Daily Objects With Symmetry

7/26/2019 Daily Objects With Symmetry

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For centuries, symmetry has remained a subject thats fascinated

philosophers, astronomers, mathematicians, artists, architects, and physicists.

The ancient Greeks were downright obsessed with itand even today we

tend to side with symmetry in everything from planning our furniture layout to

styling our hair.

o ones sure why its such an ever!present property, or why the mathematics

behind it seem to permeate everything around usbut the ten e"amples

below prove that its definitely there.

#ust be warned$ once youre aware of it, youll likely have an uncontrollable

urge to look for symmetry in everything you see.

%&Romanesco Broccoli


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'ou may have passed by romanescobroccoli in the grocery store and

assumed, because of its unusual appearance, that it was some type of

genetically modified food. (ut its actually just one of the many instances of

fractal symmetry in naturealbeit a striking one.

)n geometry, a fractal is a comple" pattern where each part of a thing has the

same geometric pattern as the whole. *o with romanseco broccoli, each floret

presents the same logarithmic spiral as the whole head +just miniaturied-.

ssentially, the entire veggie is one big spiral composed of smaller, cone!like

buds that are also mini!spirals.

)ncidentally, romanesco is related to both broccoli and cauliflower/ although its

taste and consistency are more similar to cauliflower. )ts also rich in

carotenoids and vitamins 0 and 1, which means that it makes both a healthy

and mathematically beautiful addition to our meals.

2Honeycomb
http://www.fourmilab.ch/images/Romanesco/http://www.fourmilab.ch/images/Romanesco/


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ot only are bees stellar honey producersit seems they also have a knack

for geometry. For thousands of years, humans have marveled at the perfecthe"agonal figures in honeycombs and wondered how bees can instinctively

create a shape humans can only reproduce with a ruler and compass. The

honeycomb is a case of wallpaper symmetry, where a repeated pattern covers

a plane +e.g. a tiled floor or a mosaic-.

3ow and why do bees have a hankering for he"agons4 5ell, mathematicians

believe that it is the perfect shapeto allow bees to store the largest possible

amount of honey while using the least amount of wa". 6ther shapes, likecircles for instance, would leave a gap between the cells since they dont fit

together e"actly.

6ther observers, who have less faith in the ingenuity of bees, think the

he"agons form by 7accident.8 )n other words, the bees simply make circular
http://gregstevens.name/2012/11/08/do-bees-make-hexagons/http://gregstevens.name/2012/11/08/do-bees-make-hexagons/http://www.sciencenews.org/sn_arc99/7_24_99/bob2.htmhttp://gregstevens.name/2012/11/08/do-bees-make-hexagons/http://gregstevens.name/2012/11/08/do-bees-make-hexagons/http://www.sciencenews.org/sn_arc99/7_24_99/bob2.htm


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cells and the wa" naturally collapses into the form of a he"agon. ither way,

its all a product of nature and its pretty darn impressive.

9Sunfowers

*unflowers boast radial symmetry and an interesting type of numerical

symmetry known as the Fibonacci se:uence. The Fibonacci se:uence is %, ;,

>, and so on +each number is determined by

adding the two preceding numbers together-.

)f we took the time to count the number of seed spirals in a sunflower, wed

find that the amount of spirals adds up to a Fibonacci number. )n fact, a great

many plants +including romanesco broccoli- produce petals, leaves, and
http://www.youtube.com/watch?v=DRjFV_DETKQhttp://www.youtube.com/watch?v=DRjFV_DETKQ


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seeds in the Fibonacci se:uence, which is why its so hard to find a four!leaf

clover.

0ounting spirals on sunflowers can be difficult, so if you want to test this

principle yourself, try counting the spirals on bigger things like pinecones,

pineapples, and artichokes.

(ut why do sunflowers and other plants abide by mathematical rules4 ?ike the

he"agonal patterns in a beehive, its all a matter of efficiency. For the sake of

not getting too technical, suffice it to say that a sunflower can pack in the most

seeds if each seed is separated by an angle thats an irrational number.

@s it turns out, the most irrational number is something known as the goldenratio, or Ahi, and it just so happens that if we divide any Fibonacci or ?ucas

number by the preceding number in the se:uence we get a number close to

Ahi +%.B%9&


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)n addition to plants, some animals, like the nautilus, e"hibit Fibonacci

numbers. For instance, the shell of a nautilusis grown in a 7Fibonacci spiral.8The spiral occurs because of the shells attempt to maintain the same

proportional shape as it grows outward. )n the case of the nautilus, this growth

pattern allows it to maintain the same shape throughout its whole life +unlike

humans, whose bodies change proportion as they age-.

