Mono Geometry
Geometric Entities in a 1-Element Framework
Mono Geometry explores foundational elements based on a single point (1P) and/or a single line (1L).
These minimal entities serve as the building blocks for more complex geometric operations and symbolic interpretations.
They are, in a sense, self-evident, but still necessary for the completeness and the description of the system of geometric elements within EPG.
Many more transformations are conceivable, in particular, but these are left to the reader’s imagination.
Only the items that are underlined have individual pages describing them.
Mono Geometry Elements
| Code | Reference | Description |
|---|---|---|
| 1P | Geometrical Point | A single point in the plane; the origin of all geometric constructions. |
| 1L | Geometrical Line | A single line, infinite in both directions; defines direction and linearity. |
| 1P-s-2P1 | Circular Points at Infinity | The bicentric set of imaginary infinity points occurring on each circle. |
| 1P-s-Tf1 | Reflection about a Point | A transformation where specified elements are reflected across a fixed point. |
| 1L-s-Tf1 | Reflection about a Line | A transformation where specified elements are reflected across a fixed line. |
Explanation of Notation
- 1P = One Point
- 1L = One Line
- s = special
- 2P1 = A set of two interrelated points that together constitute a complete system
- Tf1 = Transformation
This notation allows for compact representation of geometric and symbolic configurations within the Mono Geometry framework. It emphasizes the minimal reference base while enabling conceptual extensions such as reflection and idealization.
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