Monday Math Madness #32: The Bigger Plot of Land
11 May 2009 Daniel Sutoyo 12 comments 7,312 views
“He who would trade liberty for security, deserves neither liberty nor security.” –Benjamin Franklin
Image and Quote via Digg
The Question
Unfortunately our friends Alice and Bob have unknowingly traded their liberty away and are being fenced inside a rectangular pieces of land on the planet Earth, which is assumed to be a perfect sphere of radius 3950 miles.
Alice and Bob are granted one last choice: To decide which plot of land they want to be fenced in.
Both plots of land are bounded by four fences.
Land 1: Two fences run in an exact north-south direction and the other two run in an exact east–west direction. The north-south fences are exactly 10 miles long and east–west fences are exactly 20 miles long.
Land 2: Similar to Land 1, but the north–south fences are 20 miles long and the east–west fences are 10 miles long.
Can you help Alice and Bob to figure out which plot of land has the greater area?
Note:
- Alice and Bob can choose where to place the fences.
The Prize
The winner will receive a 10 dollar gift certificate to Amazon.com!
The Rules
- Email your answers to mondaymathmadness at gmail dot com.
- Inelgible for any one person to win more than once per year. But you should still submit your answer!
- Answer must be explained. You must show your work! We will accept answers in the form of a MATLAB script as well. We will be the final judge on whether an answer was properly explained or not.
- The deadline to submit answers is May 18th 2009, Monday 11:59 PM Pacific Standard Time
- The winners will be chosen randomly from all the submittals using a random number generator.
- The winner will be announced at 9:00 AM PST May 22nd, 2009.
- Comments for this post should only be used to clarify the problem. Please do not discuss ANY potential solutions.
- Please spread the word about our contest by stumbling this webpage!
12 Responses to “Monday Math Madness #32: The Bigger Plot of Land”
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Include MATLAB code in your comment by doing the following:
<pre lang="MATLAB">
%insert code here
</pre>
Can Alice and Bob choose where on the Earth their four fences are placed, as long as they bound a rectangle?
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The correct Ben quote is:
He who would trade liberty for security, deserves neither liberty nor security.”
“some temporary” is not part of the original quote. Otherwise the quote would suggest that it could be worth trading liberty for (permanent) security, which as you know is something that does not exists.
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I’m not really sure I understand what the problem is, or at least what the challenge is supposed to be. If Earth is spherical then wouldn’t North-South and East-West be irrelevant?
@ Ron: let’s say they can choose where to place the fence
@ Reader: Thanks for the info. I have made the changes.
@ clam: If you think the area is the same, that can be an acceptable submission.
does “exact north-south” mean the fence follows longitude lines?
[...] the latest Monday Math Madness by Daniel at BlinkDagger and win a [...]
[...] The winner for this edition of MMM is Bhaskar Bhattacharya. Although the problem seemed quite simple, it was in fact a pretty complex problem! As you can already probably guess, the answer was NOT that the two plots of land are equal. You can view the problem statement here. [...]
[...] was the topic of Monday Math Madness #32 at blinkdagger, where you can see my solution to a question about the areas of such [...]
Я более 2х лет регулярно занимаюсь этим вопросом и нахожу ваши доводы немного поверхностными
#5 The winners will be chosen randomly from all the submittals using a random number generator.
Don’t you mean the winners will be chosen randomly from all the CORRECT submittals using a random number generator. Otherwise, you are just running a lottery.