Up: The Shape of Space: Dimensions - Exploring Flatland

# Dimensions - Exploring Flatland

### Question:

Can a flatlander tie a knot?

No. Try making a knot with a piece of string without passing one over the other.You can't do it. (See also Planiverse bio section--good diagrams)

A souped-up version of this demonstration could be done with a piece of rope pressed between two pieces of plexiglass (or another clear surface. Leave the bitter ends of the rope free of the plexiglass so that you can move them. You can now move the rope in the left-right direction and topwards-bottomwardsdirection, but not out of the plane. Thus this model is a demonstration of a 3-Drope confined to two dimensions.

### Question:

How would Flatlanders carry things?

Bag: A line--whether straight or curved--forms a "wall" in 2D. Thus an open curve would function as a bag in 2D. Flatlanders could put their belongings into the bag through the open end but would need to make sure that nothing fell out of the bag through that opening.

Handle: Two lines can interlock in a C shape and its mirror image. These or similar interlocking shapes would make good handles.

### 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.)

Like a bag, a fence would be formed of a line or several lines, whether curved or straight. A picket fence could be made out of many points with spaces between them or by line segments separated by space. This fence would keep out anything larger than the distance between the points but would let Flatlanders see their garden. Flatlanders would probably prefer line segments to points: points would be very sharp and might cut Flatlanders in two.

### Question:

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

Each game would be played with some sort of 2-D disk. The object of the game would be to get the disk

### Question:

How would a Flatlander eat/digest food?