Cayley Ruled Cubic
Cayley Ruled Cubic is an algebraic surface, defined by an implicit equation, immersed.
Open Cayley Ruled Cubic in the interactive viewer →
algebraic aperiodic def-implicit immersed implemented tradition-classical
Formula
Properties
- Family
- algebraic
- Given by
- an implicit equation
- Curvature
- no condition imposed
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Fidelity
- exact
- Exactness
- elementary
Definition
Cayley's cubic RULED surface -- distinct from the four-nodal Cayley cubic this repo already ships, which is a different object with the same name attached.
Sources
Closed form reproduced numerically against the shipped implementation (math_art/surfaces/algebraic.py) over 240 sample points: matches oracle x 1 over 240 points (worst 0).
- E. W. Weisstein, "Peano Surface", "Chair", "Crossed Trough", "Handkerchief Surface", "Hunt's Surface", "Kiss Surface", "Menn's Surface", "Miter Surface", "Nordstrand's Weird Surface", "Tooth Surface", MathWorld -- A Wolfram Web Resource, mathworld.wolfram.com.
- T. Nordstrand, "Weird Cube" and the tooth/pillow object, per the MathWorld pages (Nordstrand 1997).
- G. Peano's 1899 counterexample; cf. the MathWorld page's history of the criterion it defeated.
- E. W. Weisstein, MathWorld, topic 'Algebraic Surfaces' -- the enumeration this absence was measured against.