Synopsis
Explore the geometry of symmetry with Inversion Group theory
This work presents a rigorous look at differential invariants and their behavior under the inversion group, revealing how curves and spirals transform while preserving key angles and structures.
The book walks through explicit constructions of invariants, order by order, and shows how fundamental invariants determine the shape of curves, from minimal lines to logarithmic equiangular double spirals. It connects abstract theory to concrete geometric objects, such as bicircular quartics and their contact with curves at special points.- Learn how differential invariants of increasing order are built from lower-order ones
- See how the inversion group governs the geometry of curves and spirals
- Understand the role of bicircular quartics and logarithmic spirals in this framework
- Follow theorems that tie algebraic expressions to geometric behavior
Differential Invariants Under the Inversion Group
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