Transcript for NASA Connect - Proportionality - Modeling the Future

[Danica Mckellar:] Hi,
I am Danica Mckellar

when I was your age I played
a character in Winnie Cooper

on a television show
called 'The Wonder Years'.

You may be wondering what an
actor like me knows about math

and science, one fact
I love science so much

that I measures mathematics
easier way.

On today's episode of NASA Connect,
you will discover how ratios,

proportions and mathematics are
found in nature, in our bodies

and in things we create.

We will also see how
in the near future,

you may be taking drivers add
and flyers add at the same time.

So prepare to take
off as host Van Hues

and Jennifer Pulley forward you
to this episode of NASA Connect.

[Jennifer:] Hey guys,
welcome to NASA Connect,

the show that connects
you to the world of math,

science, technology and NASA.

He is Van Hues.

[Van Hues:] And she
is Jennifer Pulley.

We are your hosts
along with Norbert?

He is going to help us take you

to in other awesome
episode of NASA Connect.

[Jennifer:] Right, every time
Norbert here is have your Q cards

and your brain ready
to look for answers

to the questions he
gives you and teachers.

When Norbert appears with a remote
that's your Q to pass the video

and think about the
problems he gives you.

Got it.

>> Oh yeah, I got it.

[Van Hues:] Today we are
in City of North Carolina.

This is where the Wright Brothers
took the very first control power

flight in 1903 and guess what...

[Jennifer:] What...

[Van Hues:] They used
mathematics like ratios.

>> What is the ratio?

[Jennifer:] Good question.

All ratio is a pair of numbers
that is use to make comparisons

and ratios are everywhere.

Get this, before the Wright
Brothers pull planes;

they were experts in one of the
most revolutionary means of travel

since the wheel, the bicycle.

[Van Hues:] So in memory of the
Wright Brothers pre-flight days

that used this bike as
an example of a ratio!

[Jennifer:] Good idea Van.

Let's say, we want to compare
the number of revolutions

or complete circles that one
tire makes to the distance

that the bike travels.

Pretend this wheel measures seventy
six centimeters or thirty inches.

By measuring the distance that the
wheel rolled after one revolution,

you can set up a ratio.

One revolution to two hundred
thirty nine centimeters.

[Van Hues:] Right, when you
find ratios you are also

using proportions.

A proportion is a number
of sentence or equation

that states the two
ratios are equal.

How could you use
ratios and proportions

to determine how far
you bike would travel

if the wheel made five revolutions?

[Jennifer:] Simple, set up
of proportion like this.

One revolution to two hundred
thirty nine centimeters equals five

revolutions to X which
is the unknown distance.

Now, like cross multiplying,

we can see that the wheel would
roll one thousand one hundred

ninety five centimeters
in five revolutions.

Notice, that the fraction
ratios are equivalent.

Hey, here's another
form we have to try.

If your bike wheel
makes one revolution

and travels two hundred
thirty nine centimeters,

how many revolutions
would your wheel make

if you travel two thousand
three hundred fifty two point

three inches?

Be sure to watch your units.

[Van Hues:] So now that you have
a better understanding of ratios

and proportions, let's get
back to the Wright Brothers.

>> How did mathematics in ratios
help the Wright Brothers test

and design their glider?

[Van Hues:] Before Fire-one the
Wright Brothers were done bicycles.

As young man, Orville and Wilbur
started the bicycle manufacturing

and repair company in
their home town of

[inaudible] Ohio.

The Wright Brothers
use the money they made

to finance their interest
in aviation.

In the winter of 1901 Orville and
Wilbur Wright used their knowledge

of math to build the wind
tunnel in order they study how

to control an aircraft.

It was then that they realized
the importance of ratios.

[Jennifer:] Right!

The Wright brothers used
something call the aspect ratio,

that is the ratio of the
wings linked to the wings

with by increasing
the length of the wing

and at the same time
decreasing the width of the wing.

The Wright Brothers cut the drag
they experienced in the wind tunnel

by half, immediately they began
designing a better working glider.

[Van Hues:] In 1903, after adding a
rudder and engine and the propeller

to the aircraft, the Wright
Brothers achieved the first self

prepared flight of an airplane and
began the era of powered flight.

>> Describe the

[inaudible] transportations
since the early 1900.

What is


>> Hi, I am

[inaudible] Williams, pilot
and air-traffic-controllers

with the Federal Aviation

Back in 1903, there
is only one aircraft.

Not much need for us to have
a traffic control system.

However, by 1960 there are over
seventy eight thousand commercial

and general aviation
aircraft and in ten years

by the year 2010 we believed
there will be almost two hundred

and twenty eight thousand.

