Puzzle
You are given one 44-meter piece of fence and 48 one-meter pieces of fence. Assume each piece is a straight and unbendable. What is the large area of (flat) land that you can enclose using these fence pieces?
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https://www.dropbox.com/s/7j7tq5qbjem8vdg/BLUESTONES.jpg
ReplyDeleteEnclosing Land by Fence Pieces
‘’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’
The wording of the problem can be understood in two different ways:
1. We are allowed to use only a part of the 44 meter rigid fence, with rest of that section still attached, but located outside the fenced area.
2. We must use the entire 44 meter fence for the enclosure.
In view of these considerations I claim the following:
In the first case a maximum area of approximately 366.7 square meters is obtained when about 30.6 meters of the of the large fence piece is used as the diameter of a halve circle.
The 48 sections are then formed into an arc, circumscribed by the circular halve circle.
In the second case the 48 one meter sections form an arc, with the 44 meter section as a base line. The enclosed area is a maximum when the arc is circular. The radius of the arc, which circumscribe the chain of the one meter sections, is about 33.5 meters
The maximum area in this case is approximately 248 square meters.
My calculations and more details can be found at the site shown on this page.
I can't find the link to the page that has your calculations. Could you please update your comment.
ReplyDeleteLarry
This is the link to the file.
ReplyDeletehttps://www.dropbox.com/s/7j7tq5qbjem8vdg/BLUESTONES.jpg