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

[mathmaniac1]

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]

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

 

[mathmaniac1]

See attachment

Are you sure there is an elephant hole in it?I know a different method...

 

[MarkFL]

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?

 

[mathmaniac1]

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]

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

 

[mathmaniac1]

But earboth's method is not clear to me...I will look practicing...

 

[MarkFL]

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

 

[mathmaniac1]

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]

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]

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

 

[alyafey22]

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 ..

 

[I like Serena]

Now for the follow-up question: how do you fit an elephant through a cube?

Here you go:

Spoiler

https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcSuRh4lp-IxqEaxSfuzWb5BqZk1-NT1eoJOOoq9jYwgROaZ22aMPQ

 

[caffeinemachine]

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.

 

[mathmaniac1]

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...

 

[mathmaniac1]

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]

I think my method produces a larger hole than yours...;)

What is you method?

 

[mathmaniac1]

Not actually mine,the e-book's to be precise...

Here it is:

View attachment 710
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...

 

[mathmaniac1]

I was wondering what is the biggest area we can produce with perimeter?What would it look like?

 

[MarkFL]

As a circular perimeter encloses the most area per unit perimeter, I would say it would be circular.