Tagged: Dimension

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During the New York World’s Fair in 1964, science fiction writer Isaac Asimov made predictions about what the world would be like 50 years later, which were published in The New York Times. By reading them today, you can see that the author managed to predict almost all modern technological achievements!

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According to Asimov, half of the electricity in 2014 will be produced by nuclear power plants, and solar plants will operate in the vast deserts of Arizona and Kazakhstan. The connection will be based on satellites and the spacecraft will successfully reach Mars.

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Actually, they were fantasies of Asimov, who confirmed that the phones will become mobile and pocket and that their screens will allow us to read books and see the photos.

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The technical devices will work without wires, and long-lasting or rechargeable batteries will be used instead.

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The films will be screened in three-dimensional form and the time to cook food and do boring household chores will be significantly reduced thanks to appliances with automatic timers: toasters, ovens, coffee makers, etc.

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According to Asimov, the view of the city of 2014 will change: some buildings and a large part of the urban area will be underground because in this way it will be possible to save energy to heat homes in the winter and cool the weather. Summer (Today there are underground garages and full shopping centers!). On the surface there will be parks, gardens and even grazing animals.

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The means of transport, in accordance with the provisions of the writer, will cease to come into contact with the road, but will fly over the ground at a height of approximately one meter. River and sea vessels will slide over the water and the speed will increase significantly.

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In addition, Asimov predicted that in 2014 the population of the Earth will increase to 6,500 million and that 350 million people will live in the United States (on June 1, 2013, the United States registered 316 million). Population growth will force humanity to seek new food resources in the Arctic and deserts. For example, microorganisms that will transform yeasts and algae into nutritious foods will be used.

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According to the author’s forecasts, the main problem of humanity in 2014 will be as strange as it seems: boredom! For this reason, psychology will be incredibly developed and psychotherapists will have great prestige.

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That a circle is one-dimensional and has no surface

It’s quite intuitive, if you think about it. A circle consists of a line that turns to infinity, as expected. Another thing that makes it intuitive is when you look at the equation of a circle, which is provided by the following:

(x-h) 2+ (y-k) 2 = r2

Note that the circle is simply a graph of the solutions to the following equations and does not define the coordinates inside the shape, but only the circumference. I will provide you with a mathematical explanation. Therefore, if you are not a math lover, you are free to ignore it, otherwise read on.

The first way to determine the number of dimensions of an object is to determine the number of parameters required in its description.  We find the number of dimensions in which an object is found by examining the number of variables constituting the equation, then subtracting that number from the total number of equations constituting the object. In this case, we have 2 variables.

Is not a variable since the radius of a circle does not change). We also see that there is only one equation here, which means that our object is one-dimensional. This begs the question of what do you find when you solve these Grade 6 geometry problems?

The part of the circle that includes the circumference and defines the inner part is given by the following inequality:

(x-h) 2+ (y-k) 2≤r2

This is called a disk and, unlike the circle, it is a 2D object.

How do we know it?

We see that the quantity of variables defining the object is 2, like the last time. However, we see that there are no real equations defining this, that is to say it is a dimension 2. Since it is in 2D, it has a surface.

If you are in the geometry of high school and you are in this part of the program that covers several circles, prepare to prepare it and give an example to your teacher as soon as these words escape him.