Difference between revisions of "Bouquet"

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|HideMME = No
 
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|ImageIntro=This is a 9-inch diameter table-top sculpture made of acrylic plastic (plexiglas). ''Bouquet'' has a very light and open feeling and gives very different impressions when viewed from different angles.
 
|ImageIntro=This is a 9-inch diameter table-top sculpture made of acrylic plastic (plexiglas). ''Bouquet'' has a very light and open feeling and gives very different impressions when viewed from different angles.
|ImageDescElem=''Bouquet'' is available in different colors. Each sculpture is made of 30 identical pieces in their respective shade of acrylic plastic (plexiglas). Each piece is an elongated S-shaped form, carefully calculated to spiral [[Image: Bouquet2.jpg|left|thumb|150 px|One of the pieces]]around in a vortex with the other parts yet only touch each other at their outside tips. The effect is that of a dozen spinning flowers constructing a three dimensional shape. It is similar to ''[[Frabjous]]'', in both construction and appearance, but they are two different sculptures.
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|ImageDescElem=''Bouquet'' is available in different colors. Each sculpture is made of 30 identical pieces in their respective shade of acrylic plastic (plexiglas). Each piece is an elongated S-shaped form, carefully calculated to spiral [[Image: Bouquet2.jpg|left|thumb|175 px|One of the pieces]]around in a vortex with the other parts yet only touch each other at their outside tips. The effect is that of a dozen spinning flowers constructing a three dimensional shape. It is similar to ''[[Frabjous]]'', in both construction and appearance, but they are two different sculptures.
|ImageDesc=''Bouquet'' is in the shape of a great stellated dodecahedron, which forms a dodecahedron when fully fleshed out (planes are created using each point as a vertex). It is more difficult to visualize a solution when compared to ''Frabjous'', however it is possible to understand a solution.
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|ImageDesc=''Bouquet'' is in the shape of a great stellated dodecahedron, which is a part of the dodecahedron "family".
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It forms this when fully fleshed out (planes are created using each point as a vertex). It is more difficult to visualize a solution when compared to ''Frabjous'', however it is possible to understand a solution.
  
 
[[image: bouquet5.png|right|thumb|200 px|Attach a rod from one vertex to the other]]
 
[[image: bouquet5.png|right|thumb|200 px|Attach a rod from one vertex to the other]]
To solve the puzzle created by the creation of said model, picture the dodecahedron in terms of a pentagon (now called the base pentagon) connected to five other pentagons by sharing a line with each. Connect each vertex of the base pentagon to the tip of the opposite pentagon. Do this with every vertex[[image: bouquet6.png|left|thumb|200 px|Adding curves to the rod]] in the dodecahedron. Unfortunately, all of the rods intersect at some point near the center. Adding two curves to the rod, one near each side, prevent the rods from colliding and gives an interesting star pattern when looked at from the correct angle. Each piece connects with the others at a 60<sup><math>^\circ</math></sup>
+
To solve the puzzle created by the creation of said model, picture the dodecahedron in terms of a pentagon (now called the base pentagon) connected to five other pentagons by sharing a line with each. Connect each vertex of the base pentagon to the tip of the opposite pentagon. Do this with every vertex[[image: bouquet6.png|left|thumb|200 px|Adding curves to the rod]] in the dodecahedron. Unfortunately, all of the rods intersect at some point near the center. Adding two curves to the rod, one near each side, prevent the rods from colliding and gives an interesting star pattern when looked at from the correct angle. Each piece connects with the others at a 60<sup><math>^\circ</math></sup>, and appears to curve counterclockwise around each point.
  
 
[[Image: Bouquet8.jpg|right|thumb|250 px|One of the sculptures when viewed from the same angle as the image to the left]]
 
[[Image: Bouquet8.jpg|right|thumb|250 px|One of the sculptures when viewed from the same angle as the image to the left]]

Latest revision as of 19:21, 15 June 2012

Inprogress.png
Bouquet
Bouquet1.jpg
Fields: Geometry and Other
Image Created By: George W. Hart
Website: Bouquet -- George W. Hart

Bouquet

This is a 9-inch diameter table-top sculpture made of acrylic plastic (plexiglas). Bouquet has a very light and open feeling and gives very different impressions when viewed from different angles.


Basic Description

Bouquet is available in different colors. Each sculpture is made of 30 identical pieces in their respective shade of acrylic plastic (plexiglas). Each piece is an elongated S-shaped form, carefully calculated to spiral

One of the pieces

around in a vortex with the other parts yet only touch each other at their outside tips. The effect is that of a dozen spinning flowers constructing a three dimensional shape. It is similar to Frabjous, in both construction and appearance, but they are two different sculptures.

A More Mathematical Explanation

Note: understanding of this explanation requires: *Geometry

Bouquet is in the shape of a great stellated dodecahedron, which is a part of the dodecahedron "family".

It forms this when fully fleshed out (planes are created using each point as a vertex). It is more difficult to visualize a solution when compared to Frabjous, however it is possible to understand a solution.

Attach a rod from one vertex to the other

To solve the puzzle created by the creation of said model, picture the dodecahedron in terms of a pentagon (now called the base pentagon) connected to five other pentagons by sharing a line with each. Connect each vertex of the base pentagon to the tip of the opposite pentagon. Do this with every vertex

Adding curves to the rod

in the dodecahedron. Unfortunately, all of the rods intersect at some point near the center. Adding two curves to the rod, one near each side, prevent the rods from colliding and gives an interesting star pattern when looked at from the correct angle. Each piece connects with the others at a 60^\circ, and appears to curve counterclockwise around each point.

One of the sculptures when viewed from the same angle as the image to the left
A computer rendering of Bouquet




Teaching Materials

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About the Creator of this Image

George W. Hart graduated with a B.S. in Mathematics from MIT (1977), a M.A. in Linguistics from Indiana University (1979), and a Ph.D. in Electrical Engineering and Computer Science from MIT (1987). He has designed several geometrical pieces of art around the world, as well as helping with North America’s only Museum of Mathematics. He has worked at the MIT Lincoln Laboratory and MIT Energy Laboratory as a computer scientist, and taught at Columbia University for eight years and briefly at Hofstra University. After two years as a visiting scholar associated with the computational geometry group in the Department of Applied Mathematics and Statistics at Stony Brook, he was a research professor in the Department of Computer Science at Stony Brook (2001-2010). He is the author of over sixty scholarly articles and conference papers.


Related Links

Additional Resources

References

http://mathworld.wolfram.com/GreatStellatedDodecahedron.html





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