Air traffic is growing and growing.

We anticipate by the year 2010
almost one billion people will be

traveling by air.

The air 2003 begin century
number two of aviation,

I hope in ten years or so you
will be one of the visionary

that one share my safe and
efficient flight by designing,

building, maintaining,
controlling or flying the aircraft.

The future aviation
is in your hands.

>> You know

[inaudible] Williams is right.

Mathematical concepts
are everywhere

and they help us explain
the world we live

in using a system with numbers.

For example, remember when

[inaudible] used a bar graph to
explain the growth in the number

of airplanes since the Wright
Brothers will give this.

We can also create a graph to
show the growth of all types

of transportation,
from cars, to planes,

to jets, to future aircraft.

Look closely at this craft
can you see a pattern?

>> Patterns like the growth of
transportation are everywhere.

You just have to look around?

Speaking of patterns, a man by
the name of Fibonacci discovered

of very famous pattern of
numbers a long time ago in Italy.

This pattern of numbers is
called the Fibonacci Secretes

and the ratio of certain numbers
in the sequence is so special,

it's called the golden ratio.

Hey, how would you
like to meet an expert

on Fibonacci, he is also a poet.

[Brad Brown:] Hi, everybody this
is Brad Brown, talking to you

from the Math and poem at Virginia
tech in Blacksburg Virginia.

The emporium is a large room
with over five hundred computers

where students can come day
or night to learn about math

and speaking of learning here
is a little words I have written

about a man called Fibonacci.

How many answers do we have
that numbers easily found

for you all have two carets,
four grains and eight grades.

Just double the previous round.

But the family tree of the
honey-bee is not like any other.

The girls good and bad
have a mom and dad.

But each boy has only a mother.

It's true each

[inaudible] has mom alone but
each female has parents too.

In addition you see she has grand
parents three, one fewer than me

or you and six alive,
great grand parents five.

That's even true for the
queen and next twice great

that number is eight and of thrice
great she has thirty now she has

asking us, don't like fuss to do
this calculation how many answers -

does that she have
in every generation.

So half to it folks, let's crack
no jokes don't stop for meals

or for slumber, just work your
mind the answer you will find is a

Fibonacci number and
now to help you on more

about Fibonacci numbers
here is Jennifer.

[Jennifer:] Before we begin student
activity lets know a little more

about the golden ratio
and Fibonacci.

Fibonacci was a thirtieth
century Italian Mathematician,

who was studying a
rabbit problem Do you want

to know how many rabbits he
will have at the end of the year

if he started with only one
pair of new born rabbits.

Fibonacci knew that new borns are
able to breed after one month,

then every month after if
the conditions were right.

He found that the sequence
one, one, two, three, five,

eight, thirteen and so one.

Demonstrated the total
number of rabbit pairs

at the end of each months.

So, at the end of first month
you have the original pair

of new born rabbits.

At the of the second month you
still have the original pair

because it took a month through
them to become old enough to breed.

At the end of the third
month you will have two pairs

of rabbits the original pair
and their new born pair.

At the end of fourth month,
you have the original pair,

their first pair born in the third
month and their new born pair,

born in the fourth month.

Following the sequence at the end

of month twelve you will have
one hundred forty four pairs

of rabbits.

Fibonacci and others soon
found the sequence occurring

in many other things in nature by
finding the spirals of pine cones,

pineapples and sunflower seed has,

for example you can
find neighboring pairs

of Fibonacci numbers.

The way in which leaves
are arranged

on the stem also displays
a Fibonacci relationship

so did the spirals
down in the sea shops.

Now Fibonacci wasn't the
only one who is fascinated

with these numbers the ratio
obtained by successive turns

in the sequence was fought
by the Ancient Egyptians

and Greeks, but it is special.

It was so pleasant that
they used this special ratio

to design their pyramids,
their temples and buildings.

You know the

[inaudible] that's a great
example of what is come to be known

as the golden ratio
or golden proportion.

Here is the Fibonacci
sequence let's see

if you can determine the operation
used and find the next four terms.

One, one, two, three, five, eight,
thirteen if you guess twenty one,

thirty four, fifty five and eighty
nine are the next four terms your

are right how did you get it.

The ratio of certain
pairs of numbers

in the Fibonacci sequence is used
to describe things in nature one

to one, one to two, two to three,
three to five, five to eight,

eight to thirteen,
thirteen to twenty one.

If you divide the
denominator of each ratio

by its numerator the
results look like this.

The ratios began to get close

to the rounded number
one point six two.

