7 Beautiful Examples Of The Fibonacci Sequence In Nature

7 Beautiful Examples Of The Fibonacci Sequence In Nature

Nature is beautiful (and so is math).
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Yes, the math major is indeed doing a math-related post. What are the odds? Hold on, I will have to calculate it later. Many people have probably learned about Fibonacci 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. 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. This pattern can also be seen as:

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

1. Shells

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

Tree -- we see them everywhere, but do you look and analyse 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

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

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

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

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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To The Person Who Has Finally Found Their Way

It's about time.
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The start was all wrong. You find yourself saying “if only I could go back and change this, maybe things would be different.” In reality, we all know that’s not possible.

Bad things were happening, parents divorcing or losing a loved one. Things couldn’t get any worse for that situation, and then you’re out of money because you had to pay the bills. You lost your job the next day.

And then, things got better.

You kept your head down and kept on trucking along, carrying all that weight with you. You made changes here and there, getting a new job and cutting toxic people from your life. You started putting yourself and your needs first. You set goals for yourself, and stretched yourself thin to reach them.

And now, you’ve made it. Finally.

After all these hardships, after all of the crap you had to go through, you are able to make a name for yourself in this world. Things are finally looking up for you in the best way.

You met a cute person at that café the other day. You might call them, if they don’t have Tinder. You have a nice job, one that you actually enjoy going to and working overtime for.

Some people would say, “Well that’s nothing compared to what I went through…” But that’s not what matters. This is not a competition of “who had it worse” but instead a proud showcasing of how you managed to make something out of nothing.

And now, you move along.

Conquering the world, or city, at your leisure.

Glancing back, you may question how you even survived. Let that fuel you to do even better things in your future endeavors.

If you begin to doubt yourself for even just a moment, don’t. Half of the people who were in a similar situation as you didn’t have the strength to get up and keep moving.

As I grew up, I would do this visual form of self-reflection. I’d go into a room with a mirror and look at myself. I’d close my eyes and think of a time when I was even younger, maybe less than 10-years-old. I’d think of what I was doing at that age, at that time. Gradually working back up to the current day, I’d reflect on all that physical, mental, emotional growth I’ve accomplished in my short time here. And eventually, I’d open my eyes and look at that person in the mirror. I would smile at myself, as if to say “Thank you for reminding me of what was and recognizing what is.”

We don’t know what lies ahead, where we’ll be or what will happen. But what matters is that in the here and now, you are doing the best you can. And when that day comes when you don’t know where to go or what to do, look in the mirror and reflect.

In the words of St. Jerome, “The face is the mirror of the mind, and eyes without speaking confess the secrets of the heart.”

Cover Image Credit: Ronald Saunders's flickr

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7 Books To Read Before The Movies Come Out

Know your stuff before it hits the theatres.
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We all say we’re going to, but this time you actually should: read the book before you watch the movie. There’s a reason they’re being made into movies because the books are THAT good. For some reason, there seems to be a lot of movies this year based on books, so here are some you should look out for.

1. Molly’s Game

A Golden Globe-winning movie, this is one you should definitely consider reading. Molly Bloom’s book From Hollywood’s Elite to Wall Street’s Billionaire Boys Club, My High-Stakes Adventure in the World of Underground Poker tells of her daring life dealing with the FBI and Russian and Italian mobs.

2. A Wrinkle in Time by Madeleine L’Engle

I’m pretty sure every middle school had this crazy adventure on their summer reading list. You could power through this book, no problem. If you’re as obsessed with Mindy Kaling as I am, it’s worth seeing just for her.

3. Fifty Shades Freed by E.L. James

Of course this is on here. If you haven’t read this series, get on it. I probably read them in a week, not even, and the third book is, in my opinion, the best one. Dive into the love story of Christian and Anastasia, you won’t regret it.

4. Annihilation

After the 11th expedition to Area X sent by a secret government agency ends in mass suicide, a 12th follows to find out what happened. This book in the Southern Reach trilogy by Jeff VanderMeer will have you on the edge of your seat.

5. The Darkest Minds

In Alexandra Bracken’s novel, a disease kills 98% of American children. The remaining 2% develop superpowers and are sent to “rehabilitation” camps. When one girl breaks out, all hell breaks loose.

6. Where’d You Go, Bernadette

Bernadette hates people and leaving the house, so when she goes missing her 15-year-old daughter Bee goes on a mission to find her, discovering a dark past. Maria Semple tells of the difficulties of motherhood and unfulfilled dreams.

7. The Black Hand by Stephan Talty

Leonardo DiCaprio stars in this mafia movie as a detective investigating organized crime in America.

Cover Image Credit: Pexels

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