Algorithm Optimisation Championship. - page 21
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A quadratic function is a parabola. A simple explanation. http://fizmat.by/math/function/quadratic_function
Actually you have to prove that the graph of a quadratic function is a parabola. The link says this as a definition. And this is a theorem by the way!
At school they are good at cramming the brain. They say, for instance, that the diameter of a circle is a double radius. And this has to be proved! Because the diameter of ANY closed line is the longest chord.
Explain in simple terms why you think so?
How do you construct a single parameter function? You plot the value of the parameter on one axis and the value of the function on the second axis - we've done this at school many times.
If the function has two parameters, you plot one parameter on one axis, the second parameter on the second axis, and the value of the function on the third axis. You can do this in excel and see the surface.
And so on.
The function of three parameters can be represented as a commode. The xyz coordinates point to a point in space - the drawer of the dresser, and the amount of money lying in the drawer is the value of the function.
And so on.
Actually, you have to prove that the graph of a quadratic function is a parabola. The link says this as a definition. This is a theorem by the way!
They do a good job of cramming the brain at school. They say, for instance, that the diameter of a circle is a double radius. And this has to be proved! Because the diameter of ANY closed line is the largest chord in length.
Agreed. You have to prove that it is a parabola.
But should we prove that if to the expression y = ax + bx + c, we add (... + d1 + d2 + d3 + d4 + d5... + dn), the number of coordinate axes on which the line obtained from the results of the equation will not exceed two?
How do you construct a single parameter function? You plot the value of the parameter on one axis and the value of the function on the second axis - we've done this at school many times.
If the function has two parameters, you plot one parameter on one axis, the second parameter on the second axis, and the value of the function on the third axis. You can do this in excel and see the surface.
And so on.
The function of three parameters can be represented as a commode. The xyz coordinates point to a point in space - the drawer of the dresser, and the amount of money lying in the drawer is the value of the function.
And so on.
What other coordinate axes besides X,Y,Z have we been told about in school?
What a brain-boil can one create if after not understanding multidimensionality one mentions also non-integer-dimensional objects/spaces )))) It's probably going to burst!
I wish it were sooner! ))
ZS And if you seriously want to understand it, it is necessary to ask not on a forum, and to remove a ban from google, if in the house the corresponding books aren't available.
If we add y = ax + bx + c to the equation y = ax + bx + cz + d, we get the coordinates of points on the x-axis, y-axis, and z-axis. But if we add y = ax + bx + cz + dq + e, we simply will not solve the equation because q is not the coordinate axis and we will not find points on it.
What coordinate axes other than X,Y,Z did they tell us about at school? And by the way, is it possible to see a uniform surface in Excel by adding parameters to a function? (I just haven't tried it, that's why I'm asking).
Decide. It is. We'll find it.
I understand your concept. The more parameters in the level of the analytic function, the more coordinate axes. True, it is not possible to draw a line through the calculated coordinates of points (even Excel does not support this), but you can strain your imagination and imagine fantastic multidimensional objects that lie beyond the boundaries of our space-time.
Far beyond the boundaries, somewhere in the realm of the ravenous...