An ant walks East a distance of 100 feet. Next he walks north a distance of 50 feet. Then west for 25 feet, and so on. He keeps turning left and halving his previous distance. We know this geometric series converges. His path encloses a single point - the only point to which he will come arbitrarily close.

One question that might be asked involves an infinite series:

What is his total path length as he approaches the limit point?

A more interesting question can be answered without a lot of math.

What is the inclination [angle] from due east, of the line drawn back to his starting point?

There are several ways to determine the second question.

A coveted bonanova gold star will be awarded to the most elegant solution.

An ant walks East a distance of 100 feet. Next he walks north a distance of 50 feet. Then west for 25 feet, and so on. He keeps turning left and halving his previous distance. We know this geometric series converges. His path encloses a single point - the only point to which he will come arbitrarily close.

One question that might be asked involves an infinite series:

What is his total path length as he approaches the limit point?

A more interesting question can be answered without a lot of math.

What is the inclination [angle] from due east, of the line drawn back to his starting point?

There are several ways to determine the second question.

A coveted bonanova gold star will be awarded to the most elegant solution.

Enjoy

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