Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2007-10-10 22:50:35

Anthony.R.Brown
Banned
Registered: 2006-11-16
Posts: 516

### Cut A Hole! In A Sheet Of Paper Problem!...

Here is an Interesting Problem I have just come up with which Answers another Problem in a New way!.

How large is it possible to Cut a Hole in a Sheet of Paper!...

For the above because there are many different possible sizes for a Sheet of Paper! it is best to use Percentage regarding Area!...

However Large it is possible to Cut a Hole in a Sheet of Paper! there must always be some Paper left around the Outside of the Hole! for the Hole to be classed as a Hole!

For the above Reason the Largest Hole possible must be < 100 Percent!

So starting with 99.1 Percent for a Large Hole Cut in a Sheet of Paper!...

We can then move on and make the Hole Bigger let´s say 99.9 and then again 99.99 So why not really move on and make the Hole Size the Largest Hole Possible!?

You may then say there is no Largest possible Hole!? for which I would then Reply that is True! But we can Accept the unknown by Knowing that however Large the Hole is! it will and must always be < 100 Percent!...

By Anthony.R.Brown 11/10/07.

--------------------------------------------------------------------------------------------------------------------------------------------------------
Genius! is only accepted by the Masses when the Masses agree with the Genius!  ( 1 / 0.9 ) x ( 0.9 ) = 0.999...

Last edited by Anthony.R.Brown (2007-10-10 22:51:14)

Offline

## #2 2007-10-12 06:51:35

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

I am dumb;  can you have a 1-dimensional rectangle of paper for the frame with zero area?

igloo myrtilles fourmis

Offline

## #3 2007-10-12 23:47:23

Anthony.R.Brown
Banned
Registered: 2006-11-16
Posts: 516

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Quote:" I am dumb;  can you have a 1-dimensional rectangle of paper for the frame with zero area? "

A.R.B

I am not sure! please explain!...

Offline

## #4 2007-10-12 23:50:17

Anthony.R.Brown
Banned
Registered: 2006-11-16
Posts: 516

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Just in case the Penny has not dropped for everyone!

The Hole could Represent Infinite/Recurring 0.9

And the Paper could Represent the Infinite/Recurring 0.1 Difference!...

A.R.B

Offline

## #5 2007-10-14 10:52:30

Maelwys
Member
Registered: 2007-02-02
Posts: 161

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Hmm... so what does it mean that I can make a hole with an area LARGER than the starting area of the piece of paper? By careful cutting, you can actually make it so the paper unfolds and you can start with an 8.5"x11" piece of paper, and cut a hole in it that's 3'x5' (or bigger, depending on how good you are with scissors).

Offline

## #6 2007-10-14 11:54:41

MathsIsFun
Registered: 2005-01-21
Posts: 7,684

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Maelwys ... that is genius.

(I tried to resist commenting ... but I couldn't!)

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Offline

## #7 2007-10-15 03:58:59

Anthony.R.Brown
Banned
Registered: 2006-11-16
Posts: 516

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Quote:" Hmm... so what does it mean that I can make a hole with an area LARGER than the starting area of the piece of paper? By careful cutting, you can actually make it so the paper unfolds and you can start with an 8.5"x11" piece of paper, and cut a hole in it that's 3'x5' (or bigger, depending on how good you are with scissors). "

A.R.B

Almost Funny!...Don't give up your day job and try to become a Comedian! Stick to Math! but that´s out of your League as well!...

Offline

## #8 2007-10-15 18:29:32

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Can you have something so thin is has no area along each straight edge?
In the mind, but not in practice.
If it is just algebra-line thin, then it isn't really there, it just is a reference line.

igloo myrtilles fourmis

Offline

## #9 2007-10-15 21:46:26

Anthony.R.Brown
Banned
Registered: 2006-11-16
Posts: 516

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Quote:" Can you have something so thin is has no area along each straight edge?
In the mind, but not in practice.
If it is just algebra-line thin, then it isn't really there, it just is a reference line. "

A.R.B

For the Quote above! what ever you are on! I want some!...........................................................................................................

Offline

## #10 2007-10-15 23:31:27

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

What A.R.B is still not realizing is that

IS NOT THE SAME AS

The hole in the paper belongs to the latter category, not the first!

It is people like ARB that is making me lose faith in Darwins theory, really. If millions of years of evolution still has not eliminated such ignorance, arrogance and stupidity from the gene pool, then somthing must be very wrong indeed.

Offline

## #11 2007-10-16 04:21:05

Anthony.R.Brown
Banned
Registered: 2006-11-16
Posts: 516

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

To JaneFairfax

Is your Photo the Result of Darwins theory! or did the gene pool go wrong some where!...

As far as your Quote: above goes! you may not realise it! but there are many people who still think you can take any two Numbers that have the same Values! Divide them! and then somehow one or Both of them then equal 1 ?

