In truth, the actual math problem has nothing to do with pizza.

Warmup:

Dissect a square into congruent pieces that all touch the center point. This is a classical dissection, and yes, you can think of it as slicing up a square with scissors. In how many ways can you do this? Hint: probably more than you think. How many pieces can you use? There are probably fewer options than you think.

Next: Dissect a square into congruent pieces that do not all touch the center point. Again, i how many ways can you do this? The answer might be smaller than you think.

Next: Dissect a square so that the center point is in the interior of a piece. Again, not hard. Again, in how many ways can you do this?

Moving on - replace “square” with “triangle”. Then “pentagon”. All three options are still possible, and again counting families and characterising solutions is an interesting exercise.

And now we’re ready for the real problem.

Dissect a circle into congruent pieces that do not all touch the center point. I know of two infinite families, one consisting of infinitely many uncountable members. That’s a lot.

But this is an open question:

Can you dissect a circle into congruent pieces such that the center point is in the interior of one of the pieces?

This isn’t especially new - I wrote[0][1] about it 5 years ago, and worked on it with Joel (one of the authors).

In truth, the actual math problem has nothing to do with pizza.

That’s why I get really annoyed when I’m getting maths news from general sites. I don’t know where else to get the news, though. It’s been a while since I’ve been in academia, so where is the news sites for mathematics people?

I don’t know of any single source - these days it seems unlikely that there can be. However, there are several sources that talk about math in general, and they usually pick up on major stories curiosities such as this. Included are:

I have trouble cutting pizza into traditional 6 or 8 slices. How the heck would anyone actually do this consistently, without a more specialized tool? Maybe I’m just horrible?

Cute but clearly shows a flagrant disregard for the importance of crust.

Actually, no.

That second one is pretty genius.

The shapes are equal, but only half of them have crust, and a lot of it.

It allows for people who like or dislike crust to enjoy the pizza equally.

In truth, the actual math problem has nothing to do with pizza.

Warmup:

Dissect a square into congruent pieces that all touch the center point. This is a classical dissection, and yes, you can think of it as slicing up a square with scissors. In how many ways can you do this? Hint: probably more than you think. How many pieces can you use? There are probably fewer options than you think.

Next: Dissect a square into congruent pieces that do not

alltouch the center point. Again, i how many ways can you do this? The answer might besmallerthan you think.Next: Dissect a square so that the center point is in the interior of a piece. Again, not hard. Again, in how many ways can you do this?

Moving on - replace “square” with “triangle”. Then “pentagon”. All three options are still possible, and again counting families and characterising solutions is an interesting exercise.

And now we’re ready for the real problem.

Dissect a circle into congruent pieces that do not all touch the center point. I know of two infinite families, one consisting of infinitely many uncountable members. That’s a lot.

But this is an open question:

Can you dissect a circle into congruent pieces such that the center point is in the interior of one of the pieces?

This isn’t especially new - I wrote[0][1] about it 5 years ago, and worked on it with Joel (one of the authors).

[0] http://www.solipsys.co.uk/new/DissectingASquare.html?L_20160108

[1] https://lobste.rs/s/1rmdpy/dissecting_a_square_-_the_prelude_to_the_pizza_slicing_paper

That’s why I get really annoyed when I’m getting maths news from general sites. I don’t know where else to get the news, though. It’s been a while since I’ve been in academia, so where is the news sites for mathematics people?

I don’t know of any single source - these days it seems unlikely that there can be. However, there are several sources that talk about math in general, and they usually pick up on major stories curiosities such as this. Included are:

They, in turn, list others. I write about this sort of stuff, but I’m not qualified to write about real advances in serious math.

In short, I don’t think there is a “math news” site that writes things “properly” without trying to make it “relevant” for ordinary people.

Excellent question. Upvoted in hope of an answer.

I have trouble cutting pizza into traditional 6 or 8 slices. How the heck would anyone actually do this consistently, without a more specialized tool? Maybe I’m just horrible?

I’m sure you could hook a pizza up to a old plotter and get this.

Add a laser cutter, and you got yourself a pizza slicing machine!

Math and pizza. Better together.