{"product_id":"the-four-pillars-of-geometry-undergraduate-texts-in-mathematics","title":"The Four Pillars of Geometry (Undergraduate Texts in Mathematics)","description":"\u003cp\u003eMany people think there is only one right way to teach geometry. For two millennia  the right way was Euclids way  and it is still good in many respects. But in the 1950s the cry Down with triangles! was heard in France and new geometry books appeared  packed with linear algebra but with no diagrams. Was this the new right way  or was the right way something else again  perhaps transformation groups? In this book  I wish to show that geometry can be developed in four fundamentally different ways  and that all should be used if the subject is to be shown in all its splendor. Euclid-style construction and axiomatics seem the best way to start  but linear algebra smooths the later stages by replacing some tortuous arguments by simple calculations. And how can one avoid projective geometry? It not only explains why objects look the way they do; it also explains why geometry is entangled with algebra. Finally  one needs to know that there is not one geometry  but many  and transformation groups are the best way to distinguish between them. Two chapters are devoted to each approach: The ?rst is concrete and introductory  whereas the second is more abstract. Thus  the ?rst chapter on Euclid is about straightedge and compass constructions; the second is about axioms and theorems. The ?rst chapter on linear algebra is about coordinates; the second is about vector spaces and the inner product.\u003c\/p\u003e","brand":"My Store","offers":[{"title":"Default Title","offer_id":44983814979637,"sku":"ByrdShop_0387255303","price":65.53,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0627\/8139\/0901\/files\/9780387255309.jpg?v=1770810823","url":"https:\/\/atxbooks.com\/products\/the-four-pillars-of-geometry-undergraduate-texts-in-mathematics","provider":"ATX Books","version":"1.0","type":"link"}