# Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3]

Voiceover:Say [unintelligible],

you’re in math class and your teacher’s talking about … Well, who knows what your

teacher’s talking about. Probably a good time to start doodling. And you’re feeling

spirally today, so yeah. Oh, and because of

overcrowding in your school, your math class is taking place in greenhouse number three. Plants. Anyway. You’ve decided there are three basic types of spirals. There’s the kind where, as you spiral out, you keep the same distance. Or you could start big but make it tighter and tighter as you go

around, in which case the spiral ends. Or you could start tight

but make the spiral bigger as you go out. The first kind is good if you really want to fill up a page with lines. Or if you want to draw curled up snakes. You can start with a wonky

shape to spiral around but you’ve noticed

that, as you spiral out, it gets rounder and rounder. Probably something to

do with how the ratio between two different

numbers approaches one as you repeatedly add

the same number to both. But you can bring the wonk back by exaggerating the bumps and it gets all optical illusiony. Anyway, you’re not sure what the second kind of spiral is good

for, but I guess it’s a good way to draw snuggled up slug cats, which are a species you’ve invented just to keep this kind of spiral

from feeling useless. This third spiral, however, is good for all sorts of things. You could draw a snail

or a nautilus shell. And elephant with a curled up trunk, the horns of a sheep,

a fern frond, a cochlea in an inner ear diagram, an ear itself. Those other spirals

can’t help but be jealous of this clearly superior kind of spiral. But I draw more slug cats. Here’s one way to draw

a really perfect spiral. Start with one square and draw another next to it that is the same height. Make the next square fit

next to both together, that is each side is length two. The next square has length three. The entire outside shape will always be a rectangle. Keep spiraling around, adding bigger and bigger squares. This one has side length one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13. And now 21. Once you do that you can add a curve going through each square,

arcing from one corner to the opposite corner. Resist the urge to zip quickly across the diagonal, if you want

a nice smooth spiral. Have you ever looked

at the spirally pattern on a pine cone and thought, “Hey, sure are “spirals on this pine cone?” I don’t know why there’s pine cones in your greenhouse. Maybe the greenhouse is in a forest. Anyway, there’s spirals and there’s not just one either. There’s one, two, three, four, five, six, seven, eight going this way. Or you could look at the spirals going the other way and there’s one, two, three, four, five, six, seven,

eight, nine, 10, 11, 12, 13. Look familiar? Eight and 13 are both numbers in the Fibonacci series. That’s the one where you start by adding one and one to get two, then one and two to get three, two and three to get five. Three plus five is eight, five plus eight is 13, and so on. Some people think that instead of starting with one plus one you should start with zero and one. Zero plus one is one, one plus one is two, one plus two and three, and it continues on the same way as

starting with one and one. Or, I guess you could

start with one plus zero and that would work too. Or why not go back one

more to negative one and so on? Anyway, if you’re into

the Fibonacci series, you probably have a bunch memorized. I mean, you’ve got to know one, one, two, three, five. Finish off the single digits with eight and, ooh with 13, how spooky. And once you’re memorizing double digits, you might as well know

21, 34, 55, 89 so that whenever someone turns a Fibonacci number you can say, “Happy Fib Birthday.” And then, isn’t it interesting

that 144, 233, 377? But 610 breaks that

pattern, so you’d better know that one too. And oh my goodness, 987 is a neat number and, well, you see how these things get out of hand. Anyway, ’tis the season for decorative scented pine cones and if you’re putting glitter glue spirals on your pine cones during math class, you might notice that the number of spirals are five and eight or three and five or three and five again. Five and eight. This one was eight and thirteen and one Fibonacci pine cone is one

thing, but all of them? What is up with that? This pine cone has this wumpy weird part. Maybe that messes it up. Let’s count the top. Five and eight. Now let’s check out the bottom. Eight and 13. If you wanted to draw a mathematically realistic pine cone, you might start by drawing five spirals one way and eight going the other. I’m going to mark out starting and ending points for my spirals first as a guide and then draw the arms. Eight one way and five the other. Now I can fill in the

