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 March 5th, 2015, 07:25 PM #1 Newbie   Joined: Feb 2015 From: Wisconsin Posts: 6 Thanks: 0 Weird question about my math learning experience First off I'm at Calculus 1 and an American. In America and I think Europe how math is taught is that you are told math equations and are expected to just "go with it" and after you learn everything at school THEN you use what you learned and apply it. I on the other hand has started to use and apply the math heavily while learning it at the same time. By doing this method I encounter problems in math while applying it to things like computers that things just can't be solved with the level I am at. When this happens it feels that what I am trying to do will be explained or examined in a higher level math but the problem is I don't know for sure! What I try to do I don't know what type of math it is or it could be just "very" high level math I am currently at, or it might not even be math at all! It could be physics instead or combination of both. When this happens I tend to assume things in math and I don't know if I have right or flawed logic. For example, I have worked with the -|y| shape and I wanted to get a parabola -y^2 instead but I couldn't get the parabola with "normal" means. So I assumed "there is a math that can turn -|y| into -y^2" I then asked my math professor that question and it turns out that Topology is the math that does this. So my assumption was right! I have taken a discrete mathematics class before, and when I assume something like I said before I try to find a contradiction in something to see if I am right or not. However math is VERY crazy at times and when you think something is "impossible" there ends up being a way of getting it and it seems finding a contradiction doesn't always work. For example The distance formula: (((x2-x1)^2)+((y2-y1)^2))^.5 Sometimes if the variables are a distance that is "not normal" (this is almost impossible to explain and it can happen on a computer) it is still possible to get an imaginary number. And by squaring the variable values it does NOT get rid of the negatives. To stop this you need to do this: |(((x2-x1)^2)+((y2-y1)^2))|^.5 I mean it seems impossible to get a negative after squaring but it IS possible in very rare and strange situations. With things like this how do I know if my math logic and assumptions are correct about things or it is flawed?
March 5th, 2015, 09:30 PM   #2
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Quote:
 Originally Posted by Speedy9199 For example, I have worked with the -|y| shape and I wanted to get a parabola -y^2 instead but I couldn't get the parabola with "normal" means.
Uh... like multiplying? -(-|y| * -|y|) = -y^2 seems simple enough.

Quote:
 Originally Posted by Speedy9199 So I assumed "there is a math that can turn -|y| into -y^2" I then asked my math professor that question and it turns out that Topology is the math that does this.
Topologically y + 7, -|y|, y^2, sin(y), etc. are all identical, so I'm not sure if this is a useful answer here. Pretty much any continuous curve you've learned about would be as well.

Quote:
 Originally Posted by Speedy9199 The distance formula: (((x2-x1)^2)+((y2-y1)^2))^.5 Sometimes if the variables are a distance that is "not normal" (this is almost impossible to explain and it can happen on a computer) it is still possible to get an imaginary number. And by squaring the variable values it does NOT get rid of the negatives.
If x1, x2, y1, and y2 are all real numbers then (x2 - x1)^2 + (y2 - y1)^2 is a nonnegative real number and hence its square root will be a nonnegative real number.

March 5th, 2015, 10:06 PM   #3
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Quote:
 Originally Posted by Speedy9199 The distance formula: (((x2-x1)^2)+((y2-y1)^2))^.5 Sometimes if the variables are a distance that is "not normal" (this is almost impossible to explain and it can happen on a computer) it is still possible to get an imaginary number. And by squaring the variable values it does NOT get rid of the negatives. To stop this you need to do this: |(((x2-x1)^2)+((y2-y1)^2))|^.5
Are you talking about the errors that arise when you try to interpret real numbers on a discrete grid on the computer? A lot of the math in graphics programming is designed to account for those kinds of problems ... how to draw straight lines even though there are no grid points where the math equation says there should be, for example. How to determine if a point is inside or outside a given region. There are a lot of computer graphics techniques that have been created to compensate for the fact that the real numbers are infinitely divisible, but the graphics grid consists of only finitely many points.

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