Takes a little time to download Spider image.
Spider builds Number-spiral, instead of Number-line, around a clock with 12 radial lines.
The clock-base 12 can be changed to any number N with (+) or (-) buttons.
The spider will jump along the spiral every other k-th knot (k>1) if you enter k and return.
The numbers can be shown or hidden. It is prefarable to have them hidden initially, to show how usefull (and needed) is their appearance in tracing paths (leads to appreciation of numbers).
You can increase or decrease (make vanish or even drawn thrugh zero-pole) the spacing between spiral arms, make drawing slower or faster. A click on the screen will restart the whole process.
The Game involves a Fly who lands at some knot. Spider tries to catch the Fly by jumping
every second, or every third, etc... knot. This way spider tries to minimize the number of jumps.
Sometimes she catches the fly easily, sometimes it is very hard to do. Why?
The Tuturial will teach that the optimal strategy for the spider is to jump every second, third, fifth, sevrenth, eleventh etc... following the smallest prime numbers. All other types of jumps are absolutely useless. Also, the best hiding strategy for the Fly is to sit on prime numbered knots. The corresponding jumped-on knots will change their initial color.
While overlapping such spider-jumpo-paths, the viewer can see explicitely a huge set of leftover prime numbers on the web (which will have different color). The way primes are generated corresponds to the well known Eratotesthenis Sieve. After only six overlapped paths (2,3,5,7,11,13) the web will reveal all the prime numbers under 289 (=17*17) . With only four paths (2,3,5,7) all the prime numbers will be discovered under 121. This is a very effective way of generating and discovering primes.
Finally, a dramatic picture appears when the clock-base is clicked and changed to 12: all the primes increadibly rearrange into a simple alignment - along two cross-lines 1-7 and 5-11. (similar pattern happens with base 6, or 18, due to the fact that primes are of the form 6*k plus or minus 1. For new location of the fly go back to webpage and start applet again.
(With brausers this is just a demo)
This Spiral can be used in later activities related to Archimedian Spiral.
When the spacing between the arms of the spiral vanishes, it turns into "Poligons and relative Primes" activity, then into "Gears and primes".