little pine coney things. So there’s Fibonacci numbers in pine cones but are there Fibonacci

numbers in other things that start with pine? Let’s count the spirals on this thing. One, two, three, four,

five, six, seven, eight. And one, two, three,

four, five, six, seven, eight, nine, 10, 11, 12, 13. The leaves are hard to keep track of, but they’re in spirals too. Of Fibonacci numbers. What if we looked at

these really tight spirals going almost straight up? One, two, three, four, five, six, seven, eight, nine, 10, 11,

12, 13, 14, 15, 16, 17, 18, 19, 20, 21. A Fibonacci number. Can we find a third

spiral on this pine cone? Sure, go down like this. And one, two, three,

four, five, six, seven, eight, nine, 10, 11, 12,

13 (muttering) 19, 20, 21. But that’s only a couple examples. How about this thing I found on the side of the road? I don’t know what it is. It probably starts with pine, though. Five and eight. Let’s see how far the conspiracy goes. What else has spirals in it? This artichoke has five and eight. So does this artichoke

looking flower thing. And this cactus fruit does too. Here’s an orange cauliflower

with five and eight and a green one with five and eight. I mean, five and eight. Oh, it’s actually five and eight. Maybe plants just like

these numbers though. Doesn’t mean it has anything to do with Fibonacci, does it? So let’s go for some higher numbers. We’re going to need some flowers. I think this is a flower. It’s got 13 and 21. These daisies are hard

to count, but they have 21 and 34. Now let’s bring in the big guns. One, two, three, four, five, six, seven, eight, nine, 10, 11,

12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23,

24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34. And one, two, three,

four, five, six, seven, eight, nine, 10, 11, (muttering) 17, 24, (muttering) 42, 53, 54, 55. I promise, this is a

random flower and I didn’t pick it out specially to

trick you into thinking there’s Fibonacci numbers

in things, but you should really count for yourself

next time you see something spirally. There’s even Fibonacci numbers in how the leaves are arranged on this stalk, or this one, or the Brussels

sprouts on this stalk are a beautiful delicious three and five. Fibonacci is even in the arrangement of the petals on this rose,

and sunflowers have shown Fibonacci numbers as high as 144. It seems pretty cosmic

and wondrous, but the cool thing about the Fibonacci

series and spiral is not that it’s this big complicated mystical magical super math thing beyond the comprehension of our puny human minds that shows up mysteriously everywhere. We’ll find that these

numbers aren’t weird at all. In fact, it would be weird

if they weren’t there. The cool thing about it is that these incredibly intricate patterns can result from utterly simple beginnings.

Slug cats do exist. In Rainworld.

Magnolia seed (s) big white flower in the southern USA

Our math teacher actually showed us this video in class so that was a fun time

I love your voice?

I love her voice and the way she speaks.

Amazing video

I just finished reading Uzumaki, gonna trip me out.

whaat

Yes….

?????????????☀️?

"Your maths class is taking place in Greenhouse no. Three"

'Greenhouse three'.. Doesn't that sound familiar……..

OH yeah…. It's in hogwarts…

I watched this with my class…then I found it again

ok

I was there waiting for the thumbnail to load..

Fibbonaci is bullcrap

my math teacher made us watch this.

The weird thing you found on the side of the road is a magnolia.

WHO HAS THIS MUCH TIME!!!!!!!!!!!!!!!

Why does she keep drawing sheep as blocks with holes?

Omg I found you again. ❤ I have known your channel for 5 years and you've blown up. Your amazing vi.❤❤❤❤❤❤

Spiral obsession…. ever read Uzumaki??

2019?

My dad showed this to me 7 years ago, and i think its the source of my interest in math and entertaining educational youtube videos, which is why i'm going to be a math teacher.

