CU-0 CU Notation Technique
The CU notation system is designed to systematically describe geometric elements that are either located on or derived from a cubic curve. It provides a modular structure that indicates:
- Which curve is being referenced (e.g., CU for general cubics, CUc for circular cubics)
- How many points on the curve are additionally involved in defining the element
- What kind of element is being defined (e.g., intersection point, pivot, transformation)
Basic Structure
CU[-nP]–[ElementCode]
Item codes
CU |
Refers to a general cubic curve |
CUc |
Refers to a circular cubic curve |
-nP |
Optional: number of known points on the curve additionally involved in defining the element |
ElementCode |
Specific element, such as a point (P1, P2), pivot, or transformation |
Examples
CU-1P→ An element (e.g., a tangent) defined by one known point on the cubicCU-2P–P1→ A point P1 derived from two known points on the cubicCUc-5P–P1→ A pivot point P2 defined by five points on a circular cubicCU–Tfx→ A transformation derived from the cubic itself, without specific points
Additional Conventions
- P = A point on the reference cubic
- Q = A point not on the cubic
- Elements are only considered “given” if they can be constructed or calculated from the specified points and the curve
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