Geometry in Nature
By
Rebecca Dow, Sara Howard, Julie
Russell, Jessie Buchheim, and
Jordann Tomasek
Symmetry
• Definition-The preservation of form and
configuration across a point, line or a plane.
• Transformations
• Types of Symmetry
Symmetry in Nature
Symmetry Can Be Found
All Around Us.
Reflective Symmetry
• Also known as line
symmetry, means
that one half of an
image is the mirror
image of the other
half.
Reflective Symmetry
• Point symmetry any straight cut
through the center
point divides the
organism into
mirroring halves.
Reflective Symmetry
• Another example of
this particular
symmetry in nature,
is a reflection on
the water.
Reflective Symmetry
• As we look at this
photograph, the
ground acts as the
bisecting line
between the two
images.
Rotational Symmetry
• Radial symmetry is
one kind of
rotational
symmetry.
Rotational Symmetry
• The planets, with
slight variation due
to chance, exhibit
radial symmetry.
Rotational Symmetry
• Snowflakes also
provide an example
of radial symmetry.
• They have
hexagonal
symmetry around
an axis.
Rotational Symmetry
• All snowflakes
have this sort of
symmetry due to
the way water
molecules arrange
themselves when
ice forms.
Attraction to Symmetry
• (Wo)man is
naturally attracted
to symmetry.
• A face is
considered
beautiful when the
features are
symmetrical.
Attraction to Symmetry
• Many animals
choose their mates
on the basis of
symmetry.
• The same goes for
humans.
Polygons
• Polygons are closed plane figures made up
by 3 or more connecting line segments.
• Simple/Non-Simple
• Convex/Non-Complex
Polygons in Nature
Have you ever stopped to consider how many
inanimate things that we see in nature that are
geometrically arranged?
There are polygons found in nature everywhere, you
just have to take a closer look!
Polygons found in Fruit
If you slice a kiwi in
half, you will see that
the core forms a sixsided shape, also
known as a hexagon.
This is also true for an apple, except it is a
slightly different version of a pentagon, it
becomes a star.
Look closely at a pineapple and you will see that all
pineapples have the same skin, they are
tessellations of trapezoids.
Polygons found in Plants
This is an example of a polygon
found within a plant. Each leaf
is a triangle, a three-sided
polygon.
There are many types of
flowers that form polygons.
This tulip, has three triangles
on top of three other triangles.
This poppy makes the shape of a
regular pentagon.
Animals and Polygons
Most polygons found on animals are
repetitive, but slightly altered. On
these two cheetahs, almost all of the
polygons are present, except a solid
triangle.
A giraffe’s
Have you ever looked closely at a
honeycomb? Each cell wall stands at
a correct 120 angle with respect to
one another to form a tessellation of
regular hexagons.
body is
completely
covered in
regular
polygons.
On your own time:
Next time you step outside, take a look around
you and see what polygons you can find within
nature itself. You might be surprised as to what
you actually do find!
Tessellations
• Definition- repeating pattern of distinct
shapes
– Regular Tessellations- tessellations of only one
type of polygon
– Semi-regular Tessellation- tessellation of more
than one polygon.
Examples of Tessellations
Semi-regular
Tessellation
Regular Tessellation
Tessellations in Nature
• Random tessellations- vertices of all orders
and polygons of all sizes and shapes
• Quazi-symmetry- tile a surface without a
repeating pattern
• X-ray Crystallography- repeating
arrangements of identical objects in nature
Examples of Tessellations in
Nature
• Division of Cells
More Examples
•
•
•
•
•
Honey Comb
Fish scales
Shell of a turtle
Pineapple
Ear of corn
Spheres in Nature
• Geometry
– Geo-Earth
– Metry-measurement
• Angles
• Great Circle
The Earth
• Sphere
• Lines of latitude and
longitude
• Equator
Other Examples of Spheres
•
•
•
•
Sun
Moon
Planets
Oranges