Geodesic
Chains, Flowers, Rings and Peanuts: Graphical Geodesic Lines and Their Application to Penrose Tiling
Visual Mathematics, Tome 1 (1999) no. 4

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The new concept of a graphical geodesic is introduced to characterize an arbitrary two-dimensional network whose meshes are all triangles. Although locally straight, a geodesic line globally meanders and sometimes intersects with itself. Furthermore, it may be open or closed. When the method is applied to the triangulated Penrose tiling, geodesics fall into four classes: chains, flowers, rings and peanuts. The analysis shows that a Penrose tiling has strong local fluctuations of curvature which average out over a small region.
Classification : 52C23 
T. Ogawa; R. Collins. Chains, Flowers, Rings and Peanuts: Graphical Geodesic Lines and Their Application to Penrose Tiling. Visual Mathematics, Tome 1 (1999) no. 4. http://geodesic.mathdoc.fr/item/VM_1999_1_4_a5/
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     author = {T. Ogawa and R. Collins},
     title = {Chains, {Flowers,} {Rings} and {Peanuts:} {Graphical} {Geodesic} {Lines} and {Their} {Application} to {Penrose} {Tiling}},
     journal = {Visual Mathematics},
     year = {1999},
     volume = {1},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_1999_1_4_a5/}
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