(a) Suppose you have two arrows of equal length on a tabletop. If you can move them to point in any direction but they must remain on the tabletop, how many distinct patterns are possible such that the arrows, treated as vectors, sum to zero? [Note: If a pattern cannot be rotated on the tabletop to match another pattern in your list, it is a distinct pattern.]

(b) Repeat part \(a\) for three identical arrows, assuming the angle between any adjacent pair must be equal.

(c) Repeat for four arrows, keeping the angle between neighboring arrows the same throughout the pattern.

(d) What is the relationship between the number of arrows (vectors) and the number of distinct patterns?