DOODLES AND DIGITS: How It's Math

Male Narrator: Funding for this program is provided in part by... Female Narrator: We believe in getting outside, playing in the yard, growing things and connecting with the earth.

We believe good can grow anywhere.

That's why we're committed to GroMoreGood, everywhere.

And also by... Hi, friends, I'm Caroline, and this is How It's Math, where we discover the surprising ways math shows up in the real world and in amazing careers.

Have you ever wondered how veterinarians care for animals, how musicians keep a steady rhythm, or how designers and animators bring ideas to life?

Today we have a very special episode all about how math supports both creativity and care.

First, we're heading to an animal hospital where professionals use math like rounding and measurement to help treat pets safely.

Next, we'll explore music, where fractions and patterns help musicians create rhythm and keep time.

After that, we'll take a look at urban design, where geometry, area and perimeter are used to play in parks, streets and outdoor spaces.

And finally, we'll go behind the scenes of animation, where multiplication and timing help bring movement to life, frame by frame, from caring to animals to creating music to designing and animating.

You're about to see that math isn't just something you do in school, it's something people use every day to create and care for the world around us.

Let's get started.

♪ Doodly doodle, doodly doodle ♪ doodly doodles and digits ♪ area, symmetry, fractions too ♪ ♪ It's all here for you ♪ Have you ever wondered how vets know exactly how much medicine to give your pet?

It's all thanks to math.

Today, we're going behind the scenes of an animal hospital to uncover the amazing math skills that help veterinarians save lives and keep our furry friends healthy.

Get ready for a wild ride full of numbers science and cuddly creatures.

Let's get into it.

Hi, My name is Dr.

Jennifer Zablackas.

I'm a small animal veterinarian.

I work at the animal hospital of Worthington.

Some of the things that veterinarians do are give check ups, diagnose illnesses, treat injuries, perform surgeries, give medicine and also give advice to pet owners.

How do you use math?

Math is part of every day as a veterinarian, from every appointment that comes in, we start out by getting the pets on a scale to see what they weigh today, we have to prescribe medication, we need to make sure the dosing is precise, so it's safe for them.

You know, medications are going to be the biggest thing.

Dogs and cats can get colds, or they might have antibiotics, like we would at home, and we have to make sure those are measured properly.

If they get too much, could give them an upset stomach.

If they get too little, it might not do the job and get rid of the infection that it needs to.

One thing that can happen a lot with sick animals is if they're coming in for an upset stomach, and a lot of times, if you've had an upset stomach, you're going to also be dehydrated.

We do have ways to kind of estimate how dehydrated a pet is in different percentages, and based on if we say they're 5% or 7% dehydrated, that's going to affect how we calculate how much fluids they need to help get them rehydrated and get them feeling better.

Do you use decimals?

We do use decimals going out a couple places, at least from there we'll usually just round up.

We do use rounding all the time for their weights, but also when we're drawing up medication, that's a liquid, we use syringes that just have the marked increments on it.

We can only take that down to such a small amount, so we do typically have to round up.

They get measured on digital scales that we weigh them in pounds, like for almost all of our medical drugs and dosing of things, we do convert to metrics.

There's a lot of converting pounds to kilograms.

What type of tools do you use?

We definitely use calculators.

We use scales, both a large scale that the bigger animals can just stand on, and we have a smaller scale for cats and small dogs that they just sit on, up on the table.

We use these little calipers that have metric measurements on it to measure lumps and bumps and maybe even wounds that are on dogs.

And we have a tool that kind of works as like a big caliper that we actually can put on their body, that we measure for our patients when we're getting ready to take X-rays of them.

A lot of monitors, we're keeping a check on their heart rate, their respiratory rate.

Dentistry is a really big part of our practice, and it's a really big part of keeping your pet healthy.

Just like you and I brush our teeth every day, our dogs do not.

So, dogs and cats actually need that too, because everything they eat, that plaque kind of builds up.

And we do full dental procedures where they do have to be under general anesthesia, so they can't, you know, bite our fingers or don't like having that stuff put in their mouth, but they get scaled and polished, and we even take full X-rays of all of their teeth, so we make sure nothing's missing, nothing's broken.

