Duo Geometry
Geometric Entities in a 2-Element Framework
Duo Geometry explores configurations and transformations derived from two distinct points (2P). These dual references allow for symmetry, directionality, and perspective-based constructions that go beyond the static nature of Mono Geometry.
Only the items that are underlined have individual pages describing them.
Duo Geometry Elements
| Code | Reference | Description |
|---|---|---|
| 2P-Items | ||
| 2P-s-P1 | 2P-Midpoint | The midpoint between two points; the center of symmetry and balance. |
| 2P-s-P2 | 2P-Infinity Point | The point at infinity defined by the direction from one point to another. |
| 2P-s-2P1 | 2P-Reflection Points | Each point reflected across the other. |
| 2P-s-L1 | 2P-Connecting Line | The straight line passing through both points; defines linear relation. |
| 2P-s-L2 | 2P-Perpendicular Bisector | A line perpendicular to the connecting line, passing through the midpoint. |
| 2P-s-Tf1 | Harmonic Conjugate / | A transformation yielding a third point in perspectival relation to the original two. |
| Perspective Midpoint / | ||
| Vanishing Point | ||
| 2P-s-Tf2 | 4th Perspective Point / | A derived point completing a harmonic or perspectival set with three collinear points. |
| Perspective Reflection Point | ||
| 2P-s-Tf3 | MidReflect Transformation | A transformation centered on the midpoint, reflecting structure or symmetry. |
| (see QFG#3143) | ||
| 2P-s-iRg1 | Regular Lighthouse n-Gons | A geometric construction of n-gons, |
| derived from intersections of regularly radiating lines from two points. | ||
| 2L-Items | ||
| 2L-s-P1 | 2L-Intersection Point | The intersection point of two lines (will be an infinity point in case of parallel lines). |
| 2L-s-2L1 | 2L-Angle Bisectors | The set of two angle bisectors formed by the intersection of two lines. |
Explanation of Notation
- 2P = Two Points
- 2L = Two Lines
- s = special
- P1, P2, 2P1 = Derived points from the original pair
- L1, L2 = Lines constructed from or between the points
- Tf1–Tf3 = Transformations involving symmetry, perspective, or reflection
- iRg1 = Indexed Regular Geometry (e.g., n-gons or rotational structures)
This notation system enables compact representation of relational geometry, emphasizing how dual references unlock deeper spatial and symbolic meaning.
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