[Prof. Templeton]

1.) A utility company had to run electrical poles 10 miles between town A and town B over a hill. They discovered that the railroad company was also running a track from town A to town B but was making a level cut through the hill that would make their track 9 miles long. The utility company decided to run their poles alongside the level track, through the hill, instead over it. The utility poles need to be 99 feet apart. How many poles did the utility company save be running them alongside the track and not over the hill?

2.) There is a particular village in Madagascar that lies in a very low valley and yet at noon the sun is over 3,000 miles closer to the inhabitants of this village then when it either rises or sets. What part of the country must the village be in?

3.) If the end of the world were to occur on the first day of a new century sometime in the next 2000 years, what are the chances that it will happen on a Sunday?

4.) Leading up to a temple in Nepal there is a stairway with eight steps, not counting the landings, and the monks who worship there have a curious ritual. They start from the bottom and step onto the top landing twice (having to finish there) and return to the bottom landing once being careful to step on each step the same number of times. They always do this in the least number of steps. How many steps do the monks take?

[Prof. Templeton]

Well, maybe, but ... by whatever means it was determined to be 10 miles to the town, it would also be determined that your poles are 110 feet apart. If you wired on poles along the track, then used the same wire and poles along the hill, the wire, at 99 feet per pole, would not reach the town.

Quite true. So now we also know how much wire the utility company saved. But you should know I wouldn't ask a question that straight-forward.

[Yoruichi-san]

Well, maybe, but ... by whatever means it was determined to be 10 miles to the town, it would also be determined that your poles are 110 feet apart. If you wired on poles along the track, then used the same wire and poles along the hill, the wire, at 99 feet per pole, would not reach the town.

Quite true. So now we also know how much wire the utility company saved. But you should know I wouldn't ask a question that straight-forward.

Well, the way I'm looking at it...the 10 miles is like the 'arc length' of the hill 'curve' between the towns. The distance b/w the towns along the x-axis is 9 miles. So I guess the poles have to be 99 feet apart along the x-axis...and I guess making an analogy to the mathematical term 'pole', this makes sense...

...and actually, I don't think you'd save exactly 10% wire...since I assume the wire b/w the poles would be straight and not follow the curvature of the hill exactly...you'd save less than 10%...the difference b/w the hill 'curve' and the wire would be proportional to the error when approximating the 'curve' using the Trapezoidal Rule...

...will stop now ;P

[bonanova]

People can't believe this when I tell them, but I used to be nit-picky.

[Yoruichi-san]

*Sigh*...and there used to be a time where I didn't look at everything through calculus-colored glasses...ah, the end of innocence...