But we do have a regular X-ray machine that we can look at.

Depending on what part of the body we're measuring, if a dog has a cough, they have to measure the size of the chest, and we have to have the size right, so that the radiation used for the X-rays penetrates it properly, so we can see everything we need to see.

My dog, Biscuit, weighs 11.7 pounds.

The vet needs to round his weight to the nearest pound.

What is Biscuit's weight rounded to the nearest pound?

[clock ticking] 11.7 rounded to the nearest pound is 12 pounds.

Biscuit's weight rounded to the nearest pound is 12 pounds.

Did you get it correct?

One thing that's kind of interesting, when you go to school to be a veterinarian, even if you think you only want to work on dog and cat, we have to learn all the different species.

And there's definitely big differences between a large animal vet and a small animal, but everybody kind of has to get that baseline.

Some people end up working in zoos with exotic animals.

Every animal kind of comes with its own little quirks and things you need to know about them, so it's a lot of information.

Yes.

Caroline: Have you ever seen a chicken?

I have never seen a chicken in practice.

Yep, I've never worked on a chicken.

My name is Dr Jennifer Zablackas, and this is How It's Math.

Did you know that math is hiding in your favorite songs?

Today, we're visiting the Westerville Jazz Orchestra to see how music and math go hand in hand.

We'll find out how musicians use numbers to count beats, how different notes are like fractions and how patterns help make music sound just right.

We'll even talk to a real composer to learn how math helps create brand new songs from scratch.

Let's dive into the world of jazz and discover the rhythm of math.

Let's talk to a composer to see how he uses math.

When you're playing music, it's almost an automatic thing to use math, the basic fundamentals of math, and you're doing it all the time, as far as counting rhythms and deciphering how long and how short to hold notes.

Okay, let's talk music and math.

Did you know that notes are like fractions?

Yup, a whole note is the longest.

It takes up the whole measure, kind of like eating a whole cookie, yum.

But if we split that cookie in half, we get two half notes.

And if we split it into four equal parts, you guessed it, it's quarter notes.

Musicians use these note fractions to count beats and keep the rhythm.

It's like math that you can hear.

Cool, right?

Music in general, the terminology is all mathematics and numbers like the names of the notes or fractions.

And we have a whole note, a half note, quarter note, eighth note, 16th, and the smaller you get, the shorter the note becomes.

And then you're trying to add how many beats to hold a note, you know?

So, sometimes it's a whole number, sometimes the number in a fraction.

So, those things happen constantly when you're playing, particularly when you're reading music.

So, it really is a mathematical process.

Did you know that math and music go way back, even to ancient Greece.

A mathematician named Pythagoras discovered something really cool about sound and numbers.

When you pluck a long string like this, it makes a low sound, but when the string is shorter, the sound is higher.

Pythagoras figured out that if you cut a string in half, like going from 12 inches to six inches, it makes a note that sounds really good with the first one.

That's because the lengths are in a special ratio, 2:1.

Musicians still use these math ideas today when they tune their instruments and write music.

So, when you're hearing your favorite song, just remember those awesome sounds are made up with the help of math.

By his method, those 12 notes are what we call a chromatic scale.

Did you know composers use patterns to write music?

One common pattern is called ABA.

That means the music starts with one part, then changes to something different, and then goes back to the first part again.

So, it might sound like this, ♪ Twinkle, twinkle, little star ♪ ♪ How I wonder what you are ♪ ♪ Up above the world so high ♪ ♪ Like a diamond in the sky ♪ Twinkle, twinkle, little star ♪ How I wonder what you are.

It's just like how we use patterns in math to figure out what comes next.

Patterns help composers make music that feels exciting, but also makes sense to our ears.

When I compose a piece of music, I think an idea, a concept, and then I use the math to translate my idea onto paper, into the language.

I have to figure out -- what notation do I use to make that look right and play right for a player to look at it and read it.

[trumpet playing] The composer is writing a song.

He wants to turn this quarter note into eighth notes.

