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blackhash wrote:Does degree of an equation represent degree of curvature of the curve given by the equation?
VazScep wrote:The degree of an equation is just the highest power that appears on one of its variables. The degree of an equation in x and y can tell you something about the shape of the graph. So degree 1 equations graph as straight lines, and such equations are called "linear", while degree 2 equations graph as parabolas.
The parabola, ellipse and hyperbola are the three kind of curves you get by taking a cross-section of an infinite cone. But, in general, you're looking at all sorts of curve, subject to the constraint that if you draw a straight line across, it'll only cut the curve a finite number of times, corresponding to the degree.blackhash wrote:VazScep wrote:The degree of an equation is just the highest power that appears on one of its variables. The degree of an equation in x and y can tell you something about the shape of the graph. So degree 1 equations graph as straight lines, and such equations are called "linear", while degree 2 equations graph as parabolas.
That is the point. From straight line to curves(parabola,ellipse,hyperbola etc). From curves to...........?
You'd have to count "repeated roots" with that definition. x^2 = 0 has only one solution, but degree 2.crank wrote:It is the number of solutions of the equation if set to zero, but in the complex plane generally. To go to zero at some number of points does imply curvature dependence to some degree. I hope I'm not bollixing that up, it's highschool maths.
VazScep wrote:You'd have to count "repeated roots" with that definition. x^2 = 0 has only one solution, but degree 2.crank wrote:It is the number of solutions of the equation if set to zero, but in the complex plane generally. To go to zero at some number of points does imply curvature dependence to some degree. I hope I'm not bollixing that up, it's highschool maths.
blackhash wrote:I was thinking of derivations wrt an independent variable. We get the slope for an equation with degree 2. For the same equation second derivative gives us rate of change of slope(I hope I am right here). It is a constant.
So by induction I assumed for equations with degree more than 2 for independent variables we might be having successive derivations till we get a constant.
So I reached the conclusion that the degree of independent variable tells us about degree of curvature.
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