Program Information

NASA Connect Segment explaining surveying and how surveyors use geometry.

NASA CONNECT™ is a series of Emmy®-award-winning, math-focused programs. Each program supports the national math, science, and technology standards and has three components that include (1) a 30-minute television broadcast; (2) a companion educator's guide; and (3) an online activity that further explores topics presented in the broadcast. These programs establish a connection between the math, science, and technology concepts taught in the classroom to those same concepts used everyday by NASA researchers.

Transcript

Surveying is the measurement
of angles and distances,
elevation and direction.

It's especially useful for
locating property boundaries,
construction layouts,
and mapmaking.

Okay, Terry, can you tell me
how surveyors
use this equipment and geometry
to survey land?

Yes, let's look
at this transit.

It contains a telescope,
a compass, and a protractor.

And it's used to measure
horizontal and vertical angles.

You can measure angles
in the field with this
and measure those same angles
back at your desk
with a protractor.

This instrument is used
to lay out objects
like football fields,
baseball fields, soccer fields.

Today let's demonstrate
how we use this
by laying out
this football field.

All right.

(Tyler)
First we pick a starting point
and set the transit
over the point.

We call this point
corner number one.

Then we measure 300 feet
to the next corner
and call it corner number four.

We mark this corner
with a corner marker.

With zero on the scale,
we look through the telescope
and line up corner number four.

We know that the angle
between the sides of a rectangle
is 90 degrees,
so we turn the telescope
towards corner number two
until we can read 90 degrees
on the transit circle, or scale.

Now we measure the width
of the football field, 150 feet,
and mark corner number two.

Next, we move the transit
over corner number two.

With zero on the scale,
we look through the telescope
at the corner number one marker.

We turn the telescope
towards corner number three
until we can read 90 degrees
on the scale.

We measure 300 feet
and mark corner number three.

We now have
all of the corners marked.

Applying one of the basic rules
of geometry,
we know that the sum
of the interior angles
of a 4-sided polygon
is 360 degrees.

So our last angle must measure
90 degrees for a correct layout.

You know, Jennifer,
the art and science of surveying
have been used
for over 3,400 years
to map and measure our world.

Today, scientists at NASA
are preparing
to measure and map the planets
of our solar system.

Hmm,
who knows?

Maybe one day, one of you
will help survey Mars.

To understand angles
and circumference,
let's look at something
we can all relate to:
pizza.

Take this slice
of pizza.

Can you tell
just by looking at it
how many slices were
in the original pizza
and how big around it was?

Sure, you can.

All it takes
is a little geometry.

A pizza usually has
eight identical slices,
but not always.

So let's measure the angle width
of this slice.

That's the part
you put in your mouth first.

Excuse me, sir,
what does this protractor read?

(man)
The protractor reads
an angle width of 45 degrees.

Right,
so what is the measurement
of all the other angles
touching the center?

They have to be equal,
or the same measurement,
45 degrees.

(Jennifer)
Right.

Now, most pizzas are circular,
and circles measure 360 degrees.

If you divide 360 degrees
by 45 degrees,
the original pizza
had eight slices.

Now let's figure
the circumference of this pizza.

Most pizzas
are measured in inches,
so, using the pizza
with eight slices,
if the length of the crust arc
is 5.5 inches,
how round is your pizza?

If there are eight slices
and the crust arc
measures 5.5 inches long,
then 8 x 5.5 inches
equals 44 inches.

The pizza has a circumference
of 44 inches.

Great.

Try this one.

What if the angle width
of your pizza slice
measures 30 degrees,
and the crust arc is 2.5 inches?

How many slices would there be
in the original pizza,
and what is the circumference?

I've got it.

360 degrees
divided by 30 degrees
equals 12 slices.

12 slices x 2.5 inches
equals a circumference
of 30 inches.

So, sir, would you
rather eat
a 12-slice pizza
or an 8-slice pizza?

Hmm, I'll choose
the eight slices;
I couldn't possibly
eat 12.

Virginia Standards