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tkpenvs3000w22 · 2 years

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Math within Nature.

Unit 09 Blog

Though they may seem so different, math and nature intersect with a common ground rooted in symmetry, the natural constant, and Fibonacci’s sequence.

Symmetry can occur in three different ways: rotational symmetry, bilateral symmetry, and translational symmetry. Rotational symmetry can be described as when you rotate an object upon its own axis, its shape still looks the same. Rotational symmetry is replicated in nature very frequently in flowers, for example, but they are also an example of bilateral symmetry at the same time. Bilateral symmetry occurs when an image is inverted perpendicularly through the plane, this could also be considered reflection or mirror symmetry. Butterflies are a classic example of bilateral symmetry in nature, so are many other insects. Lastly, translational symmetry occurs when each point in a figure is moved the same distance in the same direction. This was certainly the one furthest from my mind, but upon further inspection, looking at many images of nature enlightened me to the fact that it the structures of crystals and honeycombs present in a beehive.

Have you noticed any other types of symmetry in nature? If not, do any particular examples of symmetry in nature fascinate you? Explain why. Personally, I quite enjoy bilateral symmetry as it reminds me of that form of art I would do as a child where I would fold a paper in half, open it and place paint on one side in a design, fold it closed along the already formed crease, and reopen it to a beautiful, bilaterally symmetrical, image. Moreover, I believe it is appealing to the human eye as we humans are, mostly, bilaterally symmetric and familiarity is comforting.

As for the natural constant, mathematically known as “e”, is something known as Euler’s number (Ping, 2016). Named after famous mathematician Leonhard Euler, Euler’s number is a constant that appears with exponential growth or decay (Ping, 2016). What is riveting about this mathematical constant is that it is easily found in the natural world within the growth of plants or ammonite shells (Ping, 2016). There are countless occurrences of it within the natural, but you may recognize it from logarithmic equations in math classes.

Lastly, I want to mention the Fibonacci sequence. If you are like me, you recall learning about this string of numbers in which each number that appears is a sum of the previous two numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, etc. (Carlson, 2019). What is unique about these numbers is that the ratio between any number and the one prior it follows a 1:1.618 ratio famously known as the golden ratio (Carlson, 2019). In nature, it can be observed in the shell of a snail, the petals of flowers, the pattern of sunflower seeds, or the spiral pattern of a pine cone (Carlson, 2019). In the media, you may have heard references to the golden ratio in related beauty: it is commonly held as the mathematical symmetry algorithm underlying what we perceive as attractive (Carlson, 2019). This related back to nature’s presence in our lives as a “gift of beauty” (Beck et al., 2018). All of this said, if math is in nature and nature is beautiful, then math can be beautiful. Do you agree? Can’t wait to hear what you think!

Can you think of any other examples of math in nature?

Talk to you soon fellow nature nerds!

Beck, L., Cable, T.T. & Knudson, D.M. (2018). Interpreting Cultural and Natural Heritage for a Better World. Sagamore-Venture Publishing.

Carlson, S. C. (2019). Golden ratio. Encyclopedia Britannica. https://www.britannica.com/science/golden-ratio

Ping, X. (2016). Why natural constant “e” is called “natural”. The University of Melbourne. https://blogs.unimelb.edu.au/sciencecommunication/2016/09/04/why-natural-constant-e-is-called-natural/

#naturenerds

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barinacraft · 6 years

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Faucet Spouts The Golden Ratio

Fibonacci Spirals Around The Water Spigot Too

Wet bars are convenient for ease of use and also free your home’s kitchen from unwanted party traffic as well as the extra supply replenishing trips required when entertaining. An integral part this setup is the water supply and this twisted, right angle home bar faucet displays the elegance of a ballerina when the liquid flows.

More specifically, this bibcock was inspired by the “Fifth Position” in ballet and rotates along some fascinating curves that are found throughout nature as you'll see below.

Watch The Water Flow

The curlicue water spout geometry of the Nastro (ribbon) spigot tap is actually designed in proportion to the golden ratio.* Its continuous, repetitive pattern is mathematically identical and shown above as a mesmerizing animated GIF.†

Is it a coincidence that it sort of looks like water swirling around a sink?

A Quick Geometry Lesson: Fibonacci Turns Golden

Feel free to fast forward thru the math by clicking here if you want.

The Golden Ratio, also known as the golden section, golden mean, divine proportion and others, is where the ratio of the sum of the quantities to the larger quantity is the same as the ratio of the larger quantity to the smaller one OR [ (a + b) / a ] = [ a / b ]. The result is approximately equal to 1.618 and typically symbolized by the lowercase Greek letter Phi as φ.

See any resemblance?

It wouldn't be a stretch to say the Fibonacci spiral may have played a role in the twists and turns of this water faucet design as well. After all, they're very similar.

Italian mathematician Leonardo Fibonacci of the Republic of Pisa first recorded the series of numbers, later named after him, in his Liber abaci in 1202 which were based on his earlier solution of a mathematical rabbit breeding problem regarding how many pairs of rabbits could be born in one year when starting with one male and one female.

A few assumptions were made, but basically, the Fibonacci sequence starts as 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc. and continues on so that when written as a rule its Xn = Xn-1 + Xn-2. If you want to get technical, you could correlate the equations with a closed form expression that uses the golden ratio within the Fibonacci formula itself.

But, who wants to do that? Let's keep things simple.

Both of these so-called logarithmic spirals are illustrated above inside a golden rectangle where Fibonacci's path is shown as a blue curving line going through each of the many golden rectangles inside one another and the Golden Spiral follows along the outside of the arcs of the corresponding pie shaped, shaded areas overlayed on top.

The two trajectories actually converge at higher number values which is starting to become apparent in the graphic above.

Not that you really care, but . . .

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The Golden Ratio Is All Around Us

And, its pretty cool.

20+ Examples Of The Fibonacci Sequence In Nature:

Whirlpools

Hurricanes

Seed Heads

Ocean Waves

Flower Petals

Tree Branches

DNA Molecules

Aloe Polyphylla

Chameleon Tails

Some Spider Webs

Fern Fiddleheads

Inner Ear Cochlea

Elliptical Honeycombs

Horns of Goats and Rams

Honeybee Colony Lineage

Pine Cones and Pineapples

Calla Lilies and Comfrey Flowers

Cauliflower and Romanesco Broccoli

The Milky Way and other Spiral Galaxies

Conch, Nautilus, Mollusk, Snail and Seashells

Along with all the au naturel spirals listed above, countless other exemplars from architecture, music, painting and much, much more (including you) exhibit patterns that are either partially or what appear to be fully derived from or mimic the Golden Spiral / Fibonacci sequence. This video sheds some eye-popping light on the phenomenon.

Wow!

So, why is all this so important anyway?

Its not, but if you decide to add a Nastro tap to your nautilus shell shaped basin or winding river sink you'll certainly have a nice lead in with lots to talk about if you need a conversation starter. Of course, there's always sports.

But, we digress.

Don't Let Your Party Spiral Out Of Control

The graceful design of the Ritmonio Nastro water faucet would be a handsome accent to your wet bar and a very handy piece of what might best be described as ancillary or auxiliary bartending equipment. Styles are available with dual levers for hot and cold running water as well as for other applications like kitchen and bathroom sinks, tubs, etc.

References

* - Nastro faucet design by.

† - Animated GIF of Fibonacci sequence in a purple, pink, green and golden spiral outwards via.

#bartending #equipment #faucet #home bars #Wet Bars

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