Unlock a bold approach to geometry with directional calculus, a framework built on Grassmann’s methods to illuminate plane problems.
This edition foregrounds a practical path for using vectors, conjugates, and linear forms to model and solve geometric questions. You’ll encounter inversion techniques, self-conjugate functions, and the way these ideas simplify operations in plane space.
Through clear development of concepts like conjugate functions, inversion formulas, and self-conjugate forms, readers learn to express and manipulate second-degree terms and to find centers, tangents, and loci in plane geometry. The text shows how to reframe classical problems into a vector language that highlights invariants and structural properties, with concrete steps and worked examples.
- Understand how to write and invert linear and quadratic forms using conjugate functions.
- See how centers, tangents, and loci arise from changing the origin and using invariant quantities.
- Explore applications to plane geometry with practical formulas and worked cases.
- Gain a foundation for broader uses in geometry, mechanics, and related fields.
Ideal for readers of advanced geometry and vector calculus who want a rigorous, hands-on approach to plane problems.