{"product_id":"miniquaternion-geometry-an-introduction-to-the-study-of-projective-planes-paperback-9780521090643","title":"Miniquaternion Geometry; An Introduction to the Study of Projective Planes (Paperback \/ softback) 9780521090643","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eMiniquaternion Geometry\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eAn Introduction to the Study of Projective Planes\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eThis tract provides an introduction to four finite geometrical systems and to the theory of projective planes.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eT. G. Room (Author), P. B. Kirkpatrick (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521090643, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 27 November 2008\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e188 pages\u003cbr\u003e21.6 x 14 x 1.1 cm, 0.25 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis tract provides an introduction to four finite geometrical systems and to the theory of projective planes. Of the four geometries, one is based on a nine-element field and the other three can be constructed from the nine-element 'miniquaternion algebra', a simple system which has many though not all the properties of a field. The three systems based on the miniquaternion algebra have widely differing properties; none of them has the homogeneity of structure which characterizes geometry over a field. While these four geometries are the main subject of this book, many of the ideas developed are of much more general significance. The authors have assumed a knowledge of the simpler properties of groups, fields, matrices and transformations (mappings), such as is contained in a first course in abstract algebra. Development of the nine-element field and the miniquaternion system from a prescribed set of properties of the operations of addition and multiplication are covered in an introductory chapter. Exercises of varying difficulty are integrated with the text.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePart I. Algebraic Background: 1. Two algebraic systems with nine elements\u003cbr\u003e Part II. Field-Planes: 2. Projective planes\u003cbr\u003e 3. Galois planes of orders 3 and 9\u003cbr\u003e Part III. Miniquaternion Planes: 4. The planes ? and ?D\u003cbr\u003e 5. The plane ?.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46006376694040,"sku":"9780521090643","price":33.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521090643i_d8d5f7a8-9a95-40d2-9c2b-44428a989fb1.jpg?v=1694970400","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/miniquaternion-geometry-an-introduction-to-the-study-of-projective-planes-paperback-9780521090643","provider":"Freshly Printed Books","version":"1.0","type":"link"}