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Correcting typos
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Colin D Wright
Colin D Wright
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Edited - some comments may now be out-of-date.

I thought I had a complete set of solutions to this:

Cut a square into indenticalidentical pieces so
that they all touch the center point.

It became clear after some discussions that I was very, very wrong.

There are infinite familesfamilies of solutions, and a sporadic. So I ahvehave two questions:

  1. What do you think is a complete set of solutions?

  2. What techniques and approaches can I use to prove that the ones I have are all there are?

Hope that's clearer. Thanks.

Edited - some comments may now be out-of-date.

I thought I had a complete set of solutions to this:

Cut a square into indentical pieces so
that they all touch the center point.

It became clear after some discussions that I was very, very wrong.

There are infinite familes of solutions, and a sporadic. So I ahve two questions:

  1. What do you think is a complete set of solutions?

  2. What techniques and approaches can I use to prove that the ones I have are all there are?

Hope that's clearer. Thanks.

Edited - some comments may now be out-of-date.

I thought I had a complete set of solutions to this:

Cut a square into identical pieces so
that they all touch the center point.

It became clear after some discussions that I was very, very wrong.

There are infinite families of solutions, and a sporadic. So I have two questions:

  1. What do you think is a complete set of solutions?

  2. What techniques and approaches can I use to prove that the ones I have are all there are?

Hope that's clearer. Thanks.

Clarified and re-phrased the question
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Colin D Wright
Colin D Wright
  • 119
  • 1
  • 6

There's a math problem I've been working on forEdited - some time that looks like it's finally been solvedcomments may now be out-of-date. To explain it to people 

I usually start withthought I had a warm-upcomplete set of solutions to this:

Cut a square into indentical pieces so
that they all touch the center point.

As I say, this is a warm up. It's fairly easy to do, and serves to introduce the ideas involved. So we doIt became clear after some discussions that I was very, and we move onvery wrong.

Recently, though, I wondered how many solutions thereThere are to the above problem. I rapidly came up with a small numberinfinite familes of solutions, and was reasonably content.

I was wronga sporadic. I now have what I think is the complete answer, but I was wondering if (a) I might have missed more, and (b) how can So I prove that my current answer is complete.ahve two questions:

I'd be interested in the musings and approaches taken here.

  1. What do you think is a complete set of solutions?

  2. What techniques and approaches can I use to prove that the ones I have are all there are?

Hope that's clearer. Thanks.

There's a math problem I've been working on for some time that looks like it's finally been solved. To explain it to people I usually start with a warm-up:

Cut a square into indentical pieces so
that they all touch the center point.

As I say, this is a warm up. It's fairly easy to do, and serves to introduce the ideas involved. So we do that, and we move on.

Recently, though, I wondered how many solutions there are to the above problem. I rapidly came up with a small number, and was reasonably content.

I was wrong. I now have what I think is the complete answer, but I was wondering if (a) I might have missed more, and (b) how can I prove that my current answer is complete.

I'd be interested in the musings and approaches taken here.

Thanks.

Edited - some comments may now be out-of-date. 

I thought I had a complete set of solutions to this:

Cut a square into indentical pieces so
that they all touch the center point.

It became clear after some discussions that I was very, very wrong.

There are infinite familes of solutions, and a sporadic. So I ahve two questions:

  1. What do you think is a complete set of solutions?

  2. What techniques and approaches can I use to prove that the ones I have are all there are?

Hope that's clearer. Thanks.

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Colin D Wright
Colin D Wright
  • 119
  • 1
  • 6

Dissecting a square

There's a math problem I've been working on for some time that looks like it's finally been solved. To explain it to people I usually start with a warm-up:

Cut a square into indentical pieces so
that they all touch the center point.

As I say, this is a warm up. It's fairly easy to do, and serves to introduce the ideas involved. So we do that, and we move on.

Recently, though, I wondered how many solutions there are to the above problem. I rapidly came up with a small number, and was reasonably content.

I was wrong. I now have what I think is the complete answer, but I was wondering if (a) I might have missed more, and (b) how can I prove that my current answer is complete.

I'd be interested in the musings and approaches taken here.

Thanks.