We live out our lives in a three dimensional world. However, our understanding of what this means is meager, and the study of 3D Geometry is markedly absent from our educational system. Essential 3D Geometry: Unraveling the Mathematical Wonders bridges the gap between current mathematical knowledge and our fascinating-and unexplored-3D world.Originally developed by and for high school students, the material in Essential 3D Geometry has been successfully developed into a college-level text for pre-service teachers.The book offers an original and unique approach for learning mathematics-iMAT engineering-which is based on the principle that learning mathematics is an integrated activity calling for multi-type presentations of mathematical objects through the use of different technologies.The text begins with a thorough study of the building blocks of spatial structures, the five Platonic Solids. The material integrates 2D and 3D geometry, as well as algebra and trigonometry. Subsequent chapters cover a variety of topics including Thales' Theorem, the volume of the Platonic solids and non-regular tetrahedrons, circumcircles and circum-spheres, Archimedean Bodies, and spatial transformations.Students will learn to produce and make use of three types of representation of 3D objects: solids or lattice models, Cabri 3D or GSP files, and constructions using a straight-edge and compass or free hand drawings. Representations will be developed using paper and pencil, craft technology, and computer technology.Essential 3D Geometry is an excellent tool for introducing math educators to the concepts of 3D geometry, helping them go on to develop similar courses for their own students.Bernardo Camou has 20 years of experience teaching mathematics in secondary education. In 2009, he began work on his Ph.D. in mathematics education at the University of Georgia, graduating in May 2012. His dissertation topic, and his passion, is to help others discover the wonders of 3D Geometry.Graciela García studied economics at the Universidad de la Republica for two years before going on to earn the title of Math Teacher at the Instituto de Profesores Artigas. She currently teaches at the Woodlands School, after having spent 37 years teaching math in public high schools.Maria Margarita Colucci earned the title of Math Teacher at the Instituto de Profesores Artigas. For the past fifteen years she has been a high school math teacher at the Liceo N 15, as well as teaching at the Woodlands School where she is also coordinator of M.I.P.Dr. John Olive is Professor Emeritus of Mathematics Education at the University of Georgia. For over 30 years his research has focused on students' mathematical thinking, and the development and use of technological tools to support that thinking.
