Best Answer bonanova, 05 December 2013 - 04:51 AM

The heat-sinking missiles act like the ants and thus travel a distance * s*.

The shape of their path is a spiral of some type.

For * n*-gons, (

*different from 4) the interior angles*

**n***differ from 90*

**a**^{o}. The target thus moves away from (

*>4) or toward (*

**n***<4) the pursuer by a fraction*

**n***= sin (*

**f***-90*

**a**^{o}) of the distance its pursuer moves toward it. The missiles collide in any case, but after traveling a distance

*multiplied by a factor (1+*

**s***).*

**f****Obviously, the path length increases with**

*. It approaches infinity as the*

**n***-gon becomes similar to a circle, and it decreases to*

**n***/2 for the degenerate*

**s***-gon (line segment.)*

**2**

The whole story:

s multiplier n sides

---------------------

0.50 2

0.67 3

1.00 4

1.45 5

2.00 6

2.66 7

3.41 8

5.24 10

7.46 12

20.4 20

127 50

507 100

2026 200

12665 500

50661 1000

202645 2000

1266515 5000

5066201 10000