Synopsis
Explore how two triangles reveal their hidden invariants and hidden symmetries.
This mathematical treatise presents foundational ideas about invariant relations between triangles using projective geometry, poles, and polars, offered in accessible, stepwise form.
This edition surveys how three fundamental invariants arise from dual plane curves and how they govern the relations between a pair of triangles that may be apolar or have special alignments. It traces the development from general constructions to concrete special cases, including the behavior when a triangle degenerates and when conics relate to the triangles. The work emphasizes how these invariant quantities encode mutual properties of the two triangles and their circumscribed or inscribed conics, with insights that connect classical geometry to modern invariant theory.- Learn about the three fundamental invariants associated with two plane curves and how they translate into triangle geometry.
- See how the concept of polarity and polar lines helps classify when a collineation maps points and lines in structured ways.
- Discover special forms and degenerations, including when one triangle collapses or when a conic circumscribes or inscribes both triangles.
- Understand how Feuerbach-type conics arise in the study of two triangles and their mutual relations.
This edition presents the material in its original scholarly voice, focused on the invariant approach to two triangles and the projective structures that connect them.
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