Pool or Pocket Billiards and Geometry. Reflection Symmetry - Video and News

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M.C. Escher's Symmetry E70; Butterflies and Golden Rectangles

Golden Rectangles and Droste Effect
The Droste effect is a specific kind of recursive picture. An image exhibiting the Droste effect depicts a smaller version of itself in a place where a similar picture would realistically be expected to appear. It is a visual example of a strange loop, a self-referential system of instancing which is the cornerstone of fractal geometry.

Click the figure below to see the interactive illustration.


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Snowflakes: Hexagonal Symmetry

Golden Rectangle
Snowflakes are snow crystals form when tiny supercooled cloud droplets (about 10 μm in diameter) freeze. The individual ice crystals often have hexagonal symmetry. Although the ice is clear, scattering of light by the crystal facets and hollows/imperfections mean that the crystals often appear white in colour due to diffuse reflection of all spectrum of light by the small ice particles.

Click the figure below to see the interactive illustration of the Snowflakes: Hexagonal Symmetry.



See also:
Snowflakes: Hexagonal Symmetry
Golden Rectangles

Symmetry drawing E67 by M. C. Escher

Kaleidoscope
Maurits Cornelis Escher, a 20th century Dutch artist famous for his etchings and illustrations, uses painstaking perspective and geometry to create his art - challenging the viewer to second guess what is physically possible.



Continue reading at:
gogeometry.com/escher/escher_symmetry_e67_1.html

Symmetry drawing E59 by M. C. Escher

Kaleidoscope
Maurits Cornelis Escher, a 20th century Dutch artist famous for his etchings and illustrations, uses painstaking perspective and geometry to create his art - challenging the viewer to second guess what is physically possible.



Continue reading at:
gogeometry.com/escher/escher_symmetry_e59_1.html

Symmetry drawing E57 by M. C. Escher

Kaleidoscope
Maurits Cornelis Escher, a 20th century Dutch artist famous for his etchings and illustrations, uses painstaking perspective and geometry to create his art - challenging the viewer to second guess what is physically possible.



Continue reading at:
gogeometry.com/escher/escher_symmetry_e57_1.html

Symmetry drawing E85 by M. C. Escher

Kaleidoscope
Maurits Cornelis Escher, a 20th century Dutch artist famous for his etchings and illustrations, uses painstaking perspective and geometry to create his art - challenging the viewer to second guess what is physically possible.



Continue reading at:
gogeometry.com/escher/escher_symmetry_e85_1.html

Symmetry drawing E70 by M. C. Escher

Kaleidoscope
Maurits Cornelis Escher, a 20th century Dutch artist famous for his etchings and illustrations, uses painstaking perspective and geometry to create his art - challenging the viewer to second guess what is physically possible.



Continue reading at:
gogeometry.com/escher/escher_symmetry_e70_1.html

Symmetry drawing E78 by M. C. Escher

Kaleidoscope
Maurits Cornelis Escher, a 20th century Dutch artist famous for his etchings and illustrations, uses painstaking perspective and geometry to create his art - challenging the viewer to second guess what is physically possible.



Continue reading at:
gogeometry.com/escher/escher_symmetry_e78_1.html

Symmetry drawing E72 by M. C. Escher

Kaleidoscope
Maurits Cornelis Escher, a 20th century Dutch artist famous for his etchings and illustrations, uses painstaking perspective and geometry to create his art - challenging the viewer to second guess what is physically possible.



Continue reading at:
gogeometry.com/escher/escher_symmetry_e72_1.html

Symmetry drawing E21 by M. C. Escher

Kaleidoscope
Maurits Cornelis Escher, a 20th century Dutch artist famous for his etchings and illustrations, uses painstaking perspective and geometry to create his art - challenging the viewer to second guess what is physically possible.



Continue reading at:
gogeometry.com/escher/escher_symmetry_e21_1.html

Symmetry drawing E101 by M. C. Escher

Kaleidoscope
Maurits Cornelis Escher, a 20th century Dutch artist famous for his etchings and illustrations, uses painstaking perspective and geometry to create his art - challenging the viewer to second guess what is physically possible.



Continue reading at:
gogeometry.com/escher/escher_symmetry_e101_1.html

Symmetry drawing E69 by M. C. Escher

Kaleidoscope
Maurits Cornelis Escher, a 20th century Dutch artist famous for his etchings and illustrations, uses painstaking perspective and geometry to create his art - challenging the viewer to second guess what is physically possible.



Continue reading at:
gogeometry.com/escher/escher_symmetry_e69_1.html

Symmetry drawing E42 by M. C. Escher.

Kaleidoscope
Maurits Cornelis Escher, a 20th century Dutch artist famous for his etchings and illustrations, uses painstaking perspective and geometry to create his art - challenging the viewer to second guess what is physically possible.



Continue reading at:
gogeometry.com/escher/escher_symmetry_e42_1.html

Symmetry (1966) by Philip Stapp

Symmetry (1966)
Greatest film, a fantasy of dancing images breaking apart, spinning, and converging. Produced by the University of Washington, the Commission on College Physics, and the Polytechnic Institute of Brooklyn.


See animation at:
www.gogeometry.com/geometry/symmetry_plane_isometries.htm