Room 3 of 11 · Ground floor
Same Dots, New Loops
“Can the same pieces make a different pattern?”
Lamp waiting
▶ Hear the storyteller tell this roomLook
Four beads sit on a board. A basket of strings waits beside them.
Try
Tie strings between beads. Then untie them and tie a new way.
Notice
Try the experiment first. Then this will fill in.
What keeps this room working?
The connections count as part of the structure, not only the pieces.
What would break this room?
If knowing all the pieces automatically told you the whole arrangement.
Child-sized version
“Same pieces can make a different pattern.”
Try to break the room
For grown-upsShow me the math
A structure is a set together with its relations. Two arrangements of the same four points can be genuinely different shapes.
- Graph
- Points plus the lines between them. Same points, different lines, different graph.
- Structure
- A set together with the relations on it.
- Non-isomorphic
- Two arrangements of the same pieces that cannot be matched up.