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Let's say the earth is smooth all the way around at the equator. Let's also say that if I string a line around the equator it would be snug to the surface of the earth, correct?
Now, If I cut that string and add just 20 feet to it you would grant me that it would now be lose around the equator, correct? (sorta like a belt that's too big for your gut).
Here's the question: is it lose enough for a person to be able to crawl under it? Remember, I'm just adding 20 ft to a circle that's 7K (approx) mile in diameter.
Yes/no? Also prove your answer one way or the other.
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C'mon, no one wants to take a stab at it???
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The circumference of the earth is 24,901 miles = 131,477,280 feet.
The diameter of the earth would be then 418,505,015 feet.
Add 20 feet to the circumference = 131,477,300 feet.
The new diameter is 418,505,021 feet.
If you are under 6 feet tall you could walk under it.
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I don't think you could fit under it. Just because the circumference is 6 feet more, spread out over that distance its probably less than an inch at any particular point.
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(07122019, 10:55 AM)Cooler Wrote: The circumference of the earth is 24,901 miles = 131,477,280 feet.
The diameter of the earth would be then 418,505,015 feet.
Add 20 feet to the circumference = 131,477,300 feet.
The new diameter is 418,505,021 feet.
If you are under 6 feet tall you could walk under it.
Close but not quite. Simpler method is that if you add 20' to the circumference you gain 20/ pi to the diameter. where pi is about 355/113 or 3.1416. That's 6.4', so the radius goes up half that or 3.2'. If your child is 3' tall, he/she could walk underneath the string all the way around the globe.
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(07122019, 10:57 AM)Large Wooden Badger Wrote: I don't think you could fit under it. Just because the circumference is 6 feet more, spread out over that distance its probably less than an inch at any particular point.
I didn't do the math. I relied on a circumference/diameter calculator online.
The diameter grew by 6 feet, not the circumference.
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Yes you can! Here's the proof. from 4th grade math you'll remember that:
C= 2 (pi)r
Now, the C will increase by 20 ft, correct? That'll cause the r to increase by (x), right? So, let's write that down:
C +20 = 2* pi(r+x)
Factor it out and you get:
C +20 = 2*pi+r +2*pi*x
but from above C = 2*pi*r, correct? So I'll just substitute C on the LH side of the equation for this and you get:
2*pi*r +20 = 2*pi*r + 2*pi*x
now let's drop the 2+pi*r from both sides of the equation and you're left with:
20 = 2*pi*x, right? move the 2 to the other side by dividing and you get:
10 = pi*x Let's call pi = 3.141 so dividing 10 by that and you get approx 3.18 ft, more than enough room for someone to crawl under
As a side note, since the r factors out, it doesn't matte the size of your circle (i.e. you could tie a string around the universe (assuming it is round)) and you'd get the same results.
Pretty slick, eh?
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(07122019, 11:14 AM)Edwin Hackleman Wrote: Close but not quite. Simpler method is that if you add 20' to the circumference you gain 20/pi to the diameter. where pi is about 355/113 or 3.1416. That's 6.4', so the radius goes up half that or 3.2'. If your child is 3' tall, he/she could walk underneath the string all the way around the globe.
I figured to pull up the string in one place for my needs only.
The question was could a person crawl under it (which implied one person at one location). I was not worried about children in Australia walking under the string, only if I could walk under the string.
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(07122019, 10:55 AM)Cooler Wrote: The circumference of the earth is 24,901 miles = 131,477,280 feet.
The diameter of the earth would be then 418,505,015 feet.
Add 20 feet to the circumference = 131,477,300 feet.
The new diameter is 418,505,021 feet.
If you are under 6 feet tall you could walk under it.
The math is correct.
If the rope is equally suspended above the earth, it would be half the 6 feet or 3 feet. So you'd need to do the limbo to walk under it  or be very short in stature.
It would be easier to step over the rope than to walk under it. Just let the extra 20 feet fall to to the surface.
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07122019, 04:45 PM
(This post was last modified: 07122019, 09:55 PM by FrankAtl.)
Re: 'nother math problem by Dumb_Polack (Let's say the earth ...)
(07122019, 10:55 AM)Cooler Wrote: The circumference of the earth is 24,901 miles = 131,477,280 feet.
The diameter of the earth would be then 418,505,015 feet.
Add 20 feet to the circumference = 131,477,300 feet.
The new diameter is 418,505,021 feet.
If you are under 6 feet tall you could walk under it.
Hmmm...don't think I've ever seen a circle with the diameter larger than the circumference.
