There came a time when I needed to mark six equidistant points on a ping pong ball. Thus I needed to mark the poles, an equator, and a couple of lines of longitude. After some discussion on our forum I went with an idea posted by Pendrake that can also be used for other spheres:
The first step was to get several ping pong balls, put them on a sheet of A4 paper, and roll it around them to create a paper tube whose an internal diameter was the same as the external diameter of the ball. Sticky tape was used on the outside seam of the tube to hold it.
The next step was to push the balls 'through' the tube until one popped out of the end. I then put the ball back in the end of the tube and drew around the edge of the tube onto the ball.
Note that this line is NOT around the widest point because the balls are quite tight in the tube so by the time a ball pops out, there is a little over half of the ball poking out of the tube. The solution however is simple: after drawing the first line, turn the ball through 180 degrees (such that the line on the ball is parallel with the end of the tube) and draw another line. The widest point of the ball is an imaginary line half way between the two drawn lines.
The image to the right shows a ball with two pairs of lines already drawn, and the ball set up to draw the second line of a final pair. Note that in order to get the pairs of lines at 90 degrees to each other I 'sighted' the lines on the ball using the seam line on the paper tube i.e. I lined them up by eye, by looking along the length of the tube and lining up the imaginary line on the ball with the seam line on the tube.
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