Geometry in Our Three-Dimensional World

The book presents a comprehensive overview of various aspects of three-dimensional geometry that can be experienced on a daily basis. By covering the wide range of topics — from the psychology of spatial perception to the principles of 3D modelling and printing, from the invention of perspective by Renaissance artists to the art of Origami, from polyhedral shapes to the theory of knots, from patterns in space to the problem of optimal packing, and from the problems of cartography to the geometry of solar and lunar eclipses — this book provides deep insight into phenomena related to the geometry of space and exposes incredible nuances that can enrich our lives.The book is aimed at the general readership and provides more than 420 color illustrations that support the explanations and replace formal mathematical arguments with clear graphical representations.Contents: PrefaceAbout the AuthorsOur World is Three-DimensionalThe Eight Basic Elements of Spatial ThinkingSpatial RepresentationThe Geometry on a SphereThe Earth, the Sun and the MoonSimple Solid ShapesHow to Sew a Ball — A Polyhedral ApproachPatterns: Voronoi, Kindergarten, Economy, and EpidemicsPacking ProblemsFascinating ShapesManipulating Two Dimensions in a Three-Dimensional World — Origami in SpaceKnot TheoryKinematics — The Geometry of MotionThe Art of Designing Three-Dimensional ModelsA View of a World with More Than Three DimensionsIndexReadership: All people interested in geometry and science. General audience with a basic knowledge of high-school math. Teachers seeking ideas for a modern approach to teaching geometry with applications.Geometry;3D;Three-dimensional;Mathematics;Spherical Geometry;Topology;Cartography;Projections;Spatial Perception;Spatial Understanding;Spatial Abilities;Spatial Thinking;STEM;Perspective;Platonic Solids; Polyhedra;Patterns;Voronoi;Packing Problems;Mƶbius Strip;Klein Bottle;Origami;Knot Theory;Kinematic Geometry;3D Modelling;3D Printing;Hyperspace;Hypercube;Hypersphere0Key Features:Accessible for the general audienceExtremely wide range of topics related to spatial geometrySpecial focus on topics that are important for everyday lifeModern approach to theoretical topics like spherical geometry, topology, knot theory, and higher-dimensional geometryUnusual topics such as the psychology of 3D perception, the art of perspective drawing, optical illusions, origami art and the geometry of the balls used in sportsEmphasis on practical aspects of spatial geometry: kinematic geometry (geometry of mechanical machines), 3D modeling and printingReaders will learn how to make a virtual modelReaders can train their spatial skillsMore than 420 color illustrations that significantly enhance the perceptions