7 Fibonacci Sequence Examples in Nature | The Odyssey Online
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# Fibonacci Sequence Examples: 7 Beautiful Instances In Nature

## Nature is beautiful (and so is math). The last one will blow your mind.

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Yes, the math major is doing a math-related post. What are the odds? I'll have to calculate it later. Many people have probably learned about the Fibonacci sequence in their high school math classes. However, I thought I would just refresh everyone's memories and show how math can be beautiful and apply to physical things everywhere around us with stunning examples.

Math doesn't have to be anxiety-inducing or tax calculating; it can be cool and amazing too. For those who are unfamiliar, Fibonacci (real name Leonardo Bonacci) was a mathematician who developed the Fibonacci sequence. The sequence is found by adding the previous two numbers of the sequence together. It looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34... And on it goes.

The Fibonacci sequence is found all throughout nature, too. It is a natural occurrence that different things develop based upon the sequence.

## 1. Shells

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As you may have guessed by the curve in the box example above, shells follow the progressive proportional increase of the Fibonacci sequence. Shells are probably the most famous example of the sequence because the lines are very clean and clear to see. They are also fun to collect and display. And then, there you have it! You're own little piece of math.

## 2. Trees

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Tree -- we see them everywhere, but do you look and analyze the structure of how the branches grow out of the tree and each other? No, because you're normal and have better things to do. But if you did, you would see the Fibonacci sequence evolve out of the trunk and spiral and grow the taller and larger the tree becomes. Some truly majestic trees are in existence today, utilizing this pattern.

## 3. Flower Pistils

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The part of the flower in the middle of the petals (the pistil) follows the Fibonacci sequence much more intensely than other pieces of nature, but the result is an incredible piece of art. The pattern formed by the curve the sequence creates used repeatedly produces a lovely and intricate design.

## 4. Flower Petals

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Flowers of all kinds follow the pattern, but roses are my favorite kind to use as an example of the Fibonacci sequence. I like it because the petals aren't spread out and the spiral is more obvious and clear, like with the shell. The petals unfold more and more and the sequence increases. Roses are beautiful (and so is math).

## 5. Leaves

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Leaves follow Fibonacci both when growing off branches and stems and in their veins. I, personally, find the veins much more interesting and amazing to look at. Similar to a tree, leaf veins branch off more and more in the outward proportional increments of the Fibonacci sequence.

## 6. Storms

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Specifically hurricanes and tornadoes, many storm systems follow the Fibonacci sequence. I suppose this is not beautiful, but more interesting. On a map, at least, hurricanes look cool. I guess we could say this example proves math can be beautiful and destructive.

## 7. You!

Yes! You are an example of the beauty of the Fibonacci sequence. The human body has various representations of the Fibonacci sequence proportions, from your face to your ear to your hands and beyond! You have now been proven to be mathematically gorgeous, so go forth and be beautiful! ...and maybe think math is a little bit better than you first thought?

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Student Life

## 7 Types Of Students You Will Meet In College

### You wish you could be #5, but you know you're probably a #6.

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There are thousands of universities around the world, and each school boasts its own traditions and slogans. Some schools pride themselves on sports, while others emphasize their research facilities. While there is a myriad of differences among each and every school, there will always these seven types of students in class.

## 1. The one who sits in the front row

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There's at least one of these people in every single class, whether it's a required General Education class or an upper division major course. These students always sit in the front row and ask at least five questions every lecture. They attend all the discussions and office hours, and try to turn in homework at least a week in advance. These are also the people who remind professors about assigned homework and upcoming exams. Nothing bad about being studious, but are they even human?

## 2. The one who is always online shopping

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It doesn't matter whether it's fall, winter, spring or summer - these people are online shopping every single lecture. They usually sit a row or few in front of you, and while the professor is lecturing, instead of taking notes or even trying to act like they're listening, they just aimlessly scroll through Aritzia, Forever 21 and Zara. The only time their eyes ever leave their computer screen is when class ends, so they're basically just there for giggles.

## 3. The one who always falls asleep

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This person comes to class every day, but somehow never stays awake for more than 20 minutes. You can sometimes hear the occasional snore from a corner of a large lecture hall, or catch their heads nodding like a pendulum near the front of the class if they're the studious type. But let's be real here: we've all been one of those students at some point.