What if we divide the
small number in the pair

by the large number well you
get point six two rounded.

If something in nature can
be described using the ratios

in the Fibonacci sequence well
that get set to be golden.

For more Fibonacci fun let's
visit fair view elementary in

[inaudible] Ohio and rose about
middle score in Springfield Ohio.

These students are in the

[inaudible] program.

>> NASA Connect asked us to help
you learn this lesson there are

many ways to divide the class up
to check with the Fibonacci ratio

and objects you have collected.

But we've decided to
have three groups.

The first group will measure
natural objects first count the

number of sides of the unpeeled
banana, write this number

on the worksheet on the pineapple
count the number of squares

into adjacent spirals.

Are they adjacent numbers
in the Fibonacci sequence,

count the segments of the half
great through it's the great

through golden examine this pine
count for the number of spirals

that got at the right and
compare that number to the number

of spirals that go to the
left, look at the Daisy,

compare the number of paddles
that grow in a clockwise direction

to the number that grow in a
counter clockwise direction.

Ensure Daisy golden now check
any other natural objects

that you have brought to class.

The second group uses
body measurements

that approximate the golden ratio.

Write the ratio of finger segments
and one finger to the number

of fingers on one hand.

Is your hand golden, now
measures each student's height

and record the results
on the worksheet.

Measure each student from the
top of their head to the top

of the middle finger of the out
stretched arm, record the results.

What is the ratio of the height
to the measure of the length

from the top of the head to
the end of the out stretch arm?

Does that approximate the
golden ratio measure the height

of each student and enable
to floor height of each.

Write the result as a ratio of body
height to enable to floor height

as the result close to the golden
ratio measure each student arm

length and finger tip to
the elbow, write the result

as a ratio is it golden.

Group three measures manmade
objects clarify the Fibonacci

numbers by measuring
the length and width

of an index card try
this with an ID card.

Measure other objects in the
classroom or brought to class.

When all groups finished with their
explorations they can summarize

their findings and report
it to the rest of the class.

Special thanks to our AISS student

[inaudible] University


Great job guys, after you
completed the activity

on the golden ratio you should
analyze your observations

and respond to the following.

In four sentences describe the
activity you just completed.

Was everything you examined
golden, how do you determine

if an object is golden?

Do you think that there is another
special ratio like the golden ratio

that exists in nature, what?

Teacher, check out our
NASA Connect website.

>>: Hi, NASA engineers
using Fibonacci sequence

and the golden ratio to research,
design and develop airplane.

>>: When NASA engineers are
designing airplanes they want

to be sure that all their
airplanes handle the same way.

Its kind of like driving a
car or a truck whatever car

or truck you drive should perform
the same way anyway NASA engineers

have designed a new airplane with a
larger wing than a previous design.

They have to use ratios to scale

or size parts like the
ailerons to fit the new wing.

Ailerons are the movable parts of
airplane wings that control role.

If the ailerons are
not the correct size

with the new wing size the plane
might not fly the way it should.

So you see the golden ratio helps
designers determine the geometric

relationship needed to keep
the plane flying the same.

>>: Hey! Guys meet Bruce Hops;
he is an Aeronautical Engineer

at NASA Langley Research
Center in Hampton Virginia.

So, Bruce let us how
you worked on here NASA.

[Bruce Hops:] Well is I have told
you our transportation demand

in this country is so
beyond supply new century,

the twenty-first century and we
have just got to figure out how

to make more places available
to more people in less time

and so we are working with
smaller airports, smaller aircraft

that fly ever faster and
ever safer than before

to meet this twenty-first
century demand.

>>: You are telling me smaller
airplanes you mean like smaller

like this smaller right here.

How is that going to happen, Bruce?

[Bruce Hops:] For many people
don't know that the ratio

of the total number of
the airports in a country

to the number that help

[inaudible] Airlines Services.

It is about ten to one and so we
can go ten times as many places

and save time for people
if we can figure out how

to use this smaller
airplane in smaller airports.

I mean there are several ratios
that our craft designers used

to first score themselves
the design of the airplane,

wing loading for example is
where you take the whole way

to the airplane and divide by the
wing area that you see out here.

And that gives you a
sense of the relationship

between the way the vehicle
to how much area supporting.

Another ratio that's very useful
is the total lift efficiency

or lift capability wing divided
by the way did the airplane

and that tells you how efficient
our lifting device the airplane is

and as it also tells you how
long the runway needs to be

because it tells you how slowly
you can land the airplane,

very important ratio.

>>: Okay, so I guess
that you are saying is

that smaller airplanes
means smaller runways.

