Cutting an elephant-sized hole in a sheet of paper

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    Cutting Hole Paper
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Discussion Overview

The discussion revolves around the theoretical challenge of cutting a hole in a sheet of paper large enough for an elephant to pass through. Participants explore various methods and concepts related to geometry, area, and perimeter, while engaging in playful banter about the feasibility of the task.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that by converting the area of the paper into perimeter, it may be possible to create a hole of any size.
  • Others express confusion about the methods suggested, particularly regarding earboth's approach, and seek clarification.
  • A participant suggests making specific cuts in the paper to create a long closed loop, implying this could lead to a larger hole.
  • There is a playful exchange about whether a camel could substitute for an elephant in this theoretical scenario.
  • One participant mentions a follow-up question regarding fitting an elephant through a cube, indicating a shift in the challenge's scope.
  • Another participant notes that a circular perimeter would enclose the most area per unit perimeter, suggesting a geometric consideration in the discussion.

Areas of Agreement / Disagreement

Participants express a range of ideas and methods, with no clear consensus on the best approach to the challenge. Confusion and differing interpretations of proposed methods indicate ongoing debate.

Contextual Notes

Some participants mention the need for mathematical proof regarding the feasibility of creating a hole of any size, highlighting the unresolved nature of the claims made. The discussion also touches on the limitations of the physical properties of paper and the assumptions made in the theoretical context.

Who May Find This Useful

This discussion may be of interest to those exploring mathematical concepts related to geometry, area, and perimeter, as well as individuals intrigued by theoretical challenges and playful problem-solving in a mathematical context.

mathmaniac1
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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...?
 
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mathmaniac said:
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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earboth said:
See attachment
Are you sure there is an elephant hole in it?I know a different method...
 
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?
 
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?
 
I believe you are thinking of the same thing suggested above.
 
But earboth's method is not clear to me...I will look practicing...
 
The lines represent where cuts are to be made, and the result is a long closed loop of paper.
 
MarkFL said:
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)
 
  • #10
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)
 
  • #11
mathmaniac said:
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

30aw4ee.jpg
 
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  • #12
mathmaniac said:
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 ..
 
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  • #13
Now for the follow-up question: how do you fit an elephant through a cube?

Here you go:
https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcSuRh4lp-IxqEaxSfuzWb5BqZk1-NT1eoJOOoq9jYwgROaZ22aMPQ
 
  • #14
earboth said:
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.
 
  • #15
I like Serena said:
Now for the follow-up question: how do you fit an elephant through a cube?

The idea is to convert volume into area...

- - - Updated - - -

ZaidAlyafey said:
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:
 
  • #16
earboth said:
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...;)
 
  • #17
mathmaniac said:
I think my method produces a larger hole than yours...;)

What is you method?
 
  • #18
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...
 

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  • #19
I was wondering what is the biggest area we can produce with perimeter?What would it look like?
 
  • #20
As a circular perimeter encloses the most area per unit perimeter, I would say it would be circular.
 

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