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Surveying and Geometry - Contenido educativo

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Subido el 28 de mayo de 2007 por EducaMadrid

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NASA Connect Segment explaining surveying and how surveyors use geometry.

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What is surveying? 00:00:00
How do surveyors use geometry? 00:00:06
Surveying is the measurement of angles and distances, elevation, and direction. 00:00:10
It's especially useful for locating property boundaries, construction layout, and map making. 00:00:14
Okay, Terry, can you tell me how surveyors use this equipment and geometry to survey 00:00:19
land? 00:00:24
Yes. 00:00:25
Let's look at this transit. 00:00:26
This is a telescope, a compass, and a protractor, and it's used to measure horizontal and vertical 00:00:27
angles. 00:00:33
You can measure angles in the field with this and measure those same angles back at your 00:00:34
desk with a protractor. 00:00:38
This instrument is used to lay out objects like football fields, baseball fields, soccer 00:00:40
fields. 00:00:45
Today, let's demonstrate how we use this by laying out this football field. 00:00:46
All right. 00:00:50
First, we pick a starting point and set the transit over the point. 00:00:51
We call this point corner number one. 00:00:55
Then we measure 300 feet to the next corner and call it corner number four. 00:00:57
We mark this corner with a corner marker. 00:01:02
With zero on the scale, we look through the telescope and line up corner number four. 00:01:04
We know that the angle between the sides of a rectangle is 90 degrees, so we turn the 00:01:10
telescope towards corner number two until we can read 90 degrees on the transit circle 00:01:14
or scale. 00:01:20
Now we measure the width of the football field, 150 feet, and mark corner number two. 00:01:22
Next, we move the transit over corner number two. 00:01:27
With zero on the scale, we look through the telescope at corner number one marker. 00:01:31
We turn the telescope towards corner number three until we can read 90 degrees on the 00:01:36
scale. 00:01:41
We measure 300 feet and mark corner number three. 00:01:42
We now have all of the corners marked. 00:01:46
Applying one of the basic rules of geometry, we know that the sum of the interior angles 00:01:49
of a four-sided polygon is 360 degrees. 00:01:54
So our last angle must measure 90 degrees for a correct layout. 00:01:58
The rule for checking the angles of any object is that the sum of the interior angles of 00:02:03
a closed polygon is equal to the number of sides minus two times 180 degrees. 00:02:07
You know, Jennifer, the art and science of surveying have been used for over 3,400 years 00:02:13
to map and measure our world. 00:02:18
Today, scientists at NASA are preparing to measure and map the planets of our solar system. 00:02:20
Hmm, who knows? 00:02:26
Maybe one day one of you will help survey Mars. 00:02:28
Did you know that George Washington was a surveyor before he became president? 00:02:31
Did you know Lewis and Clark used transits on the exploration mission? 00:02:36
To understand angles and circumference, let's look at something we can all relate to, pizza. 00:02:40
Take this slice of pizza. 00:02:47
Can you tell just by looking at it how many slices were in the original pizza and how 00:02:48
big a round it was? 00:02:53
Sure you can. 00:02:55
All it takes is a little geometry. 00:02:56
A pizza usually has eight identical slices, but not all of them. 00:02:57
So let's measure the angle width of this slice. 00:03:02
That's the part you put in your mouth first. 00:03:05
Excuse me, sir, what does this protractor read? 00:03:08
The protractor reads an angle width of 45 degrees. 00:03:13
Right. 00:03:16
Now, what is the measurement of all the other angles touching the center? 00:03:17
They have to be equal or the same measurement, 45 degrees. 00:03:21
Right. 00:03:25
Now, most pizzas are circular and circles measure 360 degrees. 00:03:26
If you divide 360 degrees by 45 degrees, the original pizza had eight slices. 00:03:31
Now, let's figure the circumference of this pizza. 00:03:38
Most pizzas are measured in inches. 00:03:42
So, using the pizza with eight slices, if the length of the crust arc is five and a 00:03:44
half inches, how round is your pizza? 00:03:49
If there are eight slices and the crust arc measures 5.5 inches long, then eight times 00:03:51
5.5 inches equals 44 inches. 00:04:00
The pizza has a circumference of 44 inches. 00:04:03
Great. 00:04:07
Try this one. 00:04:08
What if the angle width of your pizza slice measures 30 degrees and the crust arc is two 00:04:09
and a half inches? 00:04:15
How many slices would there be in the original pizza and what is the circumference? 00:04:16
I've got it. 00:04:21
360 degrees divided by 30 degrees equals 12 slices. 00:04:23
12 slices times 2.5 inches equals a circumference of 30 inches. 00:04:27
So, sir, would you rather eat a 12-slice pizza or an eight-slice pizza? 00:04:33
I'll choose the eight slices. 00:04:39
I couldn't possibly eat 12. 00:04:40
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Idioma/s:
en
Materias:
Matemáticas
Niveles educativos:
▼ Mostrar / ocultar niveles
      • Nivel Intermedio
Autor/es:
NASA LaRC Office of Education
Subido por:
EducaMadrid
Licencia:
Reconocimiento - No comercial - Sin obra derivada
Visualizaciones:
462
Fecha:
28 de mayo de 2007 - 16:51
Visibilidad:
Público
Enlace Relacionado:
NASAs center for distance learning
Duración:
04′ 45″
Relación de aspecto:
4:3 Hasta 2009 fue el estándar utilizado en la televisión PAL; muchas pantallas de ordenador y televisores usan este estándar, erróneamente llamado cuadrado, cuando en la realidad es rectangular o wide.
Resolución:
480x360 píxeles
Tamaño:
28.60 MBytes

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