@s is often the case, there are e"ceptions to the ruleso not every nautilus

shell makes a Fibonacci spiral. (ut they all adhere to some type of logarithmic

spiral. @nd before you start thinking that these cephalopods could have kickedyour butt in math class, remember that theyre not consciously aware of how

their shells are growing, and are simply benefiting from an evolutionary design

that lets the mollusk grow without changing shape.
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.htmlhttp://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html


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BAnimals

Dost animals have bilateral symmetrywhich means that they can be split

into two matching halves, if they are evenly divided down a center line. ven

humans possess bilateral symmetry, and some scientists believe that a

persons symmetry is the most important factor in whether we find them

physically beautiful or not. )n other words, if you have a lopsided face, youd

better hope you have a lot of other redeeming :ualities.

6ne animal might be considered to have taken the whole symmetry!to!attract!

a!mate thing too far/ and that animal is the peacock. Earwin was positively

peeved with the bird, and wrote in an %9B& letter that 7The sight of a feather in

a peacocks tail, whenever ) gae at it, makes me sick8

To Earwin, the tail seemed burdensome and didnt make evolutionary sense

since it didnt fit his 7survival of the fittest8 theory. 3e remained furious until he
http://news.nationalgeographic.com/news/2008/08/080818-body-symmetry.htmlhttp://news.nationalgeographic.com/news/2008/08/080818-body-symmetry.html


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came up with the theory of se"ual selection, which asserts that animals

develop certain features to increase their chances of mating. @pparently

peacocks have the se"ual selection thing down pat, since they are sporting a

variety of adaptations to attract the ladies, including bright colors, a large sie,and symmetry in their body shape and in the repeated patterns of their

feathers.

=Spider Webs

There are around =,&&& types of orb web spiders, and all create nearly perfect

circular webswith almost e:uidistant radial supports coming out of the middle

and a spiral woven to catch prey. *cientists arent entirely sure why orb

spiders are so geometry inclined since tests have shown that orbed webs

dont ensnare food any better than irregularly shaped webs.
http://www.pbs.org/wgbh/nova/evolution/creature-courtship.htmlhttp://www.uksafari.com/spiders5.htmhttp://www.uksafari.com/spiders5.htmhttp://www.pbs.org/wgbh/nova/evolution/creature-courtship.htmlhttp://www.uksafari.com/spiders5.htmhttp://www.uksafari.com/spiders5.htm


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*ome scientists theorie that the orb webs are built for strength, and the radial

symmetry helps to evenly distribute the force of impact when prey hits the

web, resulting in less rips in the thread. (ut the :uestion remains$ if it really is

a better web design, then why arent all spiders utiliing it4 *ome non!orbspiders seem to have the capacity, and just dont seem to be bothered.

For instance, a recently discovered spider in Aeru constructs the individual

pieces of its web in e"actly the same sie and length +proving its ability to

7measure8-, but then it just slaps all these evenly sied pieces into a

haphaard web with no regularity in shape. Eo these Aeruvian spiders know

something the orb spiders dont, or have they not discovered the value in

symmetry4

>Crop Circles

Give a couple of hoa"ers a board, some string, and the cloak of darkness, and

it turns out that people are pretty good at making symmetrical shapes too. )nfact, its because of crop circles incredible symmetries and comple"ities of

design that, even after human crop!circle!makers have come forward and

demonstrated their skills, many people still believe only space aliens are

capable of such a feat.

)ts possible that there has been a mi"ture of human and alien!made crop

circles on earthyet one of the biggest hints that they are all man!made is

that theyre getting progressively more complicated. )ts counter!intuitive tothink that aliens would make their messages more difficult to decipher, when

we didnt even understand the first ones. )ts a bit more likely that people are

learning from each other through e"ample, and progressively making their

circles more involved.
http://news.nationalgeographic.com/news/2004/06/0624_040624_tvspider_2.htmlhttp://news.nationalgeographic.com/news/2004/06/0624_040624_tvspider_2.html


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o matter where they come from, crop circles are cool to look at, mainly

because theyre so geometrically impressive. Ahysicist ichard Taylor did a

study on crop circles and discoveredin addition to the fact that about one is

created on earth per nightthat most designs display a wide variety ofsymmetry and mathematical patterns, including fractals and Fibonacci spirals.

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Daily Objects With Symmetry