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So now that you've read through our project--let's find out how much you've learned with a little "POP" quiz!
1.  What kind of sequence is represented by the nautilus shell or certain types of sunflowers?
2.  Using the above sequence, what would be the number following 8?  3, 5, 8, ?
3.  What type of molecules form snowflakes?
4.  What conditions make snowflakes unique from each other?
5.  What type of broccoli represents geometric fractals?
6.  What type of symmetry is represented within a peacock's plumage?
7.  How many different orb spider species are there estimated to be?
8.  What shape of web do all of these amazing creatures (spiders) create instinctively?

We hope you have enjoyed our project! Next time you are out in the beautiful world of nature, be sure to look around and specifically look for examples of math in nature--they really are all around us!

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"All of the estimated 5,000 types of orb web spider species create nearly perfect circular webs with almost equidistant radial support coming out of the middle and a spiral for catching prey." This is fascinating to think about when you realize that these creatures do not follow blue prints for weaving webs and just go off of instincts and create such a perfectly structured circle with amazing strength to handle the force from insects flying into them at full speed!!

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"10 Beautiful Examples of Symmetry In Nature." Listverse. N.p., 20 June 2014. Web. 30 Mar. 2017.

http://listverse.com/2013/04/21/10-beautiful-examples-of-symmetry-in-nature/

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Bilateral symmetry can be seen all over in nature, from humans to animals of all sizes. A "beautiful" example of bilateral symmetry in nature is the peacock. If split down the middle into two halves, each half will be matching of one another = bilateral symmetry.

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Smarandache, F. (2016). Mathematics for Everything with Cominatorics on Nature, A Report on the
Promoter Dr. Linfan Mao of Mathematical Cominatorics. International J. Math. Comin, Vol. (2016) 130- 133,

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Sciences function is realizing what the natural world is, and developing or society to be one with the laws of the natural world. Mathematics’ provides us the methods, theories, and tools we need in order to understand such a complex problem. In order to understand nature there needs to be a mathematical model that has typical characteristics. You start by analyzing, then you try to predict the behaviors, and then we direct people to hold on to the models essence. Anything is given a combinatorial structure in nature they are coherent and developed with no contradictions between them while in nature. This same combinatorial structure can be applied to math and used as the model to help solve this complex problem. 

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Sciences function is realizing what the natural world is, and developing or society to be one with the laws of the natural world. Mathematics’ provides us the methods, theories, and tools we need in order to understand such a complex problem. In order to understand nature there needs to be a mathematical model that has typical characteristics. You start by analyzing, then you try to predict the behaviors, and then we direct people to hold on to the models essence. Anything is given a combinatorial structure in nature they are coherent and developed with no contradictions between them while in nature. This same combinatorial structure can be applied to math and used as the model to help solve this complex problem. 

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Blitzer, Robert.  (2015).  Thinking Mathematically.  Boston, MA: Pearson Education, Inc.

Plant Dolan.  Life Facts.  (2015).  15 Beautiful Examples of Mathematics in Nature.  Retrieved from

http://www.planetdolan.com/15-beautiful-examples-of-mathematics-in-nature/

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The Fibonacci Sequence:  Nature's Living Work of Art in the Nautilus

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The Fibonacci Sequence:  Nature's Living Work of Art in the Nautilus

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The nautilus is a spiral-shelled mollusk that has multiple short tentacles around its mouth.  The nautilus is an example of the Fibonacci number, just like some sunflowers are. The Fibonacci sequence occurs when two sequential numbers added together produce the next number (such that 1, 1, 2, 3, 5, 8, so 1+1=2, 2+1=3, 3+2=5, 3+5=8 and so on).  The shell of the nautilus is in the shape of a Fibonacci spiral and it maintains this proportional shape throughout it’s lifetime.  Not every nautilus shell is identical, nor does every shell make a perfect Fibonacci spiral, but all nautilus shells do conform to a specific type of logarithmic spiral.

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MATH IN NATURE: So How Do We Find Math In Nature?

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MATH IN NATURE: So How Do We Find Math In Nature?

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Math can be found all over in nature!  Look around and you can find all kinds of specific patterns, sequences and intricate designs all adding up to Mathematics in Nature.

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The Romanesco brocolli grows in geometric fractals which means that each of its buds is a miniaturized version of the whole veggie head!

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Did you know that each arm of a snowflake is identical to the rest.  In mathematics, this is called six-fold symmetry.  Snowflakes are formed when water molecules form weak hydrogen bonds which are arranged within a certain pattern and then freeze into a solid form.  Snowflakes are like fingerprints in that no two are the same. So then, how can each snowflake be different, but yet each snowflake arm is identical to one another?  The answer is that as each flake passes through the atmosphere, it encounters unique weather conditions which give it originality; but since the whole snowflake passes through the exact same weather, each arm experiences the same condition, thus making each arm identical.  Pretty "cool" huh!