-Funding for "Doodles and Digits: How It's Math" provided in part by... -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 grow more good everywhere.

-Hi, I'm Caroline from "Doodles and Digits."

And did you know that there's math all around you?

Today, we get to go behind the scenes of three different places that use math every single day.

We're going to first start out by interviewing a structural engineer, where she tells us how she uses math to build large buildings.

Then we're going to go to a physical therapist, where she explains how she uses angles to measure different joints.

Finally, we get to go behind the scenes of a ski resort, where they show us how they use math to make snow.

Get ready to see the math in the real world.

-♪ Doodly-doodle, doodly-doodle ♪ ♪ Doodly-doodles and digits ♪ ♪ Area, symmetry, fractions, too ♪ ♪ It's all here for you ♪ [ Bell rings ] -My name is Fae Garstang, and I am a professional engineer.

I work for Schaefer, and we design structures.

So, as structural engineers, we creatively choose and design the material, the pieces and parts, to make the building possible.

-Alright, so what exactly is a structure?

-Well, you can think of a structure as anything that is built.

From a tree house to the Golden Gate Bridge, it all started with somebody's idea, and somehow all of it had to come together.

So, structural engineers, we take that vision that our client has or that we have, and we put the bones inside it and the muscles inside it, everything that it takes to hold the building up, to make it safe, to make it serve its purpose.

We have to design around the rest of the guts of the building, the HVAC, the air conditioning and heat, the electrical, the plumbing.

We have to make it all fit.

The first way that you use math as a structural engineer is that the building all has to come together, and everybody is contributing to that.

So, you have to be very precise in the way that you draw in detail the building.

You have to make sure that you leave enough room for everything that needs to happen in between the bones and muscles.

You have to make sure that the loads that you are putting on the building, that you're designing for, they are correct, that they go to the right place, that all of the connections that we design for, the, I guess, what you would call the ligaments of the structure, you know, connecting everything together, that they are strong enough to hold the building up and that they are in exactly the right place.

You also have to make it easy to build, so you have to have an understanding of what people can do with the materials, with the wood or the steel or the concrete.

All of that has to come together in the building, and each piece is dimensioned.

It has a length, a width, it has a weight.

And so we use numbers all the time for that.

And they just become all the little pieces that fit into this puzzle.

We definitely use geometry all the time just to lay out the building.

We work with the architects' plans, the way that they would like to see the building and the way they'd like the building to work.

And then we have to fit everything in.

So, geometry is a big thing.

But we don't only use geometry for laying out the physical pieces of the building.

We also use it to imagine or envision the loads on the building.

For example, if you're designing a structure or a building for a heavy snow load, the snow falls down on the building and it comes like a blanket on the roof.

But then the wind blows, and it pushes all of the snow to one side, up against a wall.

Now, that snow drift, which that forms a triangle.

And when we are designing the beams, the joists that support that roof, we have to design it for more snow on this side than we design it for on the other side.

We do that by figuring out what the height of the triangle is, and the length of the triangle, and then deciding how much of that weight goes to each part of the building underneath it.

So, that's one way that we use geometry to imagine what the structure needs to carry on the roof.

-Quick questions with a structural engineer.

What is your favorite thing about math?

-The interesting thing is that I didn't know that I liked math when I was a kid.

It's only when I started wanting to solve problems that I found out that I liked it.

Um, I thought about math like a hammer.

I was not interested in hammering things, but when it came time to build things, it became very interesting to me.

It's a tool that you use to get what you want done, and if you're a creative person, this tool works its way into your life all the time, regardless of what you're doing.

-How important is it to be precise?

-It's very important to be precise as a structural engineer.

All of the pieces of the building have to fit together perfectly, and we are working with so many different teams -- the plumbing, the HVAC, the architect has walls that need positioned exactly, and we need to be able to fit everything together in that.

Not only that, but there's a lot at stake.

You know, the primary purpose that we have as structural engineers is to make buildings safe.

