- Definition: the counterpart of any body is its mirror image/reflection – the 'perpendicular projection' of each point through a plane/line an equal distance on either side.
- Definition: two bodies are incongruent if they cannot be (rigidly) moved into the same region of space – two plane figures are incongruent if they cannot be moved into the same region of the plane. E.g., a cube and a sphere are incongruent.
- What then does it mean for things to be 'incongruent counterparts'? What are some examples?
- Here's one: screws.
- Screws are a nice example; partly because they model natural phenomena that depend on handedness: e.g., some sugar molecules (one 'isomer' digestable, one not); the weak nuclear force (only electons spinning in one direction with respect to motion feel it).
The two screws are
mirror
images, and cannot be superposed – the threads turn in opposite
directions
towards the tip of the screws.
- What makes something handed (or chiral) – i.e., the kind of thing whose counterpart is incongruent to it?
- Definition: A plane is a plane of symmetry if the two sides it creates are mirror images of each other in the plane (similarly for lines of symmetry).
- Definition: suppose a body has no plane of (mirror) symmetry, or a figure has no line of symmetry – then it is an enantiomorph.
- Fact: any enantiomorph and its reflection are
incongruent
counterparts. E.g., a hands and its counterpart.
