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Pythagoras Theorem and Ellipses - Contenido educativo

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Subido el 28 de mayo de 2007 por EducaMadrid

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NASA Connect Segment that explains who Pythagoras was and how he contributed towards geometry. Also it explains how geometry is used in everyday life.

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Who was Pythagoras, and what did he contribute to geometry? 00:00:00
Explain how geometry is used in your everyday life. 00:00:07
The word geometry comes from two Greek words, geo, which means the earth, and metron, which 00:00:11
means to measure. 00:00:17
Today, geometry is more the study of shapes than it is the study of the earth. 00:00:19
Basically, geometry is the branch of mathematics that deals with the position, the size, and 00:00:24
the shape of figures. 00:00:29
One of the greatest mathematicians was an ancient Greek named Pythagoras. 00:00:30
He discovered some of the most important mathematical concepts that came to be called geometry. 00:00:34
One observation he made was that gravity is vertical, or 90 degrees to the horizon. 00:00:40
From this observation, Pythagoras discovered that the 90 degree angles from four right 00:00:54
sided triangles make up a square. 00:01:00
Watch this. 00:01:02
If I have one right angle, and I place three other right angles around it, like this, I 00:01:03
eventually wind up with, ta-da, a square. 00:01:13
That's pretty neat. 00:01:19
Let's do the math. 00:01:20
Knowing what Pythagoras discovered about the right angle, can you calculate how many degrees 00:01:22
are in this square? 00:01:28
If you multiply 90 degrees times four, you're right. 00:01:31
This square has 360 degrees. 00:01:42
What other shape has 360 degrees? 00:01:47
A circle. 00:01:50
You know, Pythagoras proved that there are relationships between different geometric 00:01:51
shapes. 00:01:54
What relationships can you see between other geometric shapes? 00:01:55
Get this. 00:01:59
Pythagoras found out even more laws about the right triangle. 00:02:01
If we look at the same square, but just a little differently, we can see that half the 00:02:04
area of this square equals a right triangle. 00:02:13
Now, how can we use math to calculate the remaining angles of a right triangle? 00:02:18
Simple. 00:02:25
Squares are 360 degrees, we know this. 00:02:28
If we divide it in half, this triangle must equal 180 degrees. 00:02:32
Now, we know this is a right triangle. 00:02:39
This equals 90 degrees. 00:02:42
If we subtract that from 180, we get 90 degrees. 00:02:43
These two angles must add up to 90 degrees. 00:02:50
This is true for every right triangle. 00:02:54
It's true for this right triangle, it's true for this right triangle, and it's even true 00:02:57
for right triangles that look like this. 00:03:02
In order to calculate the remaining angles of a right triangle, you have to use math 00:03:14
and geometry. 00:03:19
Geometry is used in everything we do, from constructing roads and buildings to playing 00:03:21
football or pool. 00:03:25
Okay, here's a big play. 00:03:28
It's you and me, okay? 00:03:30
I'll toss the big pass to you, you go down and out, got it? 00:03:35
Got it! 00:03:38
Great! 00:03:39
Now, let's see. 00:03:40
If I toss the ball directly to Jennifer and don't anticipate where she'll be, I'll miss 00:03:41
her completely. 00:03:45
However, if I know she's cutting right, and I throw the ball at the correct angle, I should 00:03:47
get the ball to her. 00:03:53
Hey! 00:03:55
My perfect pass just created a right triangle. 00:03:57
Geometry is everywhere. 00:04:01
Hey, way to go, Van! 00:04:02
Without geometry, it would be impossible to organize precise patterns and play a simple 00:04:05
game of football. 00:04:09
My friend Lynn Chappell is an 8th grade math teacher at Huntington Middle School in Newport 00:04:11
News, Virginia. 00:04:15
Let's see what information she has about Pythagoras and geometry. 00:04:16
The most important discovery that Pythagoras made was the relationship between the longest 00:04:20
side of a right triangle and the two shorter sides. 00:04:24
