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speedy

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Assuming the Earth is a perfect sphere of 4,000 miles radius), how far would a person need to be from the Earth’s centre to see one third (1/3) of the Earth’s surface?
 
For a solution to (almost) the exact same problem, in an interesting context, see this, which I wrote 18 years ago! It's very memorable.

I would recommend, however, that you try working ahead of whatever answer you read, in order to get the maximum benefit out of it. Read line by line, trying to think what you would do next. The key in any case is either to find or derive a formula for the area of a spherical cap. If you hadn't already been shown an answer, I would have shown you only that to start with.
 
Dr.Peterson said:
For a solution to (almost) the exact same problem, in an interesting context, see this, which I wrote 18 years ago! It's very memorable.

I would recommend, however, that you try working ahead of whatever answer you read, in order to get the maximum benefit out of it. Read line by line, trying to think what you would do next. The key in any case is either to find or derive a formula for the area of a spherical cap. If you hadn't already been shown an answer, I would have shown you only that to start with.
Click to expand...

So would I be right thinking that my answer would be 1 1/2 × the diameter?
So
 
Check it out! Use one of the other sources to see if it gives the right results. But that is what my answer implies, yes.
 
Dr.Peterson said:
For a solution to (almost) the exact same problem, in an interesting context, see this, which I wrote 18 years ago! It's very memorable.
Click to expand...

Great ASCII drawing of the problem! Good solution. A nice link.

I noticed the original question said that there were no slide rules in 1828, which is incorrect. But maybe they were not very widely available or too expensive for most schools back then. More to the point a slide rule wasn't necessary for this problem!
 
Ahhh, the good old ASCII art days. Back in the day on usenet that's all there was (probably still is). No PostScript graphing. No [MATH]\LaTeX[/MATH] rendering for equations either. In fact, no [MATH]\LaTeX[/MATH] either. We tend to forget the first HP scientific handheld calculator was in the late 60's or early 70's. And the only person that could type up your Master's or Doctor's thesis was the secretary that had a special IBM Selectric ball with math symbols on it.
 
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