Applied Mathematics is a way to use math to solve problems in the real world, like in economics, engineering, and medicine. 

My goals for this project were to find mathematical relationships in nature. I decided to conduct four experiments to find mathematical relationships: (1) in the number of flower petals and vegetable leaves, (2) in the leaf arrangement in plants, (3) in the number of spirals in plants, and (4) in shell shapes.

Do flowers, leaves, and pinecones follow the same number pattern? You count petals, measure leaf angles, and trace spirals in everyday plants to find out.

Flower petals and vegetable leaves often match Fibonacci numbers. Successive leaves on flowering kale grow at about 137 to 140 degrees apart. That angle is called the Golden Angle.

You also look for Fibonacci spirals in cauliflowers, pinecones, sunflowers, and pineapples. Shells follow a different but equally clear math pattern: equiangular spirals.

Project Title: Finding Hidden Sequences In Nature

Objectives/Goals

My goals for this project were to find mathematical relationships in nature. I
decided to conduct four
experiments to find mathematical relationships: 
(1) in the number of flower petals and vegetable leaves,
(2) in the leaf arrangement in plants
(3) in the number of spirals in plants, and 
(4) in shell shapes.

Methods/Materials
In (1), I counted the number of flower petals and vegetable leaves. In (2), I
used iceberg lettuce, flowering
kale, and succulents. Starting with the outermost leaf, I measured the angle of
each successive leaf. I also
cut the leaves of the flowering kale and I numbered each successive stalk. Then
I looked for patterns and
relationships in mathematics. For (3), I looked for spirals in cauliflowers, a
pinecone, succulents, a
sunflower, and a pineapple. In (4), I observed and analyzed four kinds of shells
to find a Fibonacci spiral.

Results

I found in (1) and (2) that flower petals and vegetables with leaves had
relationships with Fibonacci
numbers. Also, I found in (2) that all the angles on my successive leaves were
from 137~140 degrees.
This was the Golden Angle. I used LOGO for spiral simulation and I confirmed
when I applied Golden
Angle to the simulation program, the result showed a well-observed spiral in
nature. In the flowering kale,
I discovered many relationships. I found that the stalk directly below stalk
number 1 was stalk 14. That
left a distance of 13, a Fibonacci number. I realized it took 5 right turns and
8 left turns to get from stalk 1
to 14, again, these are consecutive Fibonacci numbers. I also found spirals in
the cut stalks in the
flowering kale. I found 3 clockwise, and 5 counter clockwise spirals. Those are
consecutive Fibonacci
numbers. In (3), for all my experimental objects for this experiment, there were
consecutive Fibonacci
numbers in the spirals going clockwise and counter clockwise. In (4), I did not
find any Fibonacci spirals,
but I still could identify a mathematical relationship. All my shells were
formed in an equiangular and
similar manner. I learned that you could describe very different shells with the
same mathematical term.

Conclusions/Discussion

I can conclude there is much mathematics combined into nature. Many flowers,
plants, and others have
survived in long-term natural selection because Fibonacci numbers make a good
balance for living. That
is why so many living things today have the Fibonacci sequence hidden behind
them.

Summary Statement

My project was to search for various mathematical relationships existing inside
nature.


Fibonacci Numbers Hidden in Plants and Shells

Finding mathematical relationships in nature

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Math is all about numbers, patterns, and solving problems. Computer science is about using math and technology to create computer programs and solve real-world problems. Together, they help us understand how things work, how to solve problems, and how to use technology to make our lives better!

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Fibonacci Numbers Hidden in Plants and Shells

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