# Cutting an elephant-sized hole in a sheet of paper

#### mathmaniac

##### Well-known member
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
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

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#### mathmaniac

##### Well-known member
See attachment
Are you sure there is an elephant hole in it?I know a different method...

#### MarkFL

Staff member
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

##### Well-known member
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

Staff member
I believe you are thinking of the same thing suggested above.

#### mathmaniac

##### Well-known member
But earboth's method is not clear to me...I will look practicing...

#### MarkFL

Staff member
The lines represent where cuts are to be made, and the result is a long closed loop of paper.

#### mathmaniac

##### Well-known member
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....

#### MarkFL

Staff member
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.

#### earboth

##### Active member
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 ...

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#### ZaidAlyafey

##### Well-known member
MHB Math Helper
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
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
Unfortunately there isn't an elephant at hand but I hope a camel will do ...
Woah! That's brilliant.

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

#### mathmaniac

##### Well-known member
Now for the follow-up question: how do you fit an elephant through a cube?
The idea is to convert volume into area....

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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....

#### mathmaniac

##### Well-known member
Unfortunately there isn't an elephant at hand but I hope a camel will do ...
I think my method produces a larger hole than yours...

#### MarkFL

Staff member
I think my method produces a larger hole than yours...
What is you method?

#### mathmaniac

##### Well-known member
Not actually mine,the e-book's to be precise...

Here it is:

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

##### Well-known member
I was wondering what is the biggest area we can produce with perimeter?What would it look like?