Higher Geometry: Advanced Methods in Analytic Geometry by Frederick Woods
Higher Geometry: Advanced Methods in Analytic Geometry - Table of Contents
Part-I GENERAL CONCEPTS AND ONE-DIMENSIONAL GEOMETRY
1. GENERAL CONCEPTS
2. RANGES AND PENCILS
3. PROJECTIVITY
Part-II TWO-DIMENSIONAL GEOMETRY
4. POINT AND LINE COORDINATES IN A PLANE
5. CURVES OF SECOND ORDER AND SECOND CLASS
6. LINEAR TRANSFORMATIONS
7. PROJECTIVE MEASUREMENT
8. CONTACT TRANSFORMATIONS IN THE PLANE51. Point-point transformations 12052. Quadric inversion 12153. Inversion 12454. Point-curve transformations 12755. The pedal transformation 13156. The line element . 133
9. TETRACYCLICAL COORDINATES
10. A SPECIAL SYSTEM OF COORDINATES
11. CIRCLE COORDINATES
12. POINT AND PLANE COORDINATES
13. SURFACES OF SECOND ORDER AND OF SECOND CLASS
14. TRANSFORMATIONS
15. THE SPHERE IN CARTESIAN COORDINATES
16. PENTASPHERICAL COORDINATES
17. LINE COORDINATES IN THREEDIMENSIONAL SPACE
18. SPHERE COORDINATES
19. FOUR-DIMENSIONAL POINT COORDINATESSECTION
20. GEOMETRY OF N DIMENSIONS
What You Will Learn in Higher Geometry: Advanced Methods in Analytic Geometry
The book Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry by Frederick Woods explores advanced ideas in analytic geometry. It started from Woods’s lectures at MIT and best for students who already know basic geometry. It bridges the gap between intermediate studies in the field and highly specialized works. The book covers topics like different coordinate systems, complex equations, and special ideas like infinity and imaginary elements. It helps students learn harder geometry step by step.
It offers a thorough study of one-, two-, three-, and four-dimensional coordinated systems, the concepts they entail, and their associated geometrical elements. This study culminates with a discussion of n-dimensional geometry in an abstract sense, of which the earlier subjects form concrete illustrations. As each system of coordinates is introduced, the meaning of the linear and quadratic equations is studied, with principal emphasis on the interpretation of equations as well as on a knowledge of useful geometrical facts.
Book Details & Specifications
Title:
Higher Geometry: Advanced Methods in Analytic Geometry by Frederick Woods
Publisher:
Ginn & Co.
Year:
1922
Pages:
446
Type:
PDF
Language:
English
ISBN-10 #:
0486441504
ISBN-13 #:
978-0486441504
License:
Public Domain Work
Amazon:
Amazon
About the Author: Frederick S. Woods
The author Frederick S. Woods
was professor of mathematics at Massachusetts Institute of Technology (MIT). He wrote math books like Higher Geometry to help students learn hard math ideas more easily. Woods worked to make difficult math ideas easier for students to understand, especially in geometry. Besides teaching, he also did important research in advanced math topics like non-Euclidean geometry.
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