### Circle through a square hole

Posted:

**March 6th, 2018, 11:53 am**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?

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Posted: **March 6th, 2018, 11:53 am**

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?

Posted: **March 6th, 2018, 1:25 pm**

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.

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.

Posted: **March 6th, 2018, 1:34 pm**

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

Posted: **March 6th, 2018, 2:44 pm**

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

Posted: **March 6th, 2018, 4:12 pm**

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

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.

Posted: **March 6th, 2018, 5:17 pm**

Very good both of you!

Posted: **March 6th, 2018, 5:26 pm**

Push a SATA cable though the hole and attach it to this: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?

Posted: **March 11th, 2018, 12:26 pm**

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

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.