Computational formalisms in Euclidean geometry: Atrigonometric, vectorial and complex numbers approach
Document Type
Book
Publication Date
2025
Department/School
Mathematics
Abstract
This book explores three computational formalisms for solving geometric problems. Part I introduces a trigonometric-based formalism, enabling calculations of distances, angles, and areas using basic trigonometry. Part II focuses on complex numbers, representing points in the plane to manipulate geometric properties like collinearity and concurrency, making it particularly useful for planar problems and rotations. Part III covers vector formalism, applying linear algebra to both plane and solid geometry. Vectors are effective for solving problems related to perpendicularity, collinearity, and the calculation of distances, areas, and volumes. Each formalism has its strengths and limitations, with complex numbers excelling in the plane and vectors being more versatile in three-dimensional space. This book equips readers to choose the best approach for various geometric challenges. This book, designed for math majors, especially future educators, is also valuable for gifted high school students and educators seeking diverse proofs and teaching inspiration.
Recommended Citation
Calin, O. (2025). Computational formalisms in Euclidean geometry: Atrigonometric, vectorial and complex numbers approach. World Scientific.
Comments
O. Calin is a faculty member in EMU's Department of Mathematics and Statistics.
This book was featured at EMU's 2025 Faculty Scholarly and Creative Activity Showcase.