Up: The Shape of Space: Dimensions - Exploring Flatland

Dimensions - Exploring Flatland

hints

Question:

Can a flatlander tie a knot?

Hint:

Place a piece of string between two pieces of paper. (Clear paper or transparencies work well.) Your challenge is to pass one string over the other while keeping the string in the "plane" between the two pieces of paper. Pressing the pieces of paper tightly together may help you to imagine the restrictions of the plane.

Question:

How would Flatlanders carry things?

Hint:

For a bag: How would you make a bag two dimensional? Try trapping some paper cut-outs in the plane a desk or table. In Flatland these pieces could not fall off the table. They could only move in left-right and north-south directions on the table.
For a handle: Think about how toy trains connect. How would this translate into two dimensions?

Question:

What would a fence look like in Flatland? What about a picket fence? (The picket fence should keep out Flatlanders but allow them to see the flowers inside.)

Hint:

If you have an idea of how to make a 2-D bag, then think about how a fence is like a bag. Should your fence be closed or open? Decide and explain your decision.
If you don't know how to make a bag, then try to trap paper cut-outs on a table. Remember that in Flatland, your cut-outs would not fall off the table--they would always stay in the plane.
To make a picket fence or bag you can see through, think about what sort of 3-D objects you can see through. A mesh bag, for example, has cloth "missing" from the bag. How is it held together? With pieces of string connected to one another. A picket fence in Flatland would really be made out of lots of individual pickets. These pickets--unlike most fences you've probably seen--wouldn't need to be connected to one another.

Question:

How would Flatlanders play baseball? volleyball? tennis? What would be the difference between these three games?

Hint:

Draw a 3-D game from the side. Flatlanders would play with a 2-D object, just like the Flatlander's sun in the Shape of Space video.

Question:

How would a Flatlander eat/digest food?

Hint:

Flatlanders' bodies would fall into two parts if they were cut by a digestive tract. Two dimensional fasteners which are analogous to magnets, zippers, buttons, or velcro might help your Flatlanders stay whole. The fastening techniques used for handles might also be useful. Try modeling a Flatlander's digestive tract out of paper.

Up: The Shape of Space: Dimensions - Exploring Flatland

The Geometry Center Home Page