.

Knowhere

Discover how the structure of space

determines the shape of things

 

IPreface

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  II.  Geometry rules!

   III.  Structure matters

(symmetry of polyhedra)

(structure of crystals)

     Introduction.

    Atomic packing

       - The Pythagorean system

       - Simple cubic packing (CP)

       - Symmetry elements defined

       - Body centered cubic packing (BCC)

     Cubic symmetry.

       - Simple hexagonal packing (HP)

        - Axes and planes of symmetry

       - Hexagonal close packing (HCP)

     Symmetry association by inscription

       - Face centered cubic packing (FCC)

        - Octahedron

    Geometry and symmetry of elements

        - Tetrahedron

       - FCC elements

        - Icosahedron and dodecahedron

       - HCP elements

     Symmetry association by truncation ....

       - BCC and CP elements

        - Cube/tetrahedron/octahedron

       - HP elements

        - Archimedean solids

       - Diamond structure elements

     Volumetric relationships of polyhedra

    Geometry and symmetry of minerals

        - Sectioning polyhedra

       - Conventional classification system

     Space filling with polyhedra

       - Topological classification system

       - Uniary space fillers

    Topological mineral table

       - Binary space fillers

       - Tetrahedral coordination minerals

       - Tertiary space fillers

       - Octahedral coordination minerals

..

       - Tetra./octa. coordination minerals .......

       - Cubic coordination minerals
       - Triangle prism coordination minerals
. .

  IV.  Building stability  (structural engineering)

     Structural stability

     Buildings

       - Two-dimensional stability

       - Three-dimensional stability

       - Forces and reactions

       - Forces and reactions

     Columns

       - Light wood frame construction

     Beams

       - Wall bearing construction

       - Hinged cantilever beam

       - Skeleton construction

       - Fixed cantilever beam

     Long span structures

       - Simply supported beam

       - Bar joists

       - Fixed beam

       - Trusses

       - Post and lintel

       - Grids

       - Arched beam

       - Spaceframes

       - I-beam

           - triangular spaceframe

       - Truss beam

           - square spaceframe

     Bridges

           - rectangular spaceframe

       - Beam bridge

     Barrel vaults and cylinders

       - Plate girder bridge

       - Truss barrel vault and cylinder

       - Truss bridge

       - Lattice barrel vault and cylinder

       - Cantilever bridge

       - Flexible hyperbolic cylinder

       - Suspension bridge

     Folded plate structures

       - Cable stayed bridge

     Towers

       - Box girder bridge      Space trusses
.

V. Gizmoneering  (mechanical engineering)

     Gizmos        - Checkerflex
       - Piston      Gizmo combos
       - Swivel      Gizmo gallery
       - Engelwing  

Conclusion

.

 

Voted "Best Bet" for 3/22/04-3/29/04

by USA Today Education web site

 
     

Featured on MAA Online article  "Math Games"  3/29/2004

     

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