And so, if we are not precise, then that can cause a lot of problems.

We also need to be very precise because they need to be able to build it.

And if we are not precise, then the plans that they get in the field for building it and what our intent were, they're not going to match up.

They're not going to be able to construct the building.

We have many goals as structural engineers.

We want to make the building cost efficient.

We want to make sure that it fits together well for all of the different trades who are involved.

We want to make sure that the way we construct it makes sense, that it's easy to build.

But above everything and before everything, our job is to make the building safe.

And so, it's very important that we are precise in our calculations.

-Do you need to show your thinking?

-Engineers definitely need to record their work carefully.

If we don't keep track of our calculations, it would be incredibly time-consuming and difficult to make any changes or to go back and explain ourselves.

We also often come up with really original or interesting ways of doing things, and so, we need to be able to show our thinking in order to explain it to other people after the fact.

And also, if we come up with a great way of doing something, we need to show our work so that we can make tools that we can use to do it more often and more easily.

So, we often take project work that we've done something creative or something new, and we turn it into a tool that we use regularly.

-What tools do you use as a structural engineer?

-The first tool we have is the drawings.

And the drawings can either be on the computer screen -- because looking at the drawings on the computer gives you a lot of flexibility.

You can get very precise with your measurements.

You can get a bigger picture and a smaller picture, all at once.

Drawing things on paper is a great way to visualize how the connections come together.

A very efficient way to put together a detail that we're then going to use to figure out how the structure comes together.

For our calculations, we often use Microsoft Excel, which is a program that we can use to generate many calculations very quickly and efficiently.

We have very sophisticated structural design software that we use to help design the whole building.

And when we are learning how to use these tools, we need to have a good understanding of how they work.

Structural engineering programs give us a huge advantage because they take small calculations and replicate it for the entire structure.

So, by understanding how they work for each component, we can allow that structural design software to help us do the heavy lifting on the project, to do those calculations over and over.

Just like in a math problem, if you understand what the process is for addition, division, geometry, all of these concepts, then you can use a calculator and be confident in the results because you know what that calculator is doing.

But first, you have to prove it to yourself, so that you understand.

-Did you enjoy math growing up?

-I was not interested at all.

And then it came time, and I suddenly discovered that I wanted to be an engineer.

And that was a surprise to me.

[ Laughs ] I was not at all prepared.

So, if you enjoy math, then you are at a huge advantage because it'll make getting good at it easier.

If you're like me and you don't really enjoy this part of it, put the work in now, and you'll find out that it opens doors for you that you never expected.

Whatever your dream is, math is going to give you an advantage if you are comfortable with it, no matter what that is.

If you are an athlete, if you are an artist, being a good business person is going to help you no matter what you do.

And if you, very late in the game, find out that you want to be an engineer, you'll be much better positioned.

It'll be easier for you if you do the work now, even when it's hard.

-Do you ever have mathematical disagreements?

-That is actually some of the best fun that you can have in this job is getting into a real discussion about an interesting idea, or an interesting method or something in the code that people disagree on, because you've learned so much from those discussions.

If you can keep your pride out of it and just make everything a learning experience, even by disagreeing with somebody and listening to what they have to say, you learn so much.

We work very visually, often.

So, when we are talking about a detail that we want to approach two different ways -- somebody wants to frame it this way, someone wants to frame another -- we would go to a whiteboard or a common space or a piece of paper, and we just start sketching it out, and we talk about how it comes together, and then everybody has their say on it.

If it's a calculation, if it's numbers, then we start showing how we got there on the page and start talking about all the little pieces that go into it.

-What is your best piece of advice for math students?

-Put in the work now.

Even if you don't love the subject, even if you don't like doing these little tasks over and over again, building your confidence in this subject is going to give you tools that you'll use no matter what you do.

-Now that we've seen how a structural engineer uses math every single day, let's discover how a physical therapists uses math.

-Hey, I'm Dr. Kayla Borchers.

