geometry and nature - mathematicsmdelcour/geo.pdf · geometry and nature illinois geometry lab...
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![Page 1: Geometry and Nature - Mathematicsmdelcour/geo.pdf · Geometry and Nature Illinois Geometry Lab University of Illinois, at Urbana-Champaign October 9, 2013. Geometry and Nature Illinois](https://reader030.vdocument.in/reader030/viewer/2022040522/5e813565df39e351a15cf119/html5/thumbnails/1.jpg)
Geometry andNature
IllinoisGeometry Lab
MineralsTetrahedron
Cube
Octahedron
Dodecahedron
Hexagonal Prism
MoleculesTetrahedron
TruncatedIcosahedron
Hexagonal Prism
Geometry and Nature
Illinois Geometry Lab
University of Illinois, at Urbana-Champaign
October 9, 2013
![Page 2: Geometry and Nature - Mathematicsmdelcour/geo.pdf · Geometry and Nature Illinois Geometry Lab University of Illinois, at Urbana-Champaign October 9, 2013. Geometry and Nature Illinois](https://reader030.vdocument.in/reader030/viewer/2022040522/5e813565df39e351a15cf119/html5/thumbnails/2.jpg)
Geometry andNature
IllinoisGeometry Lab
MineralsTetrahedron
Cube
Octahedron
Dodecahedron
Hexagonal Prism
MoleculesTetrahedron
TruncatedIcosahedron
Hexagonal Prism
Geometric Solids
Many geometric solids actually occur in nature.
![Page 3: Geometry and Nature - Mathematicsmdelcour/geo.pdf · Geometry and Nature Illinois Geometry Lab University of Illinois, at Urbana-Champaign October 9, 2013. Geometry and Nature Illinois](https://reader030.vdocument.in/reader030/viewer/2022040522/5e813565df39e351a15cf119/html5/thumbnails/3.jpg)
Geometry andNature
IllinoisGeometry Lab
MineralsTetrahedron
Cube
Octahedron
Dodecahedron
Hexagonal Prism
MoleculesTetrahedron
TruncatedIcosahedron
Hexagonal Prism
Minerals
Mineral crystals grow into regular, geometric shapes.
![Page 4: Geometry and Nature - Mathematicsmdelcour/geo.pdf · Geometry and Nature Illinois Geometry Lab University of Illinois, at Urbana-Champaign October 9, 2013. Geometry and Nature Illinois](https://reader030.vdocument.in/reader030/viewer/2022040522/5e813565df39e351a15cf119/html5/thumbnails/4.jpg)
Geometry andNature
IllinoisGeometry Lab
MineralsTetrahedron
Cube
Octahedron
Dodecahedron
Hexagonal Prism
MoleculesTetrahedron
TruncatedIcosahedron
Hexagonal Prism
Tetrahedron
Tetrahedrite
![Page 5: Geometry and Nature - Mathematicsmdelcour/geo.pdf · Geometry and Nature Illinois Geometry Lab University of Illinois, at Urbana-Champaign October 9, 2013. Geometry and Nature Illinois](https://reader030.vdocument.in/reader030/viewer/2022040522/5e813565df39e351a15cf119/html5/thumbnails/5.jpg)
Geometry andNature
IllinoisGeometry Lab
MineralsTetrahedron
Cube
Octahedron
Dodecahedron
Hexagonal Prism
MoleculesTetrahedron
TruncatedIcosahedron
Hexagonal Prism
Cube
Pyrite
![Page 6: Geometry and Nature - Mathematicsmdelcour/geo.pdf · Geometry and Nature Illinois Geometry Lab University of Illinois, at Urbana-Champaign October 9, 2013. Geometry and Nature Illinois](https://reader030.vdocument.in/reader030/viewer/2022040522/5e813565df39e351a15cf119/html5/thumbnails/6.jpg)
Geometry andNature
IllinoisGeometry Lab
MineralsTetrahedron
Cube
Octahedron
Dodecahedron
Hexagonal Prism
MoleculesTetrahedron
TruncatedIcosahedron
Hexagonal Prism
Octahedron
Magnetite
![Page 7: Geometry and Nature - Mathematicsmdelcour/geo.pdf · Geometry and Nature Illinois Geometry Lab University of Illinois, at Urbana-Champaign October 9, 2013. Geometry and Nature Illinois](https://reader030.vdocument.in/reader030/viewer/2022040522/5e813565df39e351a15cf119/html5/thumbnails/7.jpg)