Ah, the fibonacci sequence. One of many base sequences and codes to existence. Lovely set of numbers.

The thing you found on the road is a magnolia blossom, I think

Me:

sees illousion she madetries itMy drawing:

1,00,000,000 erase marksMe: HOW U DO DAT!?

why do you have a pinecone in class?

fibongucci?

I love her doodling in math videos

More please

WOW

Brilliant!!! (Hand Clap) ???

Your videos are very inspiraling

Your voice is cute

I wish you were my math teacher

What's funny about the "slug cat" is that my cat genuinely looks like a slug

This is like ASMR

brain fried

The teacher showed us this on class and we all agreed she is high. ?

This is exactly why I have a panic attack everyone I go to maths class?

I just got tricked in to learning a bit of math and I’m not complaining

2019 anyone?

It, has everything to do with. It. It's all in the math u just explained or were u , jok in around? ??

2:35

Wow. Great reference to friday the 13th.

(Claps slowly, but gradually gets faster until It becomes the planck speed)

Video Sucks

Can you say it so it’s actually interpretable. This is actually painful to listen to

My teacher just showed this video in class, now I've watched all your videos lmao

4:11

“How about this thing I found in the side of the road? I don’t know what it is, but it probably starts with pine, though!”

you need a ted X video !

What is she holding at 4:39? She thinks is a flower.

Lmaooo

Nobody:

Vihart in math class:

Big things usually have small beginnings.

My teacher showed us this video in math class today.No wonder he didn’t turn on the volume.Probably not great to let your class hear about doodling in math class! LOL!

Also,please don’t waste food.I don’t think it’s a great idea to eat glitter-glued food.

2:00 Are you supposed to be drawing on that pinecone?

You talk way too fast.

were not paying attention t math to learn different math

Trash

Lateralus

i have a pinnapple

squishydoes that count?your artistry is illuminately captivating

maan, I'm so stupid O_O

Went back to this video to say it’s my fibirthday soon!

My teacher showed me this in math class ??. I later saw one of the other videos and immediately knew this was you. I love it

3:30

Damn, I love this channel! <3

Brain… oozing out my ear

my teacher actually played this in class and I was so proud of him :’)

so say ur me and ur in math class

Watched this in class today

Umazaki series be like:

Arigato, Gyro

I know this is 8 years late, but did you say "A sheep" and draw a box with holes? Just don't forget to draw something to keep it from eating everything

0:56

am I the only one who thought of minecraft when she said "nautilus shell"?

Simple to an intelligent creator. Piece o cake.

767476895805689369991789277073521737239462473500936993792414590762971170414053972421838788552962951090412321568104958251305958672537315916096680015791574354131667637189603239871595291143454548069913507248538315878474818381309151810472376275027339038726484850625 = a fibonacci numberlol

That “thing you found in the side of the road”

Is a Magnolia Bud!

i would actually pay attention if you were my teacher XDDD

i really have no idea what’s happening

4:21 that’s a protea and it’s the national flower of my home country South Africa ?

How long is this math class?

I hate it when the plants continuously harass me in math

"When u are putting glitter glue on a pine cone during math class"

Watching this 8 years later

I could fall in love with your voice ?

so u brought flowers in math class

our geometry teacher showed us this video

that was a good day

This uzumaki

When your math teacher sees you doing this

We done this yesterday in maths class and as soon as the teacher showed us a picture of a shell I thought of this video

I just learned how to draw pinecones

W o w

I’m confused

This really helped me with maintaining the rotation of a steel ball in my hand. and my crippled friends fingernails were spinning also.

SPIRAL OUT, KEEP GOINGGreenhouse 3 what happend to numbers 2 and 1

All this in math class without getting cot

I was learning about the Fibonacci sequence in math class today and I remembered when I watched this video a couple years ago, so I decided it was a good time to rewatch this. I’m content

very good video, just thought I would say so : )

Shooting nails is better when you shoot them while looking at a Fibonacci rectangle