The longest side of the right triangle is called the hypotenuse. 00:04:28
Now, remember that Pythagoras' theorem is A squared plus B squared equals C squared. 00:04:33
Now, who could tell me what that means? 00:04:42
Charmaine. 00:04:45
The sum of the squares of the two shorter sides, A plus B, equals the square of the 00:04:46
longest side, C, which is the hypotenuse. 00:04:52
Good answer. 00:04:55
Now, we're going to mark the right triangle that we have on this paper, and the shorter 00:04:57
sides, also called the legs, are A and B, and the longest side is C, and remember we 00:05:00
call that the hypotenuse. 00:05:07
Now, what Pythagoras did was draw a square on the side of A, and remember that a square 00:05:09
is a number times itself, A times A, and he drew a square on the side of B, B times B, 00:05:16
and he drew a square on the side of C, C times C. 00:05:25
What we're going to do is we're going to cut A squared off of the side, and then we're 00:05:30
going to cut B squared and make them fit into C squared to prove that Pythagoras was right. 00:05:36
First take your straight edge, and we're going to draw some parts of B so that we can cut 00:05:42
it and it will fit. 00:05:47
On the long side of C, come straight down through B squared until you touch the edge. 00:05:50
Now connect the lower corner of B to the bottom edge of A squared. 00:05:57
This will form a perpendicular line. 00:06:08
Now take your scissors and cut out A squared in one piece and B squared in the pieces that 00:06:12
you've cut it into, and then we'll fit it all on to C squared to prove that Pythagoras 00:06:17
was right. 00:06:21
Well, have all of you fit your pieces together? 00:06:22
Yes. 00:06:25
Then I guess Pythagoras was right. 00:06:26
And you know, Pythagoras also believed or postulated that the shortest distance between 00:06:28
two points is a straight line. 00:06:34
Well, how come if you throw a ball from point A to point B, then it curves or arcs? 00:06:36
Well, Van, that's rather very simple. 00:06:42
Ever heard of something called gravity? 00:06:45
Yeah, I've heard of gravity! 00:06:49
In 1600, Johannes Kepler, a famous astronomer, proved that the planets orbited the sun in 00:06:52
an ellipse. 00:06:58
That's another geometric shape. 00:06:59
If you take a circle and squash it a bit, you get an ellipse. 00:07:01
Like our football example, if we want to navigate from Earth to Mars, we have to take into account 00:07:05
where Mars will be within its elliptical orbit. 00:07:09
What information did scientists first discover about Mars? 00:07:13
Humans have known of Mars since before recorded history. 00:07:17
In 1609, a man by the name of Galileo first viewed Mars through his newly invented telescope. 00:07:20
Although his telescope was no better than a modern toy, it revealed enough to prove 00:07:27
that Mars was a large sphere, a world shaped like the Earth. 00:07:31
Could this other world be inhabited? 00:07:36
Besides using the telescope, how else do scientists collect information on Mars? 00:07:38
Let me tell you! 00:07:43
NASA's Mariner 4 was the first spacecraft to take close-up pictures of the red planet. 00:07:44
As it flew past Mars in 1965, it showed a heavily crated surface. 00:07:50
Six years later, in 1971, Mariner 9 arrived at Mars and became the first artificial object 00:07:56
ever to orbit another planet. 00:08:02
Mariner 9 saw the Valles Marineris, a canyon that stretches 4,500 kilometers, or 2,800 00:08:04
miles, across the face of Mars. 00:08:11
It is so long that if it were on Earth, it would stretch all the way from Los Angeles, 00:08:14
California to New York, New York. 00:08:19
All these discoveries by Mariner were seen from above the surface of Mars. 00:08:22
What we really needed was a view from the Martian surface. 00:08:28
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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:
182
Fecha:
28 de mayo de 2007 - 16:52
Visibilidad:
Público
Enlace Relacionado:
NASAs center for distance learning
Duración:
08′ 32″
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:
51.41 MBytes

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