Geometry in Nature

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Geometry in Nature

• By
• Rebecca Dow, Sara Howard, Julie Russell, Jessie
  Buchheim, and Jordann Tomasek

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Symmetry

• Definition-The preservation of form and
  configuration across a point, line or a plane.
• Transformations
• Types of Symmetry

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Symmetry in Nature

• Symmetry Can Be Found All Around Us.

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Reflective Symmetry

• Also known as line symmetry, means that one half
  of an image is the mirror image of the other half.

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Reflective Symmetry

• Point symmetry - any straight cut through the
  center point divides the organism into mirroring
  halves.

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Reflective Symmetry

• Another example of this particular symmetry in
  nature, is a reflection on the water.

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Reflective Symmetry

• As we look at this photograph, the ground acts as
  the bisecting line between the two images.

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Rotational Symmetry

• Radial symmetry is one kind of rotational
  symmetry.

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Rotational Symmetry

• The planets, with slight variation due to chance,
  exhibit radial symmetry.

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Rotational Symmetry

• Snowflakes also provide an example of radial
  symmetry.
• They have hexagonal symmetry around an axis.

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Rotational Symmetry

• All snowflakes have this sort of symmetry due to
  the way water molecules arrange themselves when
  ice forms.

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Attraction to Symmetry

• (Wo)man is naturally attracted to symmetry.
• A face is considered beautiful when the features
  are symmetrical.

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Attraction to Symmetry

• Many animals choose their mates on the basis of
  symmetry.
• The same goes for humans.

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Polygons

• Polygons are closed plane figures made up by 3 or
  more connecting line segments.
• Simple/Non-Simple
• Convex/Non-Complex

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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!
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Polygons found in Fruit
If you slice a kiwi in half, you will see that
the core forms a six-sided 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.
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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.

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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 giraffes body is completely covered in regular
polygons.
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.
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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!
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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.

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Examples of Tessellations

• Semi-regular Tessellation

Regular Tessellation
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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

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Examples of Tessellations in Nature

• Division of Cells

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More Examples

• Honey Comb
• Fish scales
• Shell of a turtle
• Pineapple
• Ear of corn

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Spheres in Nature

• Geometry
• Geo-Earth
• Metry-measurement
• Angles
• Great Circle

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The Earth

• Sphere
• Lines of latitude and longitude
• Equator

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Other Examples of Spheres

• Sun
• Moon
• Planets
• Oranges