The Algebra of Coplanar Vectors and Trigonometry by Robert Hayward
The Algebra of Coplanar Vectors and Trigonometry - Table of Contents
1. Vectors and Vector Aggregation
2. Multiplication of Coplanar Vectors
3. Trigonometrical Ratios
4. De Moivre’s Theorem and General Trigonometrical Formulae
5. Vector Indices and Logarithms
6. Excircular or Hyperbolic Trigonometry
7. Roots of Unity
8. Infinite Series — Convergency and Divergency
9. Expansions and Summations
10. Series of Factors
11. Series of Partial Fractions
12. Rational and Integral Functions
What You Will Learn in The Algebra of Coplanar Vectors and Trigonometry
"The Algebra of Coplanar Vectors and Trigonometry" by "Robert Hayward" is a classic mathematical text that unifies planar geometry, algebra, and trigonometry. The book introduces "vector algebra" for two-dimensional space, treating vectors as algebraic objects with both magnitude and direction. By applying algebraic operations to vectors, Hayward provides a systematic way to solve planar problems and connect geometric intuition with algebraic reasoning.
The book gradually develops "trigonometry" from this vector-based perspective. It covers trigonometric ratios, formulas for sums and multiples of angles, and infinite series, showing how these results naturally emerge from vector algebra. Hayward also explores geometric interpretations, diagrams, and even hyperbolic functions, making abstract algebraic operations visually meaningful. This approach helps readers understand how "geometry", "algebra", and trigonometry" are interrelated, offering a clear conceptual framework that goes beyond rote computation.
Designed for students and mathematicians seeking a rigorous yet intuitive foundation, the book emphasizes clarity, logical structure, and practical problem-solving. Its historical significance lies in bridging the gap between separate disciplines, offering insights into classical mathematical methods, and demonstrating the power of vectors in planar mathematics. Even today, it serves as a valuable resource for understanding the deep connections between "vector algebra", geometry, and trigonometry.
Book Details & Specifications
Title:
The Algebra of Coplanar Vectors and Trigonometry by Robert Hayward
Publisher:
Macmillan and co.
Year:
1892
Pages:
380
Type:
PDF
Language:
English
ISBN-10 #:
1112341706
ISBN-13 #:
978-1112341700
License:
Public Domain Work
Amazon:
Amazon
About the Author: Robert Baldwin Hayward
The author Robert Baldwin Hayward
(1858-1939) was an American mathematician and educator who specialized in "vector algebra", "trigonometry", and "geometry". He focused on making complex mathematical concepts clear and accessible, connecting algebraic operations with geometric intuition to help students and mathematicians understand planar mathematics. His book, "The Algebra of Coplanar Vectors and Trigonometry", demonstrates his approach by unifying "algebra" and geometry through vectors. Hayward's work influenced "mathematics education", offering a rigorous, visual, and practical method for learning trigonometry and planar vector analysis, bridging the gap between theory and application.
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