Preface |
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What images come to mind when
you think about "space"? Three-dimensional space?
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Outer space? The space
between these l e t t e r s ? A parking space? All of these
images |
connote the idea that space is
empty and devoid of any form of its own. Its existence is |
defined by its boundaries,
whether these are abstract dimensions, cosmological limits, or |
the surfaces of objects.
This also implies that space can assume any shape defined by |
those boundaries, which it can
of course. |
. |
Since the shape of space
appears to be completely dependent on those things that define |
it, you might assume that
space itself has no effect on the shape of the things that reside in |
it. After all, we
commonly speak of things occupying or taking up space. We speak of
it |
as though space is just a
passive recipient of the thing's form, like an empty hole that is |
filled with something.
Like it's nowhere. |
. |
However, space is not only
shaped by those things that bound it. It also forms the
boundaries |
of those things, whether they
are abstract geometrical constructions or concrete objects. |
Just as space is bounded by
dimensions, so too are the things that space surrounds. In fact, |
their dimensions are only
discernable in reference to the surrounding space. They have a |
front and a back, a top and a
bottom, a beginning and an end, an inside and an outside, a |
perimeter, a surface, and a
volume. They have a size and are separated from others by a |
specific distance. All
of these attributes are defined by the space within and without them. |
. |
However, space does more than
just form the boundaries of objects. It has a structure of its |
own that limits the structural
forms that things can exhibit. For example, each line can only |
have two end points.
Each plane has two surfaces and one perimeter. All polygons have a |
constant proportion of edges
to vertices. The ratio of the circumference to the radius of a |
circle
is an irrational constant. The sum of the interior or dihedral
angles of polygons and |
polyhedra must be constant. All polyhedra must have constant
proportions of edges, faces, |
and
vertices. Each regular and semi-regular polyhedron has a constant set
of rotational axes |
and
mirror planes ... These are just a few of the ordering
principles that spatial limitations |
impose
on the structure of objects, regardless of their size or shape. |
. |
In the following lesson,
Geometry rules,
you will see how spatial constraints determine the |
structure of abstract objects
such as polygons and polyhedra. And how those ordering |
principles account for the
striking symmetry and transformability of these objects. Next, |
Structure matters
demonstrates how
this influences the way that atoms pack together to |
form elements,
and how elements are
combined together into minerals.
Building stability |
illustrates how these same
governing principles can be used to build stable man-made |
structures. And,
finally, in
Gizmoneering,
you will learn how stable and unstable structural |
elements can be combined
together to build simple machines. |
. |
Hopefully, you will see
that space is not nothing. It's something else! |
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Back
to Knowhere |
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