## 4. The one who never pays attention

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This category of students is probably the most common. Sure, they'll go to class, but all they do is surf through memes on Facebook or watch others play Fortnite. These people are in class for the attendance grade, not to learn. On occasion, they may raise their hand in class to ask a generic, vague question that has already been covered but hey, gotta get that participation grade. They're just doing everything they can to survive college, and honestly, it's a mood.

## 5. The one who never studies (but still aces the class)

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Standing as probably the most frustrating category of people in this list, these students won't know about a midterm until two days before. The day before the exam, they'll be chilling in Malibu and partying at night. They go to class every once in a while when the class time doesn't clash with one of their many elaborate social plans, but never pay attention. Somehow, they still ace all their exams and end up with the top grade in the class.

## 6. The one who is always stressed

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These people will start studying for a midterm at least two weeks before hand, and will be so stressed about homework and classes that they spend more time worrying about the workload than actually doing the work itself. They're in desperate need of a relaxing vacation that they're too stressed to plan, and they disappear from the outside world for weeks at a time. You can usually find them in a study room in a library, where they probably have been in for the past week.

## 7. The one you've never seen before

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You didn't even know that they were in your class to begin with because they never show up until it's exam week. Are they too smart for the class or struggling too hard to care? The world may never know. Maybe they're just straight chilling in their apartments being lazy, but most of time, they probably didn't even put this class on their schedules. Catch them going to Disneyland on a weekday at least once a month, which is more than the frequency that they attend class.

Featured

## 15 Rhyme Without Reason Greek Life Function Ideas

### When you have no ideas for what to wear to this date function

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I am going to a rhyme without reason date function and I have looked at so many different rhyming words and I figured there need to be a new list of words. At these functions, there are usually at least two rockers and boxers and an umpteenth amount of dogs and frogs. I have come up with a list of creative and unique ideas for these functions.

If you like what you see, get a shopping cart going with these costumes.

## 1. Dime and a Mime

I think that this one would be super cute except one of the dates would have to not talk the entire function which would be extremely difficult.

## 2. Ramp and a Lamp

This is my personal favorite except it would be difficult to dress up like a ramp.

## 3. Hooters and Shooters

For this you could have one person dress up like hooter's girl and have one person wear plastic shot glasses with color glue in them.

## 4. Sherlock and Woodstock

For this one person could wear a cape and a Sherlock hat with a magnifying glass and the other person could dress up like the bird Woodstock or the festival.

## 5. Spaghetti and a Yeti

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This would be the coolest idea to do. To dress up like a bowl of spaghetti and a Yeti. The only thing you would have to watch would to make sure that the Yeti didn't eat the spaghetti.

## 6. Whale and snail

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This would be very cute. You could use a backpack or a laundry basket for the shell.

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I don't know if you have seen the bladder cartoon but just imagine someone dressed up like that. Wouldn't that be so cute?

## 8. Rake and Snake

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The snake could use the rake. This would be a very easy to dress up for.

## 9. Jam and Ham

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You could dress up like a thing of jam or like a dollop of jam and just wear a single color.

## 10. Pig and a Twig

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You could dress with pink and then the other person could dress with brown.

## 11. Banana and Nana

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All you need for this one is a banana costume and old lady clothes

## 12. Dairy and Fairy

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One person would dress up as a milk carton and the other as any kind of fairy.

## 13. Hibachi and Versace

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I think that this is the most creative pairing that has ever been thought of. The hibachi person would definitely have to have one of those tall hats they wear.

## 14. Trash bag and American Flag

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You could put your arms through the straps that come out of the trash bag and just wrap an American flag around yourself (as long as it doesn't touch the floor).

## 15. Gumball Machine and American Dream

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This would be super cute if the person who was the gumball put puffballs onto their shirt and wore silver pants.

## What is a rhyme without reason date function?

A rhyme without reason date function is a social gathering when partners show up wearing outfits that rhyme with each other. It opens up an opportunity for creativity. It is most popular on college campuses, though it can be extended to other parts of society as a fun way to play dress-up. It also gains additional popularity around Halloween time, given the interest in costumes and dressing up for that holiday.

## What are some top ideas for a rhyme without reason?

There are so many options: A Dog and a Frog could be fun. A Ramp and a Lamp, a Whale and a Snail, a Rake and a Snake, a Trash Bag and a Flag, and Bob Ross and Dental Floss are just some ideas for a rhyme without reason date function. Using your own creativity, you could think of countless more options and if you explore the web, you'll find lists out there to provide inspiration. Rhyming without reason at the end of the day is all about having fun.

