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outrun
Topic Author
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Joined: April 29th, 2016, 1:40 pm

### Circle through a square hole

I have a piece of paper with a unit 1x1 square cut out in the middle. What's the largest circular disk I can push through the hole?

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Re: Circle through a square hole

The diameter depends on what we can do to the circle:

1. Rigid: sqrt(2) with the circle slotted diagonally

2. Bend of radius 1: pi/2 with the circle gently bent to fit along two sides of the square.

3. Bend of minimum radius r < 1/2: (1/2+r)*pi/t where t is the thickness and the circle is rolled into a spiral*

4. Bend of radius 0: 2/t where t is the thickness and the circle is rolled into a square spiral.

*Note: #3 is wrong there's another radius r solution but I need to think about it.

Paul
Posts: 10418
Joined: July 20th, 2001, 3:28 pm

### Re: Circle through a square hole

Can you bend both the paper and the disk? 'Disk' sound less bendy than 'paper'!

outrun
Topic Author
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: Circle through a square hole

Can you bend both the paper and the disk? 'Disk' sound less bendy than 'paper'!
The disk is a cracker with Roquefort

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Re: Circle through a square hole

Can you bend both the paper and the disk? 'Disk' sound less bendy than 'paper'!
Excellent point!

If you pull on a piece of paper diagonally at corners 1 & 3 of a square hole, the paper will wrinkle at corners 2 & 4 to create a slot that is 2 units long for the passage of the gluten free cracker.

outrun
Topic Author
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: Circle through a square hole

Very good both of you!

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Re: Circle through a square hole

I have a piece of paper with a unit 1x1 square cut out in the middle. What's the largest circular disk I can push through the hole?
Push a SATA cable though the hole and attach it to this:

Collector
Posts: 4557
Joined: August 21st, 2001, 12:37 pm

### Re: Circle through a square hole

Can you bend both the paper and the disk? 'Disk' sound less bendy than 'paper'!
Excellent point!

If you pull on a piece of paper diagonally at corners 1 & 3 of a square hole, the paper will wrinkle at corners 2 & 4 to create a slot that is 2 units long for the passage of the gluten free cracker.
I prefer high gluten crackers, gluten protein gives high elasticity, so one can just squeeze the crackers through the hole without folding the paper. I guess the new trick of folding the paper came into play after the the popularity of gluten free crackers?

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