The Four Pillars of Geometry (Undergraduate Texts in - download pdf or read online

By John Stillwell

This new textbook demonstrates that geometry will be built in 4 essentially other ways, and that each one might be used if the topic is to be proven in all its elegance. Euclid-style development and axiomatics appear the way to begin, yet linear algebra smooths the later levels via changing a few tortuous arguments by way of easy calculations. and the way can one steer clear of projective geometry? It not just explains why items glance the way in which they do; it additionally explains why geometry is entangled with algebra. ultimately, one must be aware of that there's no longer one geometry, yet many, and transformation teams are the right way to distinguish among them. during this e-book, chapters are dedicated to every one method, the 1st being concrete and introductory, whereas the second one is extra abstract.
Geometry, of all matters, will be approximately taking assorted viewpoints, and geometry is exclusive between mathematical disciplines in its skill to appear various from assorted angles. a few scholars wish to visualize, whereas others wish to cause or to calculate. Geometry has anything for everybody, and scholars will locate themselves construction on their strengths now and then, and dealing to beat weaknesses at different instances. This e-book could be appropriate for a moment direction in geometry and comprises greater than a hundred figures and a wide choice of workouts in every one chapter.

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