[Bruce Hops:] Much smaller
runways, you know big runways

and big airports can
be ten thousand feet,

twelve thousand feet,
fifteen thousand feet long and

yet you can use a runway that's
only about two thousand feet

by one fifth the length.

>>: Okay, Bruce this plane
already exists obviously,

I mean you fly this thing around.

How are you and how is NASA going
to use an airplane like this

to help travel in the future?

[Bruce Hops:] The small
aircraft transportation system,

which is using smaller aircrafts
and smaller airports as a means

by which we can move more
people to more places.

>>: And you are working on
this right now, at NASA.

[Bruce Hops:] What we want to do is
that, make it possible for people

to have another choice
for inter-city travel

in the twenty-first century,
a bypass around her block

and bypass around dead lock.

If you want to be in those systems

for other reason that's
fine we would like

to give people alternatives.

We are proposing to make
this smaller airport all

across the country more accessible

and virtually all weather
conditions with airplanes that are

as easy to use as cars
and cost about same

as a car trip for long trips.

>>: And better small as this.

[Bruce Hops:] While the airplanes
will be little bit bigger then the

same you will be surprised
actually how big

that seem one should get in,

but those seem more like mini
vans and things like that.

>> So, if you think about
one of the other ratios

and proportion it's interesting
is how much power you have

in airplane relative to the way to
the airplane you got power loading

or thrust away ratio and the people

at NASA's Glen Research
Centre, are working on how

to get more efficiency
and more thrust

at a lesser weight in engines.

>>: This is like a little map
here, telling us how to go.

>>: Its looks quite a trip.

>>: Are we there yet.

>>: Well experience, now we
find out when you navigate pull

out the map and you just can't
look at your rudder flight figure

out where you are starting from,
where you want go too and this kind

of big mess you know
the more you got into it

and than more involved something
strange and then pick over here

and make sure that still on

>>: Alright.

>>: Put that way.

>>: Now it's already
here in the computer.

>>: Oh! It's all right here .

>>: Absolutely, so we can
navigate we can see where we are,

we can see what the weather is and
see what the traffic is or we see

where we wanted to go and we can
also have all of the frequency,

and the information
that was on that map

that stored in the computer.

>> And you have use the map.

>> Push a button and pull
it up, that's the idea.

>> Wow and you put all these
technologies into this airplane.

>> Yeah, this is an
airplane that has many

of the science technologies
that many more to come

but this is sort of the grandfather

[inaudible] airplane.

So, Jennifer and Van what do you
say we button up and fly on over

to the Research Travel Institute
and look at computerized stimulator

where we can put some
of this highway

in sky theory in that action.

>> I love computers, lets do it.

[Jennifer:] That's sound great.

You know speaking of
computers did you know

that Boeing 777 was
the first airplane ever

to be designed completely using
a computer Am I right Bruce.

[Bruce Hops:] That's right.

[Jennifer:] Yeah, they
used computer technology

and they gave engineers immediate
feedback and eliminated the need

for building expensive models.

So while Bruce, Van and I head over
to the Research Triangle Institute.

Why don't you go see
Dr. Shelly Kenrie

and design an airplane
using your own computer.

>> Many of you have been
passenger on airliner and I'm sure

at least all of you have seen
one flying across the sky.

May be you have wondered what goes

into designing one well this shows
online activity gives you the

opportunity to model your
own future passenger plan

by choosing different
wings, tails, engines

and fuselage layouts you can
put together a complete airplane

and see if it will fly.

All of this right on
your computer screen,

any five computer analysis you
have quick feedback on the effect

of each decision you make.

The program you use is called
Airplane Design Workshop

and it will give you and example
how artificial intelligence may be

used now and then the
future to assist engineers

in the modeling and design process.

Let's go to Central
Elementary School

in Pleasant Grove, Utah where Mr.

[inaudible] will guide
you through this activity.

>> Hello, I'm

[inaudible] the Technology

for Central Elementary School

and we are doing some problem
based education using desktop,

Aero's, aircraft design program
all these students are pretending

they are design engineers
for an Aeronautical Firm.

They have a contract with
airline to design airplane

and if they design the airplane
playing properly they will receive

the contract or purchase these
airplanes and construction.

If not they loose contract and
the company will be bankrupt,

but the little less
in economics too.

>> NASA Connect asked us to show
you the aircraft design workshop,

developed by Desktop
Aeronautics Incorporated.

The main challenge
with this activity is

to see how fast you can fly and
still meet the design requirements.

First we go to the NASA
Connect website and click

on the Norbert Slab Band to
link to the online activity.