Geometry andNature
IllinoisGeometry Lab
MineralsTetrahedron
Cube
Octahedron
Dodecahedron
Hexagonal Prism
MoleculesTetrahedron
TruncatedIcosahedron
Hexagonal Prism
Dodecahedron
Pyrite
![Page 8: Geometry and Nature - Mathematicsmdelcour/geo.pdf · Geometry and Nature Illinois Geometry Lab University of Illinois, at Urbana-Champaign October 9, 2013. Geometry and Nature Illinois](https://reader030.vdocument.in/reader030/viewer/2022040522/5e813565df39e351a15cf119/html5/thumbnails/8.jpg)
Geometry andNature
IllinoisGeometry Lab
MineralsTetrahedron
Cube
Octahedron
Dodecahedron
Hexagonal Prism
MoleculesTetrahedron
TruncatedIcosahedron
Hexagonal Prism
Hexagonal Prism
Quartz
![Page 9: Geometry and Nature - Mathematicsmdelcour/geo.pdf · Geometry and Nature Illinois Geometry Lab University of Illinois, at Urbana-Champaign October 9, 2013. Geometry and Nature Illinois](https://reader030.vdocument.in/reader030/viewer/2022040522/5e813565df39e351a15cf119/html5/thumbnails/9.jpg)
Geometry andNature
IllinoisGeometry Lab
MineralsTetrahedron
Cube
Octahedron
Dodecahedron
Hexagonal Prism
MoleculesTetrahedron
TruncatedIcosahedron
Hexagonal Prism
Molecules
A number of molecules also have geometric structure.
![Page 10: Geometry and Nature - Mathematicsmdelcour/geo.pdf · Geometry and Nature Illinois Geometry Lab University of Illinois, at Urbana-Champaign October 9, 2013. Geometry and Nature Illinois](https://reader030.vdocument.in/reader030/viewer/2022040522/5e813565df39e351a15cf119/html5/thumbnails/10.jpg)
Geometry andNature
IllinoisGeometry Lab
MineralsTetrahedron
Cube
Octahedron
Dodecahedron
Hexagonal Prism
MoleculesTetrahedron
TruncatedIcosahedron
Hexagonal Prism
Tetrahedron
Methane (CH4 Molecule, Natural Gas)
![Page 11: Geometry and Nature - Mathematicsmdelcour/geo.pdf · Geometry and Nature Illinois Geometry Lab University of Illinois, at Urbana-Champaign October 9, 2013. Geometry and Nature Illinois](https://reader030.vdocument.in/reader030/viewer/2022040522/5e813565df39e351a15cf119/html5/thumbnails/11.jpg)
Geometry andNature
IllinoisGeometry Lab
MineralsTetrahedron
Cube
Octahedron
Dodecahedron
Hexagonal Prism
MoleculesTetrahedron
TruncatedIcosahedron
Hexagonal Prism
Truncated Icosahedron
Buckyball (C60 Molecule Found in Soot)
![Page 12: Geometry and Nature - Mathematicsmdelcour/geo.pdf · Geometry and Nature Illinois Geometry Lab University of Illinois, at Urbana-Champaign October 9, 2013. Geometry and Nature Illinois](https://reader030.vdocument.in/reader030/viewer/2022040522/5e813565df39e351a15cf119/html5/thumbnails/12.jpg)
Geometry andNature
IllinoisGeometry Lab
MineralsTetrahedron
Cube
Octahedron
Dodecahedron
Hexagonal Prism
MoleculesTetrahedron
TruncatedIcosahedron
Hexagonal Prism
Hexagonal Prism
Graphite (Found in Pencil Lead)
![Page 13: Geometry and Nature - Mathematicsmdelcour/geo.pdf · Geometry and Nature Illinois Geometry Lab University of Illinois, at Urbana-Champaign October 9, 2013. Geometry and Nature Illinois](https://reader030.vdocument.in/reader030/viewer/2022040522/5e813565df39e351a15cf119/html5/thumbnails/13.jpg)
Geometry andNature
IllinoisGeometry Lab
MineralsTetrahedron
Cube
Octahedron
Dodecahedron
Hexagonal Prism
MoleculesTetrahedron
TruncatedIcosahedron
Hexagonal Prism
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