Did you ever wonder what life would be like if we were living on a giant donut instead of a giant sphere? Would we be able to do neat, new things? If Columbus set off from Spain in search of the New World on this new donut-shaped planet, where would he have ended up? In this activity you will find out at least one neat trick that can’t be done on our spherical earth, but could be done if we lived on a giant bagel.
Student Guide
Ball versus Donut
Experimenting with line problem solving
Is it possible to connect three “houses” to three “utilities” without crossing the lines?
This resource was originally published in PhysicsQuest 2014: Quantum.
Is it possible to connect three “houses” to three “utilities” without crossing the lines?
- Playdough
- Six toothpicks
- Ribbon
Intro
Before the experiment
Pick three objects in the room. Look at their shapes, how they are put together, what is the same and what is different? Draw them.
What would it be like for an ant that was walking on those shapes?
How many holes and loops does each of your shapes have?
Think of a donut and a coffee cup with a handle. What is the same and what is different about them?
Setting up
In this activity you are going to see if it is possible to connect three utility stations to three different houses without crossing the utility lines. Toothpicks will play the part of the houses and utility stations and ribbons will act like the lines.
Take each piece of the colored ribbons and cut them into three pieces. You should now have nine pieces of ribbon, three of each color.
Tie one end of each of the three red ribbons around a toothpick. This will be your “gas” utility station and lines. Do the same for green (electric) and blue (water).
During the experiment
Collecting data
Take the playdough and roll it into a ball. This is going to represent our current Earth.
Take the three toothpicks representing houses and place them anywhere on the ball.
Take the three “utility stations” with their “utility lines” attached and put them anywhere on the ball.
Connect each “house” to each “utility." Each house should have a red ribbon, green ribbon, and blue ribbon attached to it.
Chances are good that some of the “utility lines” are crossed, such as a water line is running over an electricity line or a gas line is running over a water line.
Try to do it without crossing the “utility lines."
If you couldn’t, try moving the “houses” and “utility stations” and try again.
Do this for at least three different locations. Draw all of your attempts.
What happened? Were you able to connect all the “houses” without crossing the lines?
Shape the playdough into a donut shape.
Repeat steps 2-6 from activity one. Were you able to connect all the “utility lines” without crossing?
What was it about the donut that allowed you to do that?
What if you had four houses instead of three? What about four utilities?
Analyzing data
What other “world shapes” can you think of that would let you connect everything without crossing lines? Try them! The best part about your playdough is that you can make a world in any shape you want.
Conclusion
What do all these worlds have in common?
Which statement is true?
- Houses and utilities could be connected without crossing lines on:
- A sphere but not a donut
- A donut but not a sphere
- A donut and a sphere
- Neither a donut nor a sphere
- Houses and utilities could be connected without crossing lines on: