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Guest Message by DevFuse

# Getting the slant

Best Answer Rob_Gandy, 21 February 2013 - 10:26 PM

Yes. Nicely done.

And the obvious next question, what are the coordinates of that point?

The star is twinkling. bona_gold_star.gif

Spoiler for The point is

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4 replies to this topic

### #1 bonanova

bonanova

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Posted 21 February 2013 - 07:54 PM

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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Vidi vici veni.

### #2 Rob_Gandy

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Posted 21 February 2013 - 09:07 PM

Well the first one is fairly simple.

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### #3 bonanova

bonanova

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Posted 21 February 2013 - 10:21 PM

Yes. Nicely done.

And the obvious next question, what are the coordinates of that point?

The star is twinkling.

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Vidi vici veni.

### #4 Rob_Gandy

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Posted 21 February 2013 - 10:26 PM   Best Answer

Yes. Nicely done.

And the obvious next question, what are the coordinates of that point?

The star is twinkling. bona_gold_star.gif

Spoiler for The point is

• 0

### #5 bonanova

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Posted 22 February 2013 - 12:04 AM

Yes. Verified by starting at the first turn and noting 80/40 = 40/[100-80]

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Vidi vici veni.

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