"The
laws of nature are but the mathematical thoughts of God"
- Euclid
Mathematics is
everywhere in this universe. We seldom note it. We enjoy nature and are not
interested in going deep about what mathematical idea is in it. Here are a very
few properties of mathematics that are depicted in nature.
SYMMETRY
Symmetry is everywhere you look in nature.
Symmetry is when a figure has two sides that are
mirror images of one another. It would then be possible to draw a
line through a picture of the object and along either side the image would look
exactly the same. This line would be called a line of symmetry.
There are two kinds of symmetry.
One is bilateral
symmetry in which an object has two sides that are mirror images of each
other.
The human body would be an excellent example of a
living being that has bilateral symmetry.
The other kind of
symmetry is radial symmetry. This
is where there is a center point and numerous lines of symmetry could be drawn.
The most obvious geometric example would be a circle.
Not all objects have symmetry; if an object is not
symmetrical, it is called asymmetric.
Symmetry in
mathematics
Symmetry occurs in many areas of mathematics. Symmetry comes from a Greek word meaning 'to measure together' and is widely
used in the study of geometry. Mathematically, symmetry means that
one shape becomes exactly like another when you move it in some way: turn, flip
or slide. For two objects to be symmetrical, they must be the same size and
shape, with one object having a different orientation from the first.
The mathematical study of symmetry is systematized and
formalized in the extremely powerful and beautiful area of mathematics called group
theory.
Symmetry can be present in the form of coefficients of
equations as well as in the physical arrangement of objects. By classifying the
symmetry of polynomial equations using the machinery of group theory, for
example, it is possible to prove the unsolvability of the general quintic equation.
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