Grasshopper
Is there a solution to this mathematical problem
Hi everyone,
I am very skeptical about this, however, in the interest of staying open minded, I feel obliged to challenging my own convictions here and ask the question :
Can one build a dome ( or a part of a dome) from perfectly equal structural members ? I.e. all the struts used in construction must have exactly the same lengths.
Based on my humble understanding of Euclidean geometry, this is not possible, but I would welcome any thoughts on the subject that would otherwise challenge my understanding.
In my research I came a cross geodesic domes, and I now know that even geodesics domes don't have equal members ( well, they have sets of equal members based on the number of subdivisions of the triangular surfaces of an icosahedron )
Thanks.
I am very skeptical about this, however, in the interest of staying open minded, I feel obliged to challenging my own convictions here and ask the question :
Can one build a dome ( or a part of a dome) from perfectly equal structural members ? I.e. all the struts used in construction must have exactly the same lengths.
Based on my humble understanding of Euclidean geometry, this is not possible, but I would welcome any thoughts on the subject that would otherwise challenge my understanding.
In my research I came a cross geodesic domes, and I now know that even geodesics domes don't have equal members ( well, they have sets of equal members based on the number of subdivisions of the triangular surfaces of an icosahedron )
Thanks.
Daniel Hambleton
Check out zonohedra or minkowski sums...
Apr 25, 2012
Rémy Maurcot
Hi heider,
Perhaps a picture or diagram rendrais understanding of your message simple.
But i Thinks is possible to divide a dome to equal lenght.
Apr 25, 2012
Daniel Piker
Hopefully my answer here is useful:
http://www.grasshopper3d.com/xn/detail/2985220:Comment:141774
That just applies to triangles though.
If for example you wanted to make a hexagonal grid on the surface, I found it is actually possible to use equal edge lengths (though a hexagonal grid wouldn't be structurally stable unless the connections are made rigid, and the angles would still vary, so I'm not sure how useful this is).
Apr 26, 2012