I am a physical therapist, board certified in orthopedic physical therapy, and I'm a prenatal and postpartum corrective exercise specialist.

-Alright.

What is a physical therapist?

-A physical therapist is a health care professional who are experts in how the body moves.

Being a physical therapist is so much fun because I get to help my patients heal through movement.

No day is the same.

Each time when a client comes in, I'm reevaluating them.

So, the plan I had in my mind, I might scrap if they're feeling way better than I thought they would, or maybe not so good because they just got back from a long car trip.

So, I'm constantly adjusting on the fly to meet my patients' needs, and they're leaving me feeling better and returning to a life really well lived.

So, as a private practice physical therapist, I'm not only a physical therapist, I'm also a business owner.

So, my day starts by opening the studio, getting the lights on, getting my table all set up, logging in, seeing if I have any client e-mails to respond to, and then checking out which clients I'm seeing for the day.

So, I'll do a chart review on them if they're a new patient, seeing their intake criteria.

So, that's where they tell me about what complaints that they've had going on, what symptoms they've had that are bringing them in.

And then for any existing clients, I'm looking at what we did last appointment and helping to derive my game plan for that day's appointments.

Alright, so, as a physical therapist, we use these things called goniometers all the time.

So, what we use this for is to look at joint angles.

So, for instance, we might see if somebody is at a right angle for their dorsiflexion.

That's considered neutral.

That's zero.

And dorsiflexion, in case you didn't know, is how much your toes move towards your shin.

So, if we're measuring that angle, we want to see how far somebody moves.

I put one arm along their shin, one arm along their foot and move it.

And then I have to subtract from 90 degrees, which was my neutral, how many degrees they moved.

So, that helps me get a comparison from their injured side to their non-injured side, or looking at them at an initial appointment, compared to when we're done with our course of care.

So, patients have scheduled appointment times.

So, it's very important to be prompt and timely.

So, if I know a patient starts at 2:00 p.m., I am going to be finishing up my patient before them probably five till 2:00, so that I have time to clean my space and be ready for that next patient.

Now, in an insurance-driven model -- which I'm no longer a part of, as a private practice owner, but when I was -- there's these 15-minute increments you need to align by.

So, if you see a patient for 45 minutes, you can bill three units because it's looking at 15-minute increments.

If you see a patient for 60 minutes, you can bill four units.

And so, keeping track of time, especially in an insurance- or hospital-based setting, is very important because it determines how much you can bill for your services.

I'm counting all the time.

We count people's repetitions.

I'm saying, you know, "Do three sets of 10 or three sets of 15," and then looking at that overall number.

So, if I'm counting somebody's repetitions, one visit, they might do three sets of 10.

So, that's 30 total repetitions, right?

3 times 10.

Then, the next time, I might have them do two sets of 15.

So, we're still getting 30 total repetitions -- again, that multiplication -- but we're doing it in two larger chunks, so it makes the exercise more challenging.

-Quick math questions with a physical therapist.

What math tools do you use?

-Alright, so my tools -- trusty goniometer, a tape measure, a calculator, and then my mind.

-Why is it important to be precise?

-It is important to be precise as a physical therapist because, as mentioned, with those angle measures, if you're not precise and you say that somebody's ankle movement is perhaps eight degrees, but you weren't precise, and somebody else measures it and finds five degrees, when you go to check for change a month down the road, your angle may say that there's been no change because they're still measuring at eight.

But if you had been precise in the beginning and found that their angle was five, you would have noticed that three-degree difference.

So, precision is very important, both you compared to you -- so, what that's called intra-rater reliability.

But it's also important, me compared to another physical therapist.

So, if I'm working with somebody in a team setting, if I'm not accurate in my measurements, and then they're doing a follow-up to somebody later on, then we may not see the differences in improvement that we want to see for the patient, because the first person or the second person hadn't been precise.

-How important is it to show your thinking?

-As physical therapists, we have to keep notes about what we do with our patients so that whenever I see them for a follow-up visit, I know what we did the last time.

