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Conclusion |
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In your trek through Knowhere you have seen how the structure of space orders things |
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around. It facilitates individual expression of form on the local level while maintaining |
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overall uniformity of composition on the extended level. |
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. |
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On the one hand, as you saw in Geometry rules, spatial ordering principles permit things |
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to have complementary mirror planes and axes of symmetry, similar surface and |
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volumetric relationships, congruent structural elements, and dual frameworks, to name |
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a few. This allows structures to be transformed into each other via truncation, sectioning |
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and rearrangement, compounding, and stellation operations. Also structures can be |
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inscribed in each other and they can be packed together to fill space. All of these |
| attributes are conducive to creating a rich mix of diverse forms that can inhabit space. |
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. |
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On the other hand, the structure of space limits diversity of form by invoking certain other |
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ordering principles that things must abide. As you probably already know from geometry, |
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two-dimensional polygons and three-dimensional polyhedra must maintain a topological |
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balance between their vertices, edges, and faces. And, as you saw in Building stability, |
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for polygons, polyhedra, lattices, and plate structures to be inherently stable they must |
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adhere to additional topological constraints. Another purely geometrical limitation is that |
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the sum of the interior or dihedral angles of polygons and polyhedra must be constant. |
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And the sum of the angles about a point must equal 360o, for example. In structural terms, |
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the bearing capacity of beams and columns is limited by spatial considerations such as |
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their moment of inertia and their length. And the strength of trusses and spaceframes |
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depends significantly on the ratio of their height, or depth, to their span. All of these |
| factors limit the possible forms that things can take. |
| . |
| Taken as a whole, these abstract ordering principles provide the structural matrix within |
| which the dynamic interaction of physical forces are played out in the real world. In |
| Structure matters, you saw how the crystal lattice structure accommodates the attractive |
| and repulsive forces of atoms of different size, ligancy, and charge so that they can pack |
| together uniformly into elements and minerals. Building stability demonstrated that the |
| omni-triangulated two-dimensional truss structure permits the internal forces induced by |
| external loads to be exactly and intimately balanced by aligning them axially. Likewise, |
| the three-dimensional spaceframe framework can bear a load perpendicular to its plane by |
| dissipating the resulting forces axially among its members by means of lattice action. The |
| stability of a plate structure is due to the fact that its plates can dissipate internal forces |
| across the entire surface of the plate, and concentrate them at its edges, as counter acting |
| shear stresses. A lattice tower can dissipate its load throughout its omni-triangulated |
| framework. And, Gizmoneering showed that machines can be engineered with different |
| combinations of rigid and moving parts to efficiently convert and transmit externally |
| applied forces into mechanical motion that can do work. |
| . |
| All of these structural systems owe their strength, stability, and efficiency in large part to |
| the structural properties of space. Without these ordering principles existence might well |
| be relegated to either a diverse sand pile of non-uniform particles at one extreme, or a |
| single, uniform entity at the other. Instead, because of these principles, we enjoy a great |
| diversity of materials and structures that contribute substantially to our welfare and |
| security. Indeed space is something else! |
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