The Pythagorean Theorem: Crown Jewel of Mathematics
by John C. Sparks
Publisher: AuthorHouse 2008
Number of pages: 190
The author chronologically traces the Pythagorean Theorem from a conjectured beginning, through 4000 years of Pythagorean proofs, from all major proof categories, 20 proofs in total. The text presents several mathematical results closely allied to the Pythagorean Theorem along with some major Pythagorean "spin-offs" such as trigonometry. The books contains some classic puzzles, amusements, and applications. An epilogue summarizes the importance of the Pythagorean theorem and suggests paths for further exploration.
Download or read it online for free here:
by John Casey, Euclid - Longmans, Green, and Co.
This edition of the Elements of Euclid is intended to supply a want much felt by teachers at the present day - the production of a work which, while giving the original in all its integrity, would also contain the modern conceptions and developments.
by Serge Tabachnikov
Mathematical billiards describe the motion of a mass point in a domain with elastic reflections from the boundary. Billiards is not a single mathematical theory, it is rather a mathematician’s playground where various methods are tested.
by Richard S. Palais - virtualmathmuseum.org
Contents: What is Geometry; Geometry of Inner-Product Spaces; Linear Maps and the Euclidean Group; Adjoints of Linear Maps and the Spectral Theorem; Differential Calculus on Inner-Product Spaces; Normed Spaces and Integration; ODE; and more.
by Ruslan Sharipov - arXiv
This is a textbook for the course of foundations of geometry. It is addressed to mathematics students in Universities and to High School students for deeper learning. It can also be used in mathematics coteries and self-education groups.