So, for instance, we'll take it away from the ankle.

Let's look at the shoulder now.

Last time, somebody moved to 160 degrees for their shoulder flexion.

Next visit, I'm going to look at how far they're moving, and if they're only moving to 150, I'm going to look at last week's notes and know, ooh, they're doing worse.

What may have changed?

You know, what can we do to improve that?

If I hadn't taken notes and just thought, "Okay, they're at 150, let's go from there," we're not seeing what progress or regression we've made since the last appointment.

-Did you enjoy math growing up?

-Oh, my dad always told me growing up that it's all about math.

It's all about math.

He said that all the time.

So, I liked math when I was in high school and junior high, elementary, all of that.

I enjoyed math, but now I use it in my day-to-day more than I realize whenever I actually sat down to think of it.

But my favorite thing is that there is a distinct answer.

So, sometimes, you know, we can get caught up in the gray and argue, you know, back and forth with people about what's right, what's wrong.

But in math, there's really just one right answer.

-What is your biggest piece of advice for math students?

-My biggest piece of advice for you at this stage in your math-learning journey is to think about how it relates to real life.

So, that's where these videos are really cool.

Let's say you want to work with the human body.

You want to help athletes return to sport.

You want to help moms feel the best during pregnancy and postpartum.

This still involves math, just in a different way than your, like, set criteria that you're maybe looking at now.

So, it may seem repetitive right now, but in your line of work, you will use it.

I use multiplication all the time.

I use joint angles all the time.

We even use a tape measure and look at circumference all the time.

Thinking of those real-world applications can be really helpful.

♪♪ ♪♪ ♪♪ -Have you ever been curious about how ski resorts always have the perfect amount of snow for skiing and snowboarding?

Well, today, we actually get to go behind the scenes of a real ski resort, where they make snow to make sure that the conditions are perfect for your winter activities.

Here in Ohio, snow isn't always the most reliable.

Sometimes there's a ton of it, sometimes there's not very much.

So, they actually make their own snow to make sure that there's always enough.

What's awesome about it?

There's tons of math involved.

So, today we get to discover exactly how they use math for creating snow, what angles have to do with skis, and also how they use charts every single day.

♪♪ ♪♪ -I'm Nate Wolleson, and I'm the marketing manager here at Snow Trails.

There's a lot of ways we use math here at Snow Trails, from our points of sale with cash being handed, credit card transactions, things like that.

We do lots of inventory and quantities.

With our snowmaking system, we use different calculations that help us to understand wet bulb and things that deal with temperature.

And in marketing, we use click-through rates, different things that help us to understand the numbers and how are we doing?

what does success look like, how do you figure out your reports and then make decisions for the future.

We always want to make the best product out here.

Our product is snow.

When you take the right temperature and the right humidity, it comes together with a calculation called wet bulb temperature.

And in order to have dry snow, to make sure it's not wet -- I mean, everybody loves to make a snowman, which is wet snow.

It packs together well.

But out here, we want it to be powdery.

We don't want it to be wet because if something gets cold, it freezes then, right, if it's wet?

So, we don't want ice.

This is snow.

We want to have a great product.

So, ultimately, being precise with snowmaking helps us to control the product, make sure that the snow is really good, and then it skis and snowboards much better.

For making snow, we have a very complex process, but it breaks down into water and air and a little bit of pressure.

So, the whole process starts in our pump house.

We have different pumps that are very powerful, that push the water out to each snow gun, and we want that water to be really cold.

So, we actually added a cooling tower as well that can first cool the water down by 13 degrees before it goes out to the snow gun.

The colder the water, the faster water can turn into a snowflake as it goes out of the snow gun.

So, it's a process that is really fun to watch.

It's something that's really incredible.

We're making snow out here.

There's nothing fake about it.

Basically, you take water and compressed air and push it out to each snow gun that has a large fan that blows the water out into the air, and then it falls, which is called cure time.

And then we have snow.

Our snowmakers are out checking each snow gun throughout the process, but we love it.