A.R.B

Offline

## #12 2007-10-16 05:05:24

Identity
Member
Registered: 2007-04-18
Posts: 934

Offline

## #13 2007-10-16 05:27:18

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Anthony.R.Brown wrote:

To JaneFairfax

Is your Photo the Result of Darwins theory! or did the gene pool go wrong some where!...

The photo is not me. Its the actress Olivia Williams playing the role of Jane Fairfax in the 1996 TV adaptation of Emma. You can insult me all you like, but please dont insult Ms Williams.

Last edited by JaneFairfax (2007-10-16 05:28:25)

Offline

## #14 2007-10-16 05:49:17

Anthony.R.Brown
Banned
Registered: 2006-11-16
Posts: 516

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

To JaneFairfax

Quote:" You can insult me all you like, but please dont insult Ms Williams. "

A.R.B

I would never do that! they have much to Good a Racing Car Team!...

Offline

## #15 2007-10-18 21:16:54

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

If you take an algebra-thin line for the frame and make it thicker by any normal constant not near infinity, but closer to zero, then the frame's hole will be the same as the area of the paper since the frame itself has no area.
Zero width of a frame is just a reference to a rectangle that doesn't have any particles in its makeup.  Waves?  I don't know.  It's just an idea of a rectangular frame, not a real paper one.

igloo myrtilles fourmis

Offline

## #16 2007-10-18 22:05:08

Anthony.R.Brown
Banned
Registered: 2006-11-16
Posts: 516

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

To John E. Franklin

Quote:" If you take an algebra-thin line for the frame and make it thicker by any normal constant not near infinity, but closer to zero, then the frame's hole will be the same as the area of the paper since the frame itself has no area.
Zero width of a frame is just a reference to a rectangle that doesn't have any particles in its makeup.  Waves?  I don't know.  It's just an idea of a rectangular frame, not a real paper one. "

A.R.B

I think Mushrooms would have less of an Effect on your Mind!...

Offline

## #17 2007-10-19 01:17:16

JohnnyReinB
Member
Registered: 2007-10-08
Posts: 453

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

I think, for any sized paper, the largest hole you can cut (without doing the tricks of turning it into a hole with a larger area than the original) is one with one with an edges thickness of an  atom/molecule's diameter. The percentage differs from paper to paper, so I don't know the percentage.

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

Offline

## #18 2007-10-19 02:45:43

Anthony.R.Brown
Banned
Registered: 2006-11-16
Posts: 516

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Quote: " I think, for any sized paper, the largest hole you can cut (without doing the tricks of turning it into a hole with a larger area than the original) is one with one with an edges thickness of an  atom/molecule's diameter. The percentage differs from paper to paper, so I don't know the percentage. "

A.R.B

An atom/molecule's diameter! is Enormous! in the World of Infinity!.............................................................................................

Offline

## #19 2007-10-20 18:11:48

JohnnyReinB
Member
Registered: 2007-10-08
Posts: 453

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

yeah, but if you destroy the atoms/molecules when cutting the paper, the paper would break down, and it would no longer be paper with a hole in it! It would just be a bunch of subatomic particles.

No longer paper

Last edited by JohnnyReinB (2007-10-20 18:12:33)

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

Offline

## #20 2007-10-20 23:02:19

Anthony.R.Brown
Banned
Registered: 2006-11-16
Posts: 516

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Quote " yeah, but if you destroy the atoms/molecules when cutting the paper, the paper would break down, and it would no longer be paper with a hole in it! It would just be a bunch of subatomic particles.

No longer paper "

A.R.B

Paper! as you know it!.. is not the Paper Known in the Enormous! World of Infinity!...

Offline

## #21 2007-11-03 20:08:43

JohnnyReinB
Member
Registered: 2007-10-08
Posts: 453

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

OK, then what is your

Paper Known in the Enormous! World of Infinity!...

Last edited by JohnnyReinB (2007-11-10 20:04:15)

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

Offline

## #22 2007-11-04 01:03:00

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

[ As a sidenote, you may have to wait quite a while for him to answer you, as he is temporarily banned. ]

Offline

## #23 2007-11-04 23:08:43

JohnnyReinB
Member
Registered: 2007-10-08
Posts: 453

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Yeah, I just saw that.I should really pay more attention to the status of a member, before posting a question to them. Thanks, Dev.

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

Offline

## #24 2007-11-05 04:24:09

Sekky
Member
Registered: 2007-01-12
Posts: 181

Yay he's banned

Offline

## #25 2007-11-06 22:32:50

JohnnyReinB
Member
Registered: 2007-10-08
Posts: 453

### Re: Cut A Hole! In A Sheet Of Paper Problem!...

Maybe we should celebrate?

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

Offline