2. Mathematics is all around us.
As we discover more and more
about our environment
and our surroundings
we see that nature
can be described
mathematically.
The beauty of a
flower, the
majesty of a tree,
even the rocks
upon which we
walk can exhibit
nature's sense of symmetry.
3. Symmetry
Symmetry in everyday language
refers to a sense of harmonious
and beautiful proportion and
balance. In mathematics,
"symmetry" has a more precise
definition, that an object
is invariant to a transformation,
such as reflection.
4. Symmetry
Symmetry is discribed from three
perspectives: in mathematics,
including geometry,
the most familiar type of symmetry
for many people;
in science and nature; and in the arts,
covering architecture, art and music.
6. People observe the symmetrical nature,
often including asymmetrical balance,
of social interactions in a variety of contexts.
These include assessments of empathy,
apology, dialog, respect, justice, and revenge.
7. Symmetrical interactions send the
message "we are
all the same" while
asymmetrical
interactions send the
message "I am special;
better than you.“
Peer relationships are
based on symmetry,
power relationships are
based on asymmetry.