It's called a bounce check.

So, we'll have a snowmaker out there with his jacket that's waterproof, and if the snow bounces off of his jacket, then that means that it's dry snow.

If it sits and melts just right on his jacket, that means that the temperatures are either a little warm, or maybe we are using too much moisture, so we'll back the gun off.

We have different banks that can make it to where you're not putting as much moisture out into the air.

With snowmaking, we have to estimate how much water is needed at certain temperatures.

And then we reference charts.

We use different resources, like our online platform that helps us to see each number and help us to estimate how much water we can use at certain times to make the best quality snow.

Yeah, in our rental center, we have equipment that's sized and set specific to you and your ability level.

So, you'll come in, and our technician will take your height, weight, and ability and look at a chart and make sure that that binding for your boot is set properly to your weight and ability.

Yeah, we have a ski shop here on site, which is really neat because it's a full-service ski shop.

And so, downstairs, we have different things that tune the equipment, skis or snowboards.

And so, specifically an edge-sharpening machine that will angle your edge, based on how much grip you need out on the snow.

That's something that you can do certain angles that makes it tune different for each skier and snowboarder.

And that's really cool because we have some angles that we're dealing with.

And in order to have the right angle, a special machine is doing that for us and for each skier and snowboarder.

Yeah, our tubing park has a conveyor carpet lift and a certain number of tubes that we allot per hour.

So, you take guests coming in each hour, and you make sure that we don't have too many guests on our conveyor carpet at one time and even going down the lanes to make sure each is staged at the top and going down each lane of snow.

So, we take that and we figure out what is the proper amount of people to have per hour.

And we set that as quantities, and we put that on our reservation system.

Yeah, our snow sports department has both ski and snowboard lessons taught at every ability level.

We'll have first-time lessons coming in, and we set those every half an hour to make sure that we're there and available for guests who need to learn how to ski or snowboard for the first time.

And then we also have other levels available for private lessons and semi-private lessons.

And so, we'll set quantities available for making sure we have enough instructors based on how many people come in.

And so, we'll just align how many instructors do we need based on how many people are coming out for, say, a group lesson of 10, and that goes out for an hour and a half.

You have to do some calculations to make sure that you have enough instructors.

And then we're serving the guests as they need, based on their lessons.

Each of our lifts have a certain number of chairs, and we make sure that we space those out properly along the rope that we call -- it's actually a wire rope.

And so, it's tensioning the system based on hydraulics and so you can know how many people you can carry uphill.

And you set these things with a system that's very sophisticated, but it's just a tensioning system to make sure that you don't have sag of the chairs and you're able to carry people up at a certain speed.

And so, there's a lot of different calculations that go on.

But it's pretty neat, and it's a fun ride and a great view.

-Do you use measurement here?

-So, in our maintenance department, we have a lot of different ways to measure, take measurements to use in building something or fixing something.

We have angles of different machines that you can get a different cut on a piece of wood or all the way to our snowcats that have different measurements for hydraulic systems, a lot of different moving parts here.

And so, a lot of that means measuring properly, taking a calculation, and then fixing something back to its spec.

That would be the proper settings or the proper pressure in order to have everything operating as you'd expect it to out here and don't have any downtime.

-How do you use charts here at Snow Trails?

-Oh, we have charts in a lot of different departments, from our maintenance facility with different measurements for our machines, to our rental center with measurements for how we set these for each individual, even into our ski shop where we have service departments that make sure that binding releases are set properly for, again, height, weight, and ability.

A lot of different charts that you can really look into further that help us.

It's not always a calculation, it's just following the chart and using that.

The other one is our wet bulb temperatures for snowmaking.

That helps you to see what's the temperature and when we can make the best snow and use the most water to do that.

Snow Trails, it's a lot of fun to get out in the winter and enjoy skiing and snowboarding, and we hope that you'll come and join us.

Funding for "Doodles and Digits: How It's Math" provided in part by... -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 grow more good everywhere.