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Chicagoist loves the Ask Tom Why column in the Tribune, where people write in 'weather' questions and meteorologists answer them. (Tom gets a little help from the weather crew.) In general the questions don't need to be answered by a weather expert; they just need to be answered by someone who's relatively well informed or who can look things up in an encyclopedia. For example, it turns out people don't know what a 40 percent chance of rain is, so they ask Tom. We're glad he helps out with stuff like that.
Every so often, though, we can get our geek on. For example, how far away is the horizon? Oh. Oh, yes. Oh sweet and velvety geometry. Tom says that you should multiply the square root of your height by 1.3 to get the distance to the horizon. Other sources say multiply by 1.17. Wanna do a little math? Do we ever!
The earth is a circle with radius r = 6378.1 kilometers, or 3963.1676 miles, or 20,925,524.9 feet. Your distance from the center of the earth is r + h, where h is your height (well, the height of your eyes). The horizon’s distance from the center of the earth is r. So we have a triangle, with legs r, r + h, and d, where d is the distance from your eyes to the horizon. (Help, I'm a visual learner.) We all remember that the angle drawn by a tangent line and radius is a right angle, so we luckily have a right triangle. Still with us? So fun. Nothing gets the juices flowing on a Monday like a little Pythagorean theorem. Yum.
So boiling down the hoohah, we get d = sqrt[(r + h)^2 – r^2]. We’re going to assume that h << r, so we simplify to d = sqrt[2rh], which we simplify further to say d = 6469.239 x sqrt[h] in feet. So with the conversion...it works out...to...wait, hang on...um, OK. Converting from feet to miles, that works out to 1.223 x sqrt[h] miles. We're going to chalk these differences up to refraction. Nerd alert.
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Margaret:
From one math nerd to another: Best. Chicagoist entry. Ever!
Except your hoohah should say "d = sqrt[(r + h)^2 - r^2]". Without that correction, it may not be clear to everyone why "h
-- James
D'oh! I hope I get partial credit...
Interesting. But didn't I learn that in 7th grade?
And if I were from anywhere in Asia, I'd have learned it in like 4th grade. And even if I were a lawyer, doctor, or um, blogger, I would know how to derive that in 5 minutes.
Why do you have to apologize every other sentence for writing down a mathematical formula? The problem with this country "exporting jobs" is not that Bush and Co. are evil, evil people, but that the understanding of math and science by native born Americans has become a joke and a reason for apology.
I'll tell you, the Chinese, Koreans, and Singaporeans who know math in the 5th grade better than most adult Americans are laughing all the way to the bank. Seeing as how many of our high-paying jobs are being exported over there.
Keep on making jokes. Pretty soon, the rich Asians will be the only ones laughing.
Hold up. Let's not rush into who knows his math. Certainly there are many math literate asians, but don't forget the Greeks. Afterall, Pythagorean was greek, and he's credited for recognizing the relationship uniqe to right triangles named after him.
ow! my head hurts!
I did it in excel like this:
=SQRT(A1)*1.3
Where the A1 cell contains my height in feet.
More than two million women are not building up any entitlement to the basic state pension, according to the Department for Work and Pensions (DWP).