How many eighth notes will he need for the same amount of time as one quarter note?

[clock ticking] [bell ringing] 2/8 notes.

Two eighths are equal to one quarter.

Here, look at these fractions.

Two over eight is equal to one over four or one quarter.

Did you get it correct?

Whether it's music or whether it's building or whatever it is, math is like a tool box that allows you to do so much in so many ways.

My name is Rick Murray, and I am a composer, and this is How It's Maths.

Have you ever wondered how cities decide where parks, playgrounds, sidewalks and streets should go?

Urban designers and landscape architects help plan and design the outdoor spaces we use every day.

They create parks, plazas, playgrounds and streets that are safe, beautiful and easy for people to use.

But designing these spaces takes more than creativity.

Urban designers use math to measure distances, calculate areas, determine slopes and make sure everything fits together correctly.

In this segment, we'll meet professionals who design outdoor spaces and discover how math helps shape the places where we live, work and play.

Let's explore how urban design uses math.

My name is Jason Sudy, and I am a planner, an Urban Planner with OHM Advisors, and there's a lot of different kinds of Urban Planners, and mostly what I do now is transportation planning.

How do you use math?

There's the world around us and all the things that you see, whether it's a road or a building or a park, someone has to figure that out.

And what Urban Planners do is figure out kind of all the spaces in between.

Sometimes it's the roads themselves.

That's what a transportation planner does to use math every single day.

So, we'll take this whole section and we'll divide it up.

So we'll say, I'm going to have a 10 foot lane, and I'm going to have an 8 foot parking lane, and I'm going to have a 5 foot tree lawn, and I'm going to have a 3 foot, no, that's too skinny, 5 foot, maybe 8 foot sidewalk, and then I'm going to have room maybe in front of the building for landscaping, and then we have to put all that math in there, and it's just a certain amount of space.

So, once we get all of that figured out, then we can actually transfer that to a hard plan that gets built, and that is done in a computer on a thing called CAD, and someone can take that and go in the field and actually build it.

My name is Anne Herron, and I am a Landscape Architect.

So, I work primarily with cities to enhance or create new spaces such as playgrounds, parks, streetscapes, all the fun stuff that you get to play in.

What does a typical day look like?

So, in my role as a landscape architect, I take ideas and concepts.

So, I take another co-worker of mine may come up with this pretty picture plan.

So, I take his little hand sketch, and I spend a lot of time putting the pieces together, making sure it fits.

A lot of times I tell him that doesn't work, because in the real world, and doing all my math problems that I'm doing as I'm putting this together, I can say this isn't possible, or we'll figure out, we problem solve and figure out a solution to make it possible.

How do you use math?

So, I use math every day, and there's kind of different levels of math that I'll use.

A lot of mine is shapes, circles, using angles to figure out how pieces come together.

So, angles are really important because there are a bunch of rules and laws that have to do with how steep things can be.

So, if you're walking down the sidewalk, you don't want it to be really, really steep, because you also have people that may be in a wheelchair, and if it's too steep, they don't have a way to stop.

So, there are rules that the steepness of that for the wheelchair can only be 8.33%, is the max slope that you can have.

So, when you're trying to figure out how someone is going to get from point A to point B, and you have a 5 foot drop, there are going to be ramps and slopes that go within that, so then someone feels safe when they're kind of getting from there -- where they're at to where they need to go.

My name is Andre Banerjee, and I am an Urban Designer here at OHM Advisors.

So, my job specifically is a visual representer of our plans and designs.

So, basically, what that means is, if you've ever played a video game like Sims or Zoo Tycoon, and you have an idea that you have in your head and you want to visually represent it in the computer, that's what I get to do every single day.

How do you use math?

So, I use area and perimeter in my everyday job.

I take what is drawn on paper and have to represent it in the computer at the measurements that it would be in real life.

So, a lot of what I work with is scale, and scale means that you are taking the measurements of the real world and shrinking them down to a size that is manageable and easy to draw on, and so that can take the form of a tree being 30 feet in real life, but maybe it's 6 inches on the screen or on a computer.