## What are some sources of rhyme without reason inspiration?

For starters, TikTok has a whole collection of rhyme without reason ideas. You could browse those for quite some time and find plenty of inspiration. You might also look toward Her Campus for plenty more ideas or our handy list. There's no shortage of options around the web, but some of the best ideas may come from you. Start with the rhyming perspective and then think about what fun pairings would be for a real-life rhyme without reason costume party.

Featured

## Yoga love

### A long over due thank you note to my greatest passion.

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Dearest Yoga,

You deserve a great thank you.

Never would I have thought a few years ago that I would be such a huge yoga fanatic, that I would be hitting the gym almost every day to get to class, and that I would be forming all these amazing relationships with so many incredible people who also share a love for you. You've enhanced my way of life in numerous ways that I need to thank you for.

Thank you for showing me my true strength. Not only physical strength, but more importantly mental strength. You've shown me that I am more than what others may think of me, and that I can rise above any obstacle that comes through my path.

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Thank you for helping me to walk through life with grace and passion.To love what I do and love the life that I share with those around me. Before experiencing yoga, I never truly understood what it was like to be passionate about something. Now that I have, not only do I know what it's like to be passionate, but also have a willing to be passionate.

Thank you for teaching me what it is like to appreciate the small things in life. Which has only helped me more to appreciate the big things. You've shown me to not only appreciate the life around me, but also to give myself the appreciation that I deserve. And more importantly, give others the appreciation that they deserve.

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Thank you for allowing me to let go. Whenever I feel as if I need a break from the world, the yoga studio is the first place I think of. As soon as I enter the studio, the outside world leaves my mind. You've allowed me an escape that I will be forever thankful for.

Thank you for turning me into a mindful person. Having mindfulness is harder than it seems, especially here in today's society. Over the past couple years, I have become more mindful to the world around me, I have been able to truly be myself and let everyone else be themselves -- all thanks to yoga.

And lastly, thank you for allowing me to breathe. As simple as it sounds, breathing is the one thing that I carry around most with me off the mat. Deep breaths are what get me through the day. Throughout tough situations, emotional battles, and stressful times, I always know to come back to my yoga, to come back to my breath.

I only hope that those around me feel the same way as I do about you, yoga. You have truly transformed my life in the best way imaginable. It is a gift and a great privilege to be able to experience the practice. Thanks to you, I have grown as a person, proved to myself the true strength I have, become more aware and have ultimately started living a better life.

You're the best,

Arts Entertainment

## Epic Creation Myths: Norse Origins Unveiled

### What happened in the beginning, and how the heavens were set in motion.

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Now, I have the everlasting joy of explaining the Norse creation myth. To be honest, it can be a bit kooky, so talking about it is always fun. The entire cosmos is included in this creation myth, not just the earth but the sun and the moon as well. This will be a short retelling, a summary of the creation myth, somewhat like I did with Hermod's ride to Hel.

File:Blake ancient of days.jpg - Wikimedia Commonscommons.wikimedia.org

The Norse cosmos began with two worlds, Niflheim and Muspellheim. These two worlds, the worlds of primordial cold and fire, were separated by a great fissure called Ginnungagap. The waters from the well Hvergelmir, at the center of Niflheim, by many rivers flowed into Ginnungagap and "when those rivers, which are called Elivagar, came so far from their source, the poisonous flow hardened like a slag of cinders running from a furnace, and became ice. ...Then layer by layer, the ice grew within Ginnungagap" (Byock 13). The northernmost regions of the gap filled with hoar frost and rime, but the southernmost were "the regions bordering on Muspell [and] were warm and bright" (Byock 13). Where the cold of Niflheim's ice and the warmth of Muspellheim's fire met in Ginnungagap the ice thawed, and "there was a quickening in these flowing drops and life sprang up" (Byock 14). From the ice came Ymir, known as Aurgelmir by the giants, the origin of all frost giants. As the wise giant Vafthruthnir says, "'down from Elivagar did venom drop, / And waxed till a giant it was; / And thence arose our giants' race, / And thus so fierce are we found'" (Bellows 76-77).