At the top of the screen you
will see a line of pictures click

on the picture of the
wing on the left side.

Here you choose the suit
size and aspect ratio

of your wings okay now choose the
next button which gives the size,

area and aspect ratio
choices where you take.

The next button over let you
choose the type object and amount

of thrust and number and placement
of engines for your airplane.

Now select the seating arrangement,

this button let's you select
the speed, altitude and amount

of fuel for your plane.

Now you pick a final
destination, all trips will start

at Washington D.C. with all
these choices made its time

to have the computer program
analyze your selection.

Click on the last button
to evaluate you airplane.

You will find out if you are ready
to fly if not you can go back

to make other choices.

The software program will suggest
to how you may improve your design.

[Jennifer:] Thanks for
watching NASA connect

from Central Elementary.


>> We hope you will
try your hand with this

on line activity the program
office in which foundation

for Thoms solving
reflection and analysis.

See what design situation
that you might create

and then use a software
to solve that.

[Jennifer:] looks little
familiar its like Langley.

>> Well it should the
Fibonacci ratio we are worrying

about is also used by
simulation engineers

to recreate a very natural life
like appearance for grass, trees,

buildings, skies, clouds.

[Jennifer:] That's really cool.

This is like big video game.

What is the purpose of this?

>> Well this is a simulator.

A measurement

[inaudible] what would you like

if flying a airplane were
lot like playing videogame.

[Jennifer:] I think


>> Well that's what we want to
happen and so what we do is we try

out all of the different
kinds of images

that give you highway in the sky.

Follow I think Jennifer and
Van should give this a try.

[Jennifer:] Oh!

We got some confidence in us Bruce.

Alright lets start it up.

>> There you go.

Now when you get up to
about eighty miles an hour,

you are going to gently pull back.

[Jennifer:] This is so weird.

>> Okay now pull that.



>> And you just left the ground.

[Jennifer:] And then
what happens in the sky.

>> And there's your
highway in the sky.

Now you can steer at the wheel.

[Jennifer:] Okay with the


Oh Bruce this is so neat.

>> And this is the bottom line,
it is lying the floor of highway

and the top of it's is the roof of
the highway now its like driving

through a tunnel if you
will no signs to distract

and that tells you where you
need to go and keeps you clear

of everything that would
be hazardous to traffic,

bad weather, obstacles, mountains.

[Jennifer:] And NASA
is on this pathway.

>>: No one this is
your own pathway.

Your computer created this for
you because you told the computer

where you are going,
where you wanted to go.

[Jennifer:] Oh, Bruce this is

so easy I mean this is
great I will be able

to fly through like this


>>: Well, we hope
anybody to do this

with a little bit practice
on simulator you say.

[Jennifer:] You said anybody I
mean anybody like even like Van

or anybody.

>>: I just got my drivers
license I could do this.

[Jennifer:] Right, why
you will take a look?

>>: Sorry, sorry I got it.

[Jennifer:] Okay, great
well Van tries to take of.

We'd like to take everyone
you have make this episode

of NASA Connect possible
than keep you own


>> Sorry.

[Jennifer:] on the road I mean
on the highway in the sky.

You know Van and I would love to
hear from you with your comments,

your questions and
your suggestions.

So write us at NASA Connect,
NASA Langley Research Center,

Mail Star four hundred, Hampton
Virginia, 23681 or email us


Hey teachers if you would
like a video tape copy

of this NASA Connect show and
the educators guide lesson plans

contact your local NASA
Educator Research Center

or call the NASA Central Operation
of Resources for educators.

All this information
and more is located

on the NASA Connect website.

The job there the
people are pretty level.

All right okay for the NASA Connect
series I am Jennifer Pulley.

[Van Hughes:] And I'm Van Hughes.

[Jennifer:] Van can
have some view please.

[Van Hughes:] Sorry.

[Jennifer:] Eyes on the highway
in the sky and we are closing

in on Richard trying to get there.

>>: Good question a
ratio is a good question.

>>: This is where the Wright
brothers flew their very


>>: What is the ratio

>> [inaudible]

>> Oh no comment.

>> Got it

>> Okay.

>> Got it this is


>>: Oh, Jennifer, Van we
just say we got enough.

>> Control, power, fly in 1903

and guess what they used
mathematics like ratios


>>: NASA Connect showed

[inaudible] you have
to do this lesson.

>>: Old ratio is a pair of
numbers that is used to make -

Now we fly all over to
the Research Institute


[Danica Mckellar:] Thank you
for watching NASA Connect.

Be sure to check out my web
site at

where I will answer all your
math questions and many more.