[Reading] ➹ Shapes, Space, and Symmetry Author Alan Holden – Marjoriejane.co.uk



10 thoughts on “Shapes, Space, and Symmetry

  1. says:

    I wish that I had glanced through this book while studying Crystallography way back when Holden starts with familiar solids such as the cube and octahedron, and proceeds by steps to solids that can fit inside others, solids that result from cutting corners or edges off offamiliar solids, solids that are made of stars, solids that interpenetrate, collections of polygons that have symmetry in three dimensions but couldn t hold water the nolids whew AndHolden even gives advice I wish that I had glanced through this book while studying Crystallography way back when Holden starts with familiar solids such as the cube and octahedron, and proceeds by steps to solids that can fit inside others, solids that result from cutting corners or edges off offamiliar solids, solids that are made of stars, solids that interpenetrate, collections of polygons that have symmetry in three dimensions but couldn t hold water the nolids whew AndHolden even gives advice on how to build models of these polyhedra, which are extensively photographed The gray scale illustrations, vintage 1971, were described by one reviewer as beautiful, but today seem drab, grainy, and out of focus I remember being excited by books like this, however few books in the seventies had photos on every page My impression is that one could learn a good dealabout three dimensional visualization by handling the models than by reading the book, and I had the opportunity to do that with wooden models in Crystallography class Ultimately the book is not so much about solid polyhedra as about patterns and symmetry relationships, and these are powerful tools in crystallography The cube and the octahedron look different, but they are really two aspects of one pattern of symmetries Toward the end of the book, Holden explores the polyhedra that can pack together to fill three dimensional space We are all familiar with the idea that sugar cubes can be packed into a box with no space left over Rectangular boxes can fill a closet or a room, and they can even be squashed into parallelepipeds and still fill the room Holden reminded me of a beautiful fact, that boxes can be the shape of garnet crystals rhombic dodecahedra and still fill three dimensions with no space left over And he informed me that the boxes don t even have to be convex You can place a pyramid on each of the faces of a rhombic dodecahedron, making the first stellation of the rhombic dodecahedron, and, remarkably, these solids will fill space neatly and completely I m not planning on storing old photos or clothing in such strangely shaped boxes, but they would make a fine novelty item


  2. says:

    This is just about the perfect book for anyone interested in polyhedra Starting with the basic Platonics, the book works its way through many other exotic polyhedra, in particular how they can be derived from one another Richly illustrated throughout and with an informal text that takes you through this journey, this is an deep but enjoyable romp through the subject Much less mathematical than Cromwell, and less formal than Wenninger, this is the book to go for for both fun, instruction and i This is just about the perfect book for anyone interested in polyhedra Starting with the basic Platonics, the book works its way through many other exotic polyhedra, in particular how they can be derived from one another Richly illustrated throughout and with an informal text that takes you through this journey, this is an deep but enjoyable romp through the subject Much less mathematical than Cromwell, and less formal than Wenninger, this is the book to go for for both fun, instruction and inspiration


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Shapes, Space, and Symmetry download Shapes, Space, and Symmetry , read online Shapes, Space, and Symmetry , kindle ebook Shapes, Space, and Symmetry , Shapes, Space, and Symmetry ec97bb1d9bce Altogether A Most Instructive, Entertaining, And Esthetically Pleasing Book ScienceSince The Ancient Greeks, The Visualization Of Space Has Been A Challenge That Has Intrigued Men Of Learning Through Centuries Of Thoughtful Looking, A Number Of Three Dimensional Figures Or Polyhedral, As The Greeks Called Them, Have Been Discovered, Admired, And Wondered At For Their Mathematical Elegance And Beauty And They Have Been Put To Use In Remarkably Diverse Ways By Engineers And Builders, Chemists And Crystallographers, Architects And SculptorsThis Book Describes Very Clearly And Simply, And Illustrates With Beautiful Photographs Of Models, A Great Number Of Three Dimensional Figures, All But A Few Consisting Of Plane Faces Bounded By Straight Lines It Examines The Nine Regular Solids The Five Commonly Called Platonic, Described By Theaetetus In The Fourth Century BC And The Four Called Kepler Poinsot, Two Each Of Which Were Discovered By Kepler And Poinsot Many Centuries Later And It Examines Many Variations Obtained By Truncation, Stellation, Dualization, And CompoundingWriting For The Layman As Well As The Student Or Professional In Mathematics, Alan Holden Explains The Structure Of The Figures And Demonstrates How They Can Be Used To Explain Mathematics Visually Rather Than By Symbol Systems, An Effort Hailed By Scientific American Magazine As A Victory Of Clear, Connected Thinking Over The Theorematic Method At The End Of The Book The Author Includes A Section Containing Instructions For Constructing Cardboard Models