Geometry/Origami

Notice: Incomplete

Geometry can be performed using reflections across lines (like in folding paper).

Axioms

1. A unique line can be formed between any two distinct points.
2. Given any pair of distinct points, a unique line can be formed reflecting one onto the other (perpendicular bisector)
3. Given any pair of distinct lines, a pair of perpendicular lines can be formed reflecting one onto the other (angle bisector)
4. Given a point and a line, there is a unique line perpendicular to the first line passing through the point.
5. Given two points and a line, if the second point is as far from the first as the line is, there's a unique line passing through the first point, reflecting the second point onto the first line. If the second point further from the first than the line is, there's a pair of lines passing through the first point, reflecting the second point onto the first line. If the second point is closer to the first than the line is, no reflection line exists.
6. j
7. k

Notes

In three dimensions, reflection lines become reflection planes. On a sphere or saddle shape, some axioms may not hold.