879 reputation
217
bio website
location
age
visits member for 10 months
seen 9 hours ago

hey :)

high-schooler with interest in math


Oct
1
comment Area Of Triangle . Given two equation and point.
Honestly, I fear that you have not tried hard enough as the answer very readily follows from the hints you have been given. Give it another try :) really think what it means to have squares.
Oct
1
comment Area Of Triangle . Given two equation and point.
intersections: (0,0), (-2,2) and (2,2), so A = 4*2*0.5 = 4 units.
Sep
27
revised Rational and irrational numbers under base pi
deleted 11 characters in body
Sep
26
comment Interpolating polynomial given only Y values
Gawd.. now that I wrote so much, I'd really like to know how you got to this question anyways :) You got me curious!
Sep
26
comment Interpolating polynomial given only Y values
Also, in my first comment I said that given any number of points, a lagrange polynomial can be constructed… It should state: "given any number of points, none of which that the same x-coordinate but differing y-coordinates, a Lagrange polynomial can be constructed". Other wise the resultant "thing", if it could be made, wouldn't even be a function. Also I meant "The constraint simply makes sure that at certain x-points, our polynomials must have HEIGHTS y an z" - my bad. Hope all this helped.
Sep
26
comment Interpolating polynomial given only Y values
So this completes the answer. So given 2 sets of y and z heights with the same x coordinates, we can construct infinitely many pairs of polynomials of the same degree (starting with a degree of 2d) which at any of the given x points (from the data sets), will have heights of y and z. As there are no unique polynomials to interpolate the data points, there are no unique roots that can be derived from the given data, we will need more constraints to be able to produce such things.
Sep
26
comment Interpolating polynomial given only Y values
So for both sets of data (with the y and z height sets, we can create infinitely many lagrange polynomials which interpolate the data sets such that the the sum of any 2 lagrange polynomials (one form the z set and one form the y set), when summed will give at a point x from the data set height k (where k is equal to y+z). Essentially, we have shown that an infinite number of polynomials will exist which will satisfy our constraints and hence we cannot recover unique original polynomials. The constraint simply makes sure that at certain x-points, our polynomials must have heats y an z
Sep
26
comment Interpolating polynomial given only Y values
A unique lagrange polynomial will exist for both sets of data and it will interpolate both of them perfectly (look up "lagrange interpolation" to see how this works). However, now consider we choose an x value outside of the ones corresponding to our data set of y's and z's. If we evaluate the f(x) of the lagrange polynomial at this x, we will clearly get some point (x,f(x)). However, we decide that we want a new polynomial that still interpolates all our previous points, but at x has a height of f(x) + k. The virtue of lagrange interpolation will allow up to construct such a polynomial too.
Sep
26
comment Interpolating polynomial given only Y values
Sure thing. So we have for 2 polynomials of the same degree and two sets of y-points with the same x-points, if I have understood correctly :) Now, though there is a constraint, it is not strong enough. Using a method called "lagrange interpolation" we can demonstrate this. This method, when given any number of points (say 2d+1, as you put it) will give a polynomial that goes through all these points and it will have a degree of 2d (1 less than num of points)! So in our case, we can state that the lagrange polynomial for our 2d+1 points must exist (we have no means of finding it explicitly).
Sep
26
answered Interpolating polynomial given only Y values
Sep
26
comment Area Of Triangle . Given two equation and point.
yes that is correct
Sep
25
answered Area Of Triangle . Given two equation and point.
Sep
24
awarded  Autobiographer
Sep
21
awarded  Benefactor
Sep
21
accepted Recurrence vs Recursive
Sep
16
awarded  Promoter
Sep
15
revised Calculating the argument of a complex number… something tends towards infinity?
added 485 characters in body
Sep
15
answered Calculating the argument of a complex number… something tends towards infinity?
Sep
14
asked Recurrence vs Recursive
Sep
13
revised Find the probability that no husband sits next to his wife
clarified own answer by removing purposeless statements