## Archive for June, 2011

### The Wonders of Algebra

Monday, June 13th, 2011

Yesterday’s “Ask Marilyn” was interesting.

Say that I place a 25,000-mile-long metal band snugly around the earth. (Assume a smooth planet.) Then I cut the band and splice another 50 feet to it, thus loosening it all around. Can I get my finger between the new-length band and the earth? Can I crawl under it?
— Zen White, Elkins, W. Va.

Amazingly, even the tallest basketball player could walk under that band, which be float about eight feet off the ground around the planet. The circumference of the object is irrelevant. Adding 50 feet to any size band — one that wraps around a cantalope or the moon — will produce the same answer: the longer bound will be about 8 feet from the object it circles.

“Surely not. That’s just wrong!” were my initial thoughts.

But then I did the math.

```c = circumference
x = increase to radius

c = 2(pi)r
(c + 50) = 2(pi)(r + x)
(c + 50) = 2(pi)r + 2(pi)x
2(pi)r + 50 = 2(pi)r + 2(pi)x
50 = 2(pi)x
x = 50 / (2pi)
x = 25 / pi
x = 7.958
```

Algebra to the rescue!

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