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Transportation Growth and Patterns - Contenido educativo

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Subido el 28 de mayo de 2007 por EducaMadrid

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NASA Connect segment exploring transportation growth since the early 1900s and how the patterns of this growth are mathematical and are related to the Fibonacci sequence.

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Describe the girth of transportation since the early 1900s. 00:00:00
What is mathematical about its girth? 00:00:07
Hi, I'm Ardeth Williams, pilot and air traffic controller with the Federal Aviation Administration. 00:00:10
Back in 1903, there was only one aircraft. 00:00:16
Not much need for us to have an air traffic control system. 00:00:18
However, by 1960, there were over 78,000 commercial and general aviation aircraft. 00:00:21
And in 10 years, by the year 2010, we believe there will be almost 228,000. 00:00:27
Air traffic is growing and growing. 00:00:32
We anticipate by the year 2010, almost 1 billion people will be traveling by air. 00:00:34
The year 2003 begins century number two of aviation. 00:00:39
I hope in 10 years or so, you will be one of the visionaries that will ensure my safe 00:00:42
and efficient flight by designing, building, maintaining, controlling, or flying the aircraft. 00:00:46
The future of aviation is in your hands. 00:00:52
You know, Ardeth is right. 00:00:56
Mathematical concepts are everywhere and they help us explain the world we live in using 00:00:58
a system of numbers. 00:01:02
For example, remember when Ardeth used a bar graph to explain the growth in the number 00:01:03
of airplanes since the Wright Brothers? 00:01:07
Well, get this. 00:01:09
We can also create a graph to show the growth of all types of transportation, from cars 00:01:11
to planes to jets to future aircraft. 00:01:16
Look closely at this graph. 00:01:20
Can you see a pattern? 00:01:21
It's like the growth of transportation are everywhere. 00:01:24
You just have to look around. 00:01:29
Speaking of patterns, a man by the name of Fibonacci discovered a very famous pattern 00:01:31
of numbers a long time ago in Italy. 00:01:37
This pattern of numbers is called the Fibonacci sequence and the ratio of certain numbers 00:01:41
in this sequence is so special, it's called the golden ratio. 00:01:47
Hey, how would you like to meet an expert on Fibonacci? 00:01:52
He's also a poet. 00:01:55
Hi everybody, this is Bud Brown talking to you from the Math Emporium at Virginia Tech 00:01:57
in Blacksburg, Virginia. 00:02:01
The Emporium is a large room with over 500 computers where students can come day or night 00:02:03
to learn about math. 00:02:08
And speaking of learning, here's a little verse I've written about a man called Fibonacci. 00:02:09
How many ancestors do we have? 00:02:14
That number is easily found, for we all have two parents, four grands, and eight greats. 00:02:16
Just double the previous round. 00:02:22
But the family tree of the honeybee is not like any other. 00:02:24
The girls, good and bad, have a mom and a dad. 00:02:27
But each boy has only a mother. 00:02:30
It's true, each drone has a mom alone, but each female has parents too. 00:02:33
In addition, you see, she has grandparents three, one fewer than me or you. 00:02:38
Sakes alive, great grandparents five, that's even true for the queen. 00:02:43
And next, twice great, that number is eight. 00:02:49
And of thrice greats, she has 13. 00:02:51
Now she's asking us, don't make a fuss, to do this calculation. 00:02:54
How many ancestors does she have in every generation? 00:02:59
So hop to it folks, let's crack no jokes, don't stop for meals or for slumber. 00:03:02
Just work your mind, the answer you'll find is a Fibonacci number. 00:03:08
Now, to help you learn more about Fibonacci numbers, here's Jennifer. 00:03:12
Before we begin the student activity, let's 00:03:17
learn a little more about the golden ratio and Fibonacci. 00:03:19
Fib-a-who? 00:03:23
Fibonacci was a 13th century Italian mathematician 00:03:25
who was studying a rabbit problem. 00:03:29
He wanted to know how many rabbits he would have at the end of the year 00:03:31
if he started with only one pair of newborn rabbits. 00:03:35
Fibonacci knew that newborns are able to breed after one month, 00:03:39
then every month after, if the conditions were right. 00:03:43
He found that the sequence 1, 1, 2, 3, 5, 8, 13, and so on, 00:03:47
demonstrated the total number of rabbit pairs at the end of each month. 00:03:56
So at the end of the first month, you have 00:04:00
the original pair of newborn rabbits. 00:04:02
At the end of the second month, you still have the original pair 00:04:05
because it took a month for them to become old enough to breed. 00:04:08
At the end of the third month, you will have two pairs of rabbits, 00:04:11
the original pair and their newborn pair. 00:04:14
At the end of the fourth month, you have the original pair, 00:04:17
their first pair born the third month, and their newborn pair 00:04:20
born the fourth month. 00:04:24
Following this sequence, at the end of month 12, you'll have 144 pairs of rabbits. 00:04:25
Fibonacci and others soon found this sequence 00:04:31
occurring in many other things in nature. 00:04:34
By counting the spirals of pine cones, pineapples, and sunflower seed heads, 00:04:37
for example, you can find neighboring pairs of Fibonacci numbers. 00:04:41
The way in which leaves are arranged on a stem 00:04:46
also displays a Fibonacci relationship. 00:04:48
So do the spirals found in seashells. 00:04:51
Now, Fibonacci wasn't the only one who was fascinated with these numbers. 00:04:54
The ratio obtained by successive terms in the sequence 00:04:58
was thought by the ancient Egyptians and Greeks to be special. 00:05:02
It was so pleasing that they used this special ratio 00:05:06
to design their pyramids, their temples, and buildings. 00:05:10
You know the Parthenon? 00:05:14
That's a great example of what has come to be known 00:05:15
as the golden ratio or golden proportion. 00:05:17
Here's the Fibonacci sequence. 00:05:20
Let's see if you can determine the operation used and find the next four terms. 00:05:22
1, 1, 2, 3, 5, 8, 13. 00:05:27
If you guessed 21, 34, 55, and 89 are the next four terms, you're right. 00:05:37
How did you get it? 00:05:45
The ratio of certain pairs of numbers in the Fibonacci sequence 00:05:46
is used to describe things in nature. 00:05:49
1 to 1, 1 to 2, 2 to 3, 3 to 5, 5 to 8, 8 to 13, 13 to 21. 00:05:53
If you divide the denominator of each ratio by its numerator, 00:06:05
the results look like this. 00:06:09
The ratios begin to get close to the rounded number 1.62. 00:06:11
What if you divide the small number in the pair by the large number? 00:06:17
Well, you'll get 0.62 rounded. 00:06:20
If something in nature can be described using the ratios in the Fibonacci sequence, 00:06:23
well then, it's said to be golden. 00:06:27
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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:
446
Fecha:
28 de mayo de 2007 - 16:53
Visibilidad:
Público
Enlace Relacionado:
NASAs center for distance learning
Duración:
06′ 31″
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:
39.19 MBytes

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