Search results
Results From The WOW.Com Content Network
In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought ...
Let E be the curve y 2 = x 3 + x + 1 over . To count points on E, we make a list of the possible values of x, then of the quadratic residues of x mod 5 (for lookup purpose only), then of x 3 + x + 1 mod 5, then of y of x 3 + x + 1 mod 5. This yields the points on E.
Curve fitting[ 1][ 2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [ 3] possibly subject to constraints. [ 4][ 5] Curve fitting can involve either interpolation, [ 6][ 7] where an exact fit to the data is required, or smoothing, [ 8][ 9] in which a "smooth" function is ...
Contact (mathematics) In mathematics, two functions have a contact of order k if, at a point P, they have the same value and their first k derivatives are equal. This is an equivalence relation, whose equivalence classes are generally called jets. The point of osculation is also called the double cusp. Contact is a geometric notion; it can be ...
In general, the two-sided offset curve of a cubic Bézier is a 10th-order algebraic curve [15] and more generally for a Bézier of degree n the two-sided offset curve is an algebraic curve of degree 4n − 2. [16] However, there are heuristic methods that usually give an adequate approximation for practical purposes. [17]
In geometry, a family of curves is a set of curves, each of which is given by a function or parametrization in which one or more of the parameters is variable. In general, the parameter (s) influence the shape of the curve in a way that is more complicated than a simple linear transformation. Sets of curves given by an implicit relation may ...
There are exactly ⌊p/12⌋ supersingular elliptic curves with automorphism groups of order 2. In addition if p≡3 mod 4 there is a supersingular elliptic curve (with j-invariant 1728) whose automorphism group is cyclic or order 4 unless p=3 in which case it has order 12, and if p≡2 mod 3 there is a supersingular elliptic curve (with j ...
The formula may also be used to calculate the genus of hyperelliptic curves. As another example, the Riemann sphere maps to itself by the function z n, which has ramification index n at 0, for any integer n > 1. There can only be other ramification at the point at infinity. In order to balance the equation