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MatheMUSEments
Spiraling
Triangles
By Ivars Peterson
Muse, February 2007, p. 26-27.
Playing with triangles can lead to amazing patterns
and three-dimensional structures. That's what Hungarian designer Dániel
Erdély (below) found when he created an intriguing geometric
form out of two spirals of triangles that get smaller and smaller.
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Photo by Regina Márkus |
He called the resulting S-shaped object a spidron.
Each of its two arms looks a bit like a seahorse's tail.
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Erdély |
The two spiral arms of a spidron consist of alternating
sequences of equilateral and isosceles triangles (above).
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Erdély |
How to Draw a Spidron's Arm (above): Start
with a regular hexagon, which has six corners. Connect every send
corner with a straight line to make a six-pointed star. Inside the
star is a smaller hexagon. Again connect every second corner. Continue
the process until the shape in the center is so small that you can't
put in any more lines. The resulting pattern contains six identical
copies of a spidron arm.
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Erdély, Marc Pelletier, Amina Buhler Allen, Walt van Ballegooijen |
Even though spidrons are irregularly shaped, they
can fit together without gaps or overlaps to cover a plane (above). For example,
you could tile your bathroom floor with this pattern of spidrons.
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Erdély, Marc Pelletier, Amina Buhler Allen, Walt van Ballegooijen |
When spidrons are laid down like tiles on a flat surface,
then creased in just the right way at the line within each spidron
arm, the flat structure can be forced to fold accordion-style into
a wavy surface (above). As the folds get steeper, the whole pattern twists
and compacts.
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Erdély, Marc Pelletier, Amina Buhler Allen, Walt van Ballegooijen |
Creased and folded spidrons can be assembled into
three-dimensional balls (above). This one is made of 120 spidrons.
Are spidrons good for anything besides artwork and
maybe bathroom floors? Erdély says spidron surfaces could be
used for collapsible solar panels or shock absorbers. And spidron-based
blocks might make an interesting toy. But mostly, he admits, they're
just interesting for their own sake.
You can learn more about spidrons at www.spidron.hu.
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