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A mathematical bagel

By David, 5 November 2013 Activity

Impress your friends by turning your bagel into a delicious, one-sided, strip of bread: a kind of Möbius strip! That means there’s more space for delicious spreads.

sharp hazard iconfood safety hazard icon
Safety: This activity uses a sharp knife, ask an adult to help. Use clean hands and equipment when handling food.

You will need

A bagel on a table. Someone is pushing a knife through the top of the bagel.

Push the knife through the top of the bagel.

  • 2 bagels
  • Serrated knife

What to do

It’s important to read all the steps in this activity before you start. It only takes one cut, but that cut is a bit tricky.

  1. Put the bagel on a chopping board. Imagine the bagel is a clock face. For the following steps, cut around the bagel clockwise.
  2. At 12 o’clock on the bagel, push the knife down through the top of the bagel.

    Someone is pushing a knife through the side of a bagel, closest to the camera.

    Push the knife through the side of the bagel, and stop when the knife reaches the hole in the middle.

  3. At 6 o’clock, on the other side of the bagel, carefully push your knife horizontally through the bread. Stop pushing when the knife reaches the hole in the middle of the bagel.
  4. Pick up the bagel and reinsert the knife into the vertical hole. Start cutting clockwise around the bagel. However, as you proceed around the bagel, tilt the knife more and more to the horizontal. Aim to be cutting horizontally when you reach the horizontal hole.
  5. When you pass half-way, keep tilting the knife. It will get more and more vertical, but the knife handle will be under the bagel, not on top. Aim to have the knife vertical when you reach the start of the cut again.
  6. You’ve just cut all the way around the bagel. How many pieces of bagel did you expect to have? How many do you have?

    A bagel from the side. Someone is cutting a curve into the bagel.

    Tilt the knife down as you cut around the bagel.

  7. To make a mathematical lunch, fill your bagel with hard-boiled egg and hyperbolic coral lettuce!
  8. If you have another bagel, try putting a full twist in your cut: poke vertical holes at 12 and 6 o’clock and horizontal holes at 3 and 9 o’clock on your bagel. Tilt the knife as you cut aiming to hit each hole. When you get half-way, take the knife out of the bottom of the bagel and stick it back in the top before continuing to cut in the same way. When you finish you should end up with two pieces linked together!

What’s happening?

A bagel cut with a spiral-like cut.

How many pieces of bagel do you have?

Although you cut the bagel, it should still be in one piece! You can check by following the edge of the bagel around. As you go around the bagel, the ‘top’ slice will become the ‘outside’ slice, then the ‘bottom’ slice, directly under where you started. The bagel is now shaped kind of like a figure 8 that’s been folded over so the two circles are on top of each other.

The secret is in the cut. Your knife traced out the path of a Möbius strip – a looped ribbon with a half twist. A Möbius strip only has one side, so its top is also its bottom. When you cut a bagel, you would typically make two new surfaces – one on the top half, and one on the bottom. A Möbius cut only makes one new surface. Both the top and bottom of your cut are part of the same face!

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