Entertainment

## 25 Throwback Songs You Forgot About

### But you know you still know every word.

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We all scroll through the radio stations in the car every once in a while, whether its because we lost signal to our favorite one or we are just bored with the same ol' songs every day. You know when you're going through and you hear a song where you're just like "I forgot this existed!" and before you know it, you're singing every word? Yeah, me too. Like, 95% of the time. If you're like me and LOVE some good throwback music, here's a list of songs from every genre that have gotten lost in time, but never truly forgotten.

## 1. "Big Pimpin'" - Jay-ZÂ ft. UGK

Jay-Z gives us a ballad about, you guessed it, pimpin' big in NYC. Jay-Z's rhymes paired with that catchy beat is just bound to get stuck in your head for the rest of the night.

## 2. "Mr. Brightside" - The Killers

If you say that you don't know any of the words to this song, you're the worst kind of person... a liar. This classic has left stamps of its lyrics on 99% of the population, and has a forever spot in my soul.

## 3. "Lose Yourself" - Eminem

This song always leaves me feeling like I could sign a record deal and launch my career as a rap/hip-hop legend... and craving spaghetti.

## 4. "Courtesy of the Red, White and Blue (The Angry American) - Toby Keith

A ballad for the ages that brings the overly patriotic American badass out of all of us.

## 5. "Drop It Like It's Hot" - Snoop Dogg ft. Pharrell Williams

SNOOOOOOOOOOOOOOOOOOOP!

## 6. "Boulevard of Broken Dreams" - Green Day

This song makes me want to walk down a lonely road, preferably a dark one, and reflect on all of my life choices. Nevertheless, it's still a fantastic song.

## 7. "I Write Sins Not Tragedies" - Panic! At The Disco

If your friends don't "chime in" by screaming the chorus at the top of their lungs in the car with you, it's time to leave them there and find new friends. Also, did anyone ever tell the groom what his bride has been up to?

## 8. "Semi-Charmed Life" - Third Eye Blind

A life anthem for all of us. Third Eye Blind has recently released another album. My inner child is tingling.

## 9. "Baby Got Back" - Sir Mix A Lot

Nicki Minaj sampled this in her song "Anaconda" in 2014. Take a minute to realize that some people have heard that, but not the REAL jam that the sample came from. Now, cry.

## 10. "Get Low" - Lil Jon ft. Ying Yang Twinz

The real question is which version is better: Lil Jon's or Sandra Bullock's?

## 11. "Check Yes Or No" - George Strait

You don't have to be a country lover to know this song. My hardcore rocker/screamo friend even knows the chorus. Don't try and tell me you don't. I don't like liars.

## 12. "Ride Wit Me" - Nelly

"Ayyyyye, must be the monaaayyy!" - frequently screamed lyric

## 13. "Pony" - Ginuwine

Even though I can't hear this song without seeing Channing Tatum's half naked body in my mind, it's still one of my favorite songs to hear. Instant day brightener when I hear that funky beat at the beginning.

## 14. "Cleanin' Out My Closet" - Eminem

As sad as these lyrics are, Eminem really hit this one out of the park.

## 15. "Gangstas Paradise" - Coolio

10/10 would recommend listening to Weird Al's parody of this song.

## 16. "It Was A Good Day" - Ice Cube

The first time I heard this may have been on Grand Theft Auto, but that doesn't mean that it isn't a great song.

## 17. "What's Your Fantasy" - Ludacris

Another song that I knew most of the lyrics to that I probably shouldn't have at a young age.

## 18. "Everybody (Backstreets Back)" - Backstreet Boys

They really were back, and we all wish they had stayed.

## 19. "Misery Business" - Paramore

I can't tell if I want to be Hayley Williams or be ON Hayley Williams. I'd be okay with either. #girlcrush

## 20. "Steal My Sunshine" - Len

This feel good song makes me want to rip open a popsicle and ride my bicycle around town.

## 21. "Fly" - Sugar Ray

As repetitive as this is, this song will never get old.

WOO-HOO!

## 23. "Buddy Holly" - Weezer

Weezer may have hated this song, but we are glad they recorded it.

## 24. "No Rain" - Blind Melon

Maybe it's just me who is obsessed with this song, but if you haven't heard it, I highly recommend.

## 25. "99 Problems" - Jay-Z

I have 99 problems, and this playlist solves all of them.