Isn't it important to show your thinking?

It is super important to show your thinking always.

When you are visually representing things in the computer, it takes a lot of time.

And as designers, things always change, and then you always have to work on your feet, and sometimes you have to go back to previous concepts that you did before.

That's why it's always important to show your work, to save your work, because if you were designing something, and somebody says, Oh, I really like what you did before, but you didn't show all your work, you didn't save your work, it's going to be really hard to go back and replicate what you did.

[bell ringing] A landscape architect is designing a fence around a playground.

The fence will be 120 feet long, and the cost of the fence is $80 per foot.

How much will the fence cost in total?

[clock ticking] Let's figure it out.

The fence costs $80 for every foot.

The total length of the fence is 120 feet.

So, we multiply 120 by 80, which equals 9,600.

The total cost of the fence is 9,600.

Landscape architects use math like this.

When creating cost estimates for projects.

They calculate the length of materials, multiplied by the cost and add everything together to figure out the total price of a project.

How did you get to the position you're at today?

I'd say, when I was younger, doing math, basic geometry, there was just something that drew me into the shapes and the spaces, two dimensional versus three dimensional, and the problem solving of putting things together.

And I also really liked art, and so landscape architecture, I discovered was kind of a blend of the natural environment and the artistic.

And then also like math and the technical part of it, so I got a degree in it, and I've been doing it for 15 years now.

Do you have any advice for us?

If you like to do any kind of puzzles, logic puzzles, or anything that involves thinking of unusual ways to solve a problem?

I would recommend that as much as you can, that's almost what we do every day.

All of that just helps you think about things in a different way.

And when you get stuck, know that you need to change to a different process.

So, I would do as many logic puzzles as you can get your hands on that you think are fun, and figure out those and whichever ones you like, just keep doing more of them, and you will absolutely use those every single day as you go forward in your career.

Today, we learned that math plays an important role in designing the places around us.

Urban designers and landscape architects use math to measure spaces, calculate slopes, estimate costs and make sure parks, sidewalks, and playgrounds are safe and accessible for everyone.

Math helps turn ideas into real places people can enjoy.

The next time you walk through a park or playground, remember math helps design that space.

Math isn't just something you use in school, it's something designers use every day.

I'm Jason Sudy.

I'm a transportation planner.

My name is Ann Herron, and I'm a landscape architect.

My name is Andre Banerjee.

I'm an Urban Designer, and this is How It's Math.

Have you ever watched a cartoon, a movie or a video game and wondered how animators make everything move so smoothly?

Animation is all about bringing pictures, characters and objects to life, but behind all that creativity is a lot of math.

Animators use numbers to measure time, control movement and make sure things look natural on the screen.

In this segment, we'll meet an animation director and discover how math helps create motion, special effects and realistic scenes.

Let's take a closer look at how animation is powered by math.

My name is Brian Finney.

I'm the Director of Animation and Motion Graphics here at Spacejunk.

So, animation is generally thought of just making stuff move, right?

It can take many different forms, from full on cartoon style animations all the way into 3D animation, but animation also encompasses things like visual effects, right?

So fire, smoke, water, so animation sometimes is a catch all term for a lot of different post production effects.

How do you use math?

So, math and animation is really important, and everything is sort of based off the frame.

And there's different frame rates.

So, there's 24 frames a second, there's 30 frames a second, 60 frames a second.

That's just the number of pictures that are shown on a screen within one second, and the number of frames that is shown in one second over the course of multiple seconds will start to generate movement.

So, how we calculate the amount of change in an object from one state to another over time is generally done via math, and that can be in terms of realistic motion, understanding how an object in real life moves, and replicating that.

So, in this particular example, we need to have this car go 15 feet down the road.

Now, its wheels are not turning right now.

We need to figure out how to go 15 feet down the road and have the wheels turn realistically.

Now, if we do that, and we don't turn them enough, it's going to cause an issue where the car looks like it's sliding even though its wheels are turning, which is obviously wrong.

You can also go too far with it, where you make the wheels turn too much, and now it looks like it's spinning out, but still moving forward at a slower rate of speed, which obviously looks wrong as well.

