Geometry: Plane and FancySpringer Science & Business Media, 6 Δεκ 2012 - 162 σελίδες GEOMETRY: Plane and Fancy offers students a fascinating tour through parts of geometry they are unlikely to see in the rest of their studies while, at the same time, anchoring their excursions to the well known parallel postulate of Euclid. The author shows how alternatives to Euclid's fifth postulate lead to interesting and different patterns and symmetries. In the process of examining geometric objects, the author incorporates the algebra of complex (and hypercomplex) numbers, some graph theory, and some topology. Nevertheless, the book has only mild prerequisites. Readers are assumed to have had a course in Euclidean geometry (including some analytic geometry and some algebra) at the high school level. While many concepts introduced are advanced, the mathematical techniques are not. Singer's lively exposition and off-beat approach will greatly appeal both to students and mathematicians. Interesting problems are nicely scattered throughout the text. The contents of the book can be covered in a one-semester course, perhaps as a sequel to a Euclidean geometry course. |
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Αποτελέσματα 1 - 5 από τα 38.
Σελίδα v
... assumed to have had a course in Euclidean geometry ( including some analytic geometry ) and some algebra , all at the high - school level . No calculus or trigonometry is assumed , except that I occasionally refer to sines and cosines ...
... assumed to have had a course in Euclidean geometry ( including some analytic geometry ) and some algebra , all at the high - school level . No calculus or trigonometry is assumed , except that I occasionally refer to sines and cosines ...
Σελίδα vi
... assuming that the sum of the angles in a triangle is always equal to , always less than , or always greater than two right angles . The last section presents a " proof " due to Saccheri that the sum of the angles in a triangle cannot be ...
... assuming that the sum of the angles in a triangle is always equal to , always less than , or always greater than two right angles . The last section presents a " proof " due to Saccheri that the sum of the angles in a triangle cannot be ...
Σελίδα 2
... assuming anything . That means we do not have geometric objects we already know about , so we can't define things . Instead , we begin the study of geometry by assuming that there are things called " points " and " lines , " etc ...
... assuming anything . That means we do not have geometric objects we already know about , so we can't define things . Instead , we begin the study of geometry by assuming that there are things called " points " and " lines , " etc ...
Σελίδα 4
... assume certain theorems as axioms does not change the theory , and often it makes the theory easier to understand . On occasion , in later sections of this book , I will announce that something is a " fact . " What I am doing in effect ...
... assume certain theorems as axioms does not change the theory , and often it makes the theory easier to understand . On occasion , in later sections of this book , I will announce that something is a " fact . " What I am doing in effect ...
Σελίδα 5
... assume that ZABC + LBAD < 180 ° . Then if we extend the lines through AD and BC far enough , they will meet . But what if the sum of the angles is really , really close to 180 ° ? How do we know they will meet ? B C A D Problem ( for ...
... assume that ZABC + LBAD < 180 ° . Then if we extend the lines through AD and BC far enough , they will meet . But what if the sum of the angles is really , really close to 180 ° ? How do we know they will meet ? B C A D Problem ( for ...
Περιεχόμενα
1 | |
Tiling the Plane with Regular Polygons | 21 |
Geometry of the Hyperbolic Plane | 48 |
Geometry of the Sphere | 74 |
More Geometry of the Sphere | 105 |
Geometry of Space | 131 |
References | 155 |
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A₁ Algebra angle sum antipodal points assume assumption axioms called Chapter closed curve color commutative law complex numbers compute congruent conjugate Möbius transformation construct convex corresponding cube defect defined described disc divide edge elliptic geometry equal equation Euclid Euclidean geometry Euler's theorem exactly example exterior angles fact fifth postulate flip formula geodesic geometric object graph h-lines hexagon hyperbolic geometry hyperbolic plane ideal point intersect inverse isometry Koch snowflake lemma length line segment Mathematics Möbius band Möbius transformation move origin orthogonal pair of antipodal parallel postulate pattern pentagons perpendicular polyhedra polyhedral surface polyhedron possible Problem projective plane proof Proposition prove quaternions radius real number rectangle regular polygons right angles rotation Schlegel diagram semiregular tilings shortest path side smaller snowflake space spherical straight line Suppose symmetry tangent tessellation translation triangle ABC unit circle vector vertex vertices