Mathematics in Nature
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Mathematics in Nature
Created by Laura
Numerical
Symmetry
Radial Symmetry
Similar parts arranged around a central axis
Fibonacci Sequence: Each number is determined by adding the two preceding numbers.
Ex) 1, 2, 3, 5, 8, 13, 21, and 34
The Sunflower
Bright,
Bold, and
Beloved by Bees!
Sunflower
Sunflower
Seeds
The Golden Ratio
21/13 = 1.61
34/21 = 1.61
Two quantities are in the golden ratio (1.618..) if their ratio is the same as the ratio of their sum to the larger of the two quantities.
Pinecone
Artichoke
Growing of branches
Honeycomb
Circles -> Hexagons
Honeycomb: Space filling or close packing of polyhedral shapes so that there are no gaps.
Bees have a knack for Geometry!
What shape is most efficient for storing the most amount of honey while using the least amount of wax??
Honeycomb
Symmetry in this ratio make the sun and moon appear almost the same size.
Sun-Moon
Symmetry
Similar Triangles
The sun is almost 400 times further from the earth than the moon.
The sun's diameter is almost 400 times greater than the moon.
Symmetry in this ratio make the sun and moon appear almost the same size.
All corresponding sides have the same ratio.
Sun-Moon Symmetry
Similar Triangles: EM/ES = M1M2 / S1S2
All corresponding angles are equal.
Axis of Symmetry
The Snowflake
Process of Crystalization:
Molecules (in this case, water molecules) align themselves to maximize attractive forces and minimize repulsive ones.
What is more beautiful than a falling snowflake?
Types of Symmetry
Snowflakes
Rotational: Looks the same after rotation by a partial turn.
Reflective (mirror or line symmetry): one half is the reflection of the other half
Six-fold Radial Symmetry