Math and engineering seems to be the topic that no one wants to face, that many want to go away, and perhaps the subject that will affect our future.

But math, and chemstry are everywhere, although I know more people than I can count who swear they haven't used either since high school. How do you cook or alter recipes? Sewing uses math if you have to fit anything. What about mixing cleaning chemicals? It seems to me that math is everywhere, if only you care to look.

What about re-fiberglassing your pool? What do you do when the contractor quotes the cost of the job and says it will be $20 per square foot. (pool shell surface)?

It is pretty easy if you have a standard rectangular pool.

But what happens if your pool is odd shaped?

I have a free form pool that was poured on fill. I would love to see how they framed the original pour, as nothing is smooth or even. The empty pool looks like one of those clay bowls we made in elementary school, roughly bowl shaped but with lumps and bulges and odd indentions where our fingers poked and smoothed the unformed clay.

Years ago, the first time we had a fiberglass liner put in this pool I did it the difficult way, taking measurements at various different points and calculating the surface area of the different cross-sections. But I didn't save the original figures from 16 years ago, just the bill. Today I am lazier.

If you look at the pool you will see that it is basically oblate. My drawing is not to scale, or even all that accurate, the primary and secondary diameters are 29 and 27 feet. The pool is deeper than it was 15 years ago as we had to raise the sides, one side more than the other, as the pool had slipped down the hill and tilted somewhat over the years.

The lazy woman immediately realized that she could assume the pool was a dome (inverted) and calculate the surface area. Armed with the radii, depth, and a computer, the calculations are pretty easy.

If we assumed the pool was one big dome (red) we might be close, but we might be a little on the high side of our estimate as the bottom curve is really not consistent. Or, if we look closer we could see that the pool could also be estimated as three separate oblate dome shapes. The small blue circle in the middle is so placed because the deep end of the pool doesn't really slope gradually from the sides, the pool is a relatively shallow bowl, and then there is this little nipple like extrusion at the bottom that suddenly becomes deeper than the rest.

You can see the view in cross-section here:

Viewed this way, you can see that the calculation for the red surface area would be a little large, and the combination of the other three inverted dome-shapes would be a little small, but close to the actual measurement.

This is all basic high-school math. Of course, when I was in high school we were not allowed to use calculators and had to do all the calculations by hand. Evenutally someone figured out that using the calculator wasn't cheating because one still had to understand what one was calculating and know what kind of formula to use. Given modern calculators and computers, the actual calculation was easy. The math took less time than I spent on the drawings.

And all of this took less time than I would have spent walking around the pool and measuring the actual size and calculating the exact surface area. I just needed a general price range so I know how much money to have available when the contractor shows up.

But if I hadn't taken "college track" math in high school would I know how to do this? Basic math requirements when I was in high school called for two years of math, of which one was basic math and the second year was plane geometry. Niether one would have covered this kind of thing, and most students who took them probably never took another math class.

I assume what was called "college track" when I was in school is the same as AP math today. But I just read that the Scarsdale schools decided to drop AP classes in high school bccause the kids are working too hard with all their extra-curricular activities. Don't parents realize this is their last chance to actually be required to learn anything. Some students will study hard in college, but more will just party their tuition and time away.

Granted, calculating the surface area of your pool is not an every day occurrence. But it seems to me that a lot of things in life are a lot easier with a bit of math and science under the belt.