Euclidean and transformational geometry : a deductive inquiry /
Libeskind, Shlomo.
Euclidean and transformational geometry : a deductive inquiry / Shlomo Libeskind. - Sudbury, Mass. : Jones and Bartlett Publishers, c2008. - ix, 371 p. : ill. (some col.) ; 29 cm.
Includes bibliographical references (p. 365) and index.
The treasure island problem -- The nine-point circle -- Morley's theorem -- The hiker's path -- The shortest highway -- Steiner's minimum distance problem -- The Pythagorean theorem -- Congruence, constructions, and the parallel postulate -- Angles and their measurement -- Congruence of triangles -- The parallel postulate and its consequences -- More on construction -- Circles -- Basic properties of arcs, central and inscribed angles -- Circles inscribed in polygons -- More on constructions -- Area and the pythagorean theorem -- Areas of polygons -- The Pythagorean theorem -- The distance formula -- Similarity -- Ratio, proportion and similar polygons -- Further applications of the side splitting theorem and similarity -- Areas of similar figures -- The golden ratio and the construction of a regular pentagon -- Circumference and area of a circle -- Other recursive formulas for evaluating [pi] -- Trigonometric functions -- Isometries -- Reflections, translations, and rotations -- Congruence and Euclidean constructions -- More on extremal problems -- Similarity transformation with applications to constructions -- Composition of transformations and transformation groups -- In search for new isometries -- Composition of rotations, the treasure island problem and other treasures -- More recent discoveries -- The nine-point circle and other results -- Complex numbers and geometry.
0763743666 9780763743666
2007031433
Geometry.
Transformations (Mathematics)
QA453 / .L53 2008
516
Euclidean and transformational geometry : a deductive inquiry / Shlomo Libeskind. - Sudbury, Mass. : Jones and Bartlett Publishers, c2008. - ix, 371 p. : ill. (some col.) ; 29 cm.
Includes bibliographical references (p. 365) and index.
The treasure island problem -- The nine-point circle -- Morley's theorem -- The hiker's path -- The shortest highway -- Steiner's minimum distance problem -- The Pythagorean theorem -- Congruence, constructions, and the parallel postulate -- Angles and their measurement -- Congruence of triangles -- The parallel postulate and its consequences -- More on construction -- Circles -- Basic properties of arcs, central and inscribed angles -- Circles inscribed in polygons -- More on constructions -- Area and the pythagorean theorem -- Areas of polygons -- The Pythagorean theorem -- The distance formula -- Similarity -- Ratio, proportion and similar polygons -- Further applications of the side splitting theorem and similarity -- Areas of similar figures -- The golden ratio and the construction of a regular pentagon -- Circumference and area of a circle -- Other recursive formulas for evaluating [pi] -- Trigonometric functions -- Isometries -- Reflections, translations, and rotations -- Congruence and Euclidean constructions -- More on extremal problems -- Similarity transformation with applications to constructions -- Composition of transformations and transformation groups -- In search for new isometries -- Composition of rotations, the treasure island problem and other treasures -- More recent discoveries -- The nine-point circle and other results -- Complex numbers and geometry.
0763743666 9780763743666
2007031433
Geometry.
Transformations (Mathematics)
QA453 / .L53 2008
516