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# Geometry in Nature

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## Gaurisha Dewan

on 17 January 2015

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#### Transcript of Geometry in Nature

Shells are a great example of fractals in nature
A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale
this shell has a fractal because we can see the shape of each section is the same
(fractal geometry is an actual separate branch of geometry)
Snowflakes demonstrate a theorem known as Metatron's cube
Metatron's Cube is a name for a geometric figure composed of 13 equal circles with lines from the center of each circle extending out to the centers of the other 12 circles.
Also called "the fruit of life", derived from the flower of life
Sunflowers
Honey Combs
Snowflakes
Leaves

Birds
Pyrite Crystals
Right angles are very rarely seen in nature, but when they are seen, they are seen in mostly crystals, and rock formations
right angles are angles that are exactly 90 degrees
it is notated with a box, instead of a curve
Peacock Feathers
GEOMETRY IN NATURE
GROUP MEMBERS:
Gaurisha Dewan
Alana Wang
Aarushi Agrawal
Sindhu Goli
When bees make their hives, they make the shape of their honey combs into regular hexagons
we can calculate the number of diagonals (d) of a polygon if we have the number of sides (n)
in this case the number of sides is 6 since we are using a hexagon
An Obtuse Angle is more than 90° but less than 180°
The angle of the bird's wings is an obtuse angle, because it can be added with other angles to form a straight line (180 degrees), but less than 90 degrees.
You can see acute angles in nature in the form of leaves
An acute angle is an angle that is less than 90° and greater than 0°
The veins of these particular leaves on the right side all consist of acute angles
Peacock feathers are a great example of reflectional symmetry
This means that one half of the feather is an exact reflection of the other
The line of symmetry can be in any direction, but in this case, it goes from the bottom of the feather to the top
Circumference can be calculated from a sunflower's circular center
Circumference-the linear distance around a circular object

C = 2π(r)
Starfish
If any internal angle is greater than 180° then the polygon is concave
a starfish is a concave polygon because, the area where the arms meet form an internal angle greater than 180 degrees
Ripples
Ripples are another example of natural circles
ripples are formed when a drop of water's momentum drives a wave of water outward (radial force)
radius is the distance from the center to the edge
diameter starts at one side of the circle, goes through the center and ends on the other side
Shells
Turtles
Turtles' shells are examples of tessellations in nature
Tessellation-the tiling of a plane using one or more geometric shapes with no overlaps
Trees
Tree trunks are examples of parallel lines
Parallel lines-two lines in a plane that do not intersect or touch at any point
the bottom right picture has a fallen trunk that crosses over two parallel trunks
Transversal: A line that cuts across two or more (usually parallel) lines.
Cauliflower
2
Romanesco Cauliflower
This is an example of Sierpinski's triangle in nature, a fractal named after Waclaw Sierpinski.
overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles
d=6(6-3)
2
d=6(3)
2
d=n(n-3)
d=9
BIBLIOGRAPHY
"Math Is Fun - Maths Resources." Math Is Fun - Maths Resources. N.p., n.d. Web. 12 Dec. 2014.
"25 Examples Of Perfect Geometry Found In Nature." List25. N.p., 27 Aug. 2013. Web. 13 Dec. 2014.
"Congruent - Math Word Definition - Math Open Reference." Congruent - Math Word Definition - Math Open Reference. N.p., n.d. Web. 18 Dec. 2014.
"Wolfram MathWorld: The Web's Most Extensive Mathematics Resource." Wolfram MathWorld: The Web's Most Extensive Mathematics Resource. N.p., n.d. Web. 11 Dec. 2014.
then we get the number of diagonals which is 9
Butterfly Wings
A butterfly's wings are an example of congruency.
Congruency: equal size and shape
The butterflies to the right have two congruent wings, which help them with lift.

Flower of Life
The Flower of Life is the name that gives to a geometrical figure composed of multiple evenly-spaced, overlapping circles.
A "Flower of Life" figure consists of seven or more overlapping circles
involves sacred geometry
Sacred geometry refers to geometric forms that were once used in the design of holy sites, including western churches and cathedrals

Spiderwebs
In spider webs you can see many different polygons and geometrical shapes
In the spiderweb below, you can see squares and triangles
In some cases, you can also see dodecagons (12 sides), and rectangles.
The sum of the interior angles of a triangle is 180°.
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