Download - Geometry in Nature By Rebecca Dow, Sara Howard, Julie Russell, Jessie Buchheim, and Jordann Tomasek
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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 NaturePolygons in Nature
There are polygons found in nature everywhere, you just have to take a closer look!
Have you ever stopped to consider how many inanimate things that we see in nature that are
geometrically arranged?
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Polygons found in FruitPolygons found in FruitIf you slice a kiwi in half, you will see that the core forms a six-sided shape, also known as a hexagon.
Look closely at a pineapple and you will see that all pineapples have the same skin, they are tessellations of trapezoids.
This is also true for an apple, except it is a slightly different version of a pentagon, it becomes a star.
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Polygons found in Polygons found in PlantsPlantsThis 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 andAnimals and PolygonsPolygonsMost polygons found on animals are repetitive, but slightly altered. On these two cheetahs, almost all of the polygons are present, except a solid triangle.
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.
A giraffe’s body is completely covered in regular polygons.
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On your own time: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