can be drawn through three points and, in both cases, the radius of the circle is the same as the long edge of the segment.

I've drawn both (1 unit = 10mm) as it's more fun than work. You can hopefully see a PDF here:
http://docs.google.com/fileview?id=0B0i ... YjUz&hl=en
(sizes in mm)

Hope this helps and thanks for the entertaining diversion.

SoupDragon · Post by **SoupDragon** » 11 Aug 2010, 16:16

Been trying to imagine this.
You have a beach ball made up of 8 panels
The diameter of this beach ball is 6
You want to know the size of a panel you wish to draw from this info?

Would your beach ball panel not need to be oval or rather, elliptical?
( ah , you did say at widest )

The one in my head is now mangled and rather concave after being jumped on in frustration

right so circumference is pi x diameter so thats 3.14 x 6 = 18.84
divide by number of panels is 18.84/8 = 2.355

and length is 18.84/2 = 9.42

but I'm baffled as to how to calculate where to put the pins to follow
of drawing the ellipsethis way

seanie · Post by **seanie** » 11 Aug 2010, 17:01

Think of lines of longitude; they converge to a point at each pole. You don't want an ellipse or an oval.

SoupDragon · Post by **SoupDragon** » 11 Aug 2010, 17:48

Ah
like chocolate orange segments

Bob Jefferson · Post by **Bob Jefferson** » 11 Aug 2010, 19:50

Thanks to all, and in particular to molehusband. You can get back to work now.

So four of my beach ball panels, with artwork applied, would look a bit like this:

Two would look like this:

And the remaining two would look like this:

Great! Now I can print them off, cut them out and make a scale model.