So, using some simple math, if you take the tire and we make some assumptions, and we assume that tire is 25 inches in diameter, so 25 inches across, we can extrapolate that over 15 feet.

So, if we have our wheel, we need to get 15 feet.

We can take that.

We know it's 6.54 feet per one rotation.

So, that's one rotation, two rotations, and then point two rotations.

So 6.54 feet plus 6.54 feet plus 54 inches, right?

And that's how much our wheel needs to turn to rotate realistically.

So, when we plug that into our wheel rotation numbers down here, which we have little parameters here that we can enter how many times the wheel needs to rotate.

When we plug all that in and we hit go on it, now the wheels will move realistically for the distance the vehicle is rolling down the street.

What data or numbers do you use daily?

The funny thing about elapsed time is it really is the core ethos behind animation.

It's how long something takes to do something.

So, say it's an animated film and someone is dropping a ball, that ball drops and bounces.

How long does it take for that ball's energy to dissipate, right?

And that is sort of elapsed time, and we have to sort of understand how much time to give the animation to play out, so that it feels natural.

What tools do you use when using math?

Especially in the 3D world, from like the moment you open the project, you are dealing with measurement.

A lot of times we refer to as world scale.

That scale becomes really important.

So, for example, we're going to add a figure, right?

We're just going to -- this is going to be our little person standing here for the moment.

Let's say we understand that our person is going to be 6 feet tall.

What I'm going to do is I'm going to essentially work off of a measuring stick.

So, I'm going to put a cube down here.

Okay, we'll just shrink the cube down here.

And this cube I'm going to go in, and I'm going to make this cube 6 feet tall on the Y-axis.

That is a 6 foot tall measuring stick, okay, in our world space.

And if I want this character to be 6 feet tall, well, now, I just need to -- so not 6 feet tall.

I could maybe adjust it up a little bit, or whatever to match, but then that gives me an understanding of what six feet is.

So that means, if I bring in a ball, let's say it's a basketball, and I know a basketball in real life is 12 inches, I can now scale this down to be 12 inches as well, and that way it'll be realistic in size and proportion to my character.

So, real scales measurement always come into play when you're working in a 3D world space.

An animator is creating a scene where a ball drops and bounces for 6 seconds.

The animation plays at 24 frames per second, meaning 24 pictures are shown every second.

How many frames are needed to create the 6 second animation?

[clock ticking] [bell ringing] Let's figure it out.

We know that animation plays 24 frames every second, and the bouncing ball scene lasts 6 seconds.

So, we multiply 24 frames per second by six seconds to equal 144 frames.

That means the animator needs 144 frames to create the full 6 second scene.

In animation, each frame is like a tiny picture.

When all those pictures play quickly, one after another, they create the illusion of movement.

So, when animators play in a scene, they use math to figure out exactly how many frames they need to make the motion look smooth and realistic.

Today, we learned that animation uses much more than drawing and imagination.

Animators use math to measure time, set key frames, scale objects and make movement look realistic, whether they're animating a bouncing ball, a turning wheel or a special effect in a movie, math helps everything line up just right.

The next time you watch an animated scene, remember, math is helping bring it to life.

Math isn't just something you use in school, It's something animators use every day.

My name is Brian Finney, and I'm a director of animation, and this is How It's Math.

Wow.

Look at all the ways math supports both creativity and care.

Today, we saw professionals using math to treat animals, create music, design spaces, and bring animation to life, whether it was rounding numbers, working with fractions, measuring spaces or calculating frames, math played an important role in every job we explored.

The next time you listen to music, visit a park, watch an animation, or take care of a pet, remember, math is helping make it all possible.

Thanks for exploring with us on How It's Math.

I'm Caroline, and I can't wait to discover more real world math with you next time.

Male Narrator: Funding for this program is provided in part by... Female Narrator: We believe in getting outside, playing in the yard, growing things and connecting with the earth.

We believe good can grow anywhere.

That's why we're committed to GroMoreGood, everywhere.

And also by...