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Cutting an elephant-sized hole in a sheet of paper

mathmaniac

Active member
Mar 4, 2013
188
Challenge:

Can anyone tell me how to cut a hole in a sheet of normal Book paper the size through which even an elephant can pass...?
 

earboth

Active member
Jan 30, 2012
74
Challenge:

Can anyone tell me how to cut a hole in a sheet of normal Book paper the size through which even an elephant can pass...?
See attachment
 

Attachments

mathmaniac

Active member
Mar 4, 2013
188

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Can you see how (if we ignore the discrete nature of matter) that in theory we can make a hole in the paper as large as we wish using the suggestion of earboth?
 

mathmaniac

Active member
Mar 4, 2013
188
I didn't understand his solution.But I know how to create a hole of any size in a paper.

The idea is that we have to convert the area of the paper into perimeter....whats your idea?
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
I believe you are thinking of the same thing suggested above.
 

mathmaniac

Active member
Mar 4, 2013
188
But earboth's method is not clear to me...I will look practicing...
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
The lines represent where cuts are to be made, and the result is a long closed loop of paper.
 

mathmaniac

Active member
Mar 4, 2013
188
The lines represent where cuts are to be made, and the result is a long closed loop of paper.
Did you imagine it on your own.I can't....(Sadface)
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
I've simply had more practice with such mental manipulations. What I suggest, is taking a piece of paper and making similar cuts in it as shown above, and then see what results. (Wink)
 

earboth

Active member
Jan 30, 2012
74
Are you sure there is an elephant hole in it?I know a different method...
Unfortunately there isn't an elephant at hand but I hope a camel will do ... :D

 
Last edited by a moderator:

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667
But I know how to create a hole of any size in a paper.

The idea is that we have to convert the area of the paper into perimeter....whats your idea?
Any any size ? , prove it mathematically ..
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,901
Now for the follow-up question: how do you fit an elephant through a cube?

Here you go:
 

caffeinemachine

Well-known member
MHB Math Scholar
Mar 10, 2012
834
Unfortunately there isn't an elephant at hand but I hope a camel will do ... :D
Woah! That's brilliant.

And here I thought we'd need to cut down the elephant to get the job done.
 

mathmaniac

Active member
Mar 4, 2013
188
Now for the follow-up question: how do you fit an elephant through a cube?
The idea is to convert volume into area....

- - - Updated - - -

prove it mathematically ..
Ah,thats good.Now let us see what is the largest area we can create when the minimum width of the paper is 1cm....:confused:
 

mathmaniac

Active member
Mar 4, 2013
188
Unfortunately there isn't an elephant at hand but I hope a camel will do ... :D
I think my method produces a larger hole than yours...;)
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775

mathmaniac

Active member
Mar 4, 2013
188
Not actually mine,the e-book's to be precise...

Here it is:

untitledfff.JPG
This and many other problems I posted here as a challenge was from the book "Mathematical Circles" written by Dmitri and Fomin...
Anybody wanting it,please let me know....I will PM you...
 
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mathmaniac

Active member
Mar 4, 2013
188
I was wondering what is the biggest area we can produce with perimeter?What would it look like?
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
As a circular perimeter encloses the most area per unit perimeter, I would say it would be circular.