unit circleb–adic expansionuniform distributioncyclic groupdirect sumLet be an arbitrary integer base and let be the number of different prime factors of with , . Further let be the set of points on the unit circle with finite –adic expansions of their coordinates and let be the set of ...
Answer to: a) Find all the points on the unit circle whose x-coordinate is 1/5. b) Find all the points on the unit circle whose y-coordinate is...
A point (-3,2) lies on a circle whose equation is (x + 3)^2 + (y + 1)^2 = r^2 . What is the radius of the circle? How might you find the equation of a circle if you are given only the endpoints of a radius of the circle?
Further let be the set of points on the unit circle with finite –adic expansions of their coordinates and let be the set of angles of the points . Then is an additive group which is the direct sum of infinite cyclic groups and of the finite cyclic group . If in case of the points ...
d 题目意思是，下面坐标表示的点不在单位圆上。其实就是验证一下横坐标和纵坐标的平方和是不是为1，如果是1，那就在单位圆上，如果不是1就不在单位圆上。结果得出应该选d
1. Understanding the Points on the Unit Circle: Since z1,z2,z3 lie on the unit circle, we can express them in terms of their arguments: z1=eiθ1,z2=eiθ2,z3=eiθ3 where θ1,θ2,θ3 are the angles corresponding to z1,z2,z3. 2. Using the Cosine Addition Formula: We know...
We consider the convex hull of a sample of n randomly placed points in a unit circle. Obviously not all of the n points are needed to construct the convex hull. We show that asymptotically only the points belonging to a certain ring are used for the convex hull, where the size of the...
Addendum to “Distribution of points on the circle” [J. Number Theory 127 (1) (2007) 127–135]Unit circleDistributionArcsIn an earlier paper we gave a result relating the value of an exponential sum with the distribution of summands in the arcs of the unit circle in the complex plane....
In an earlier paper we gave a result relating the value of an exponential sum with the distribution of summands in the arcs of the unit circle in the complex plane. In a marginal case, this result is superseded by a result of Lev. In this addendum we use an idea of Lev to give a...
How do you write an equation of a circle with 2 points on the circle? If the point P(-4/5,y) is on the unit circle in QII , then y = ... If point C(3,1) is the centre of a circle with a radius of 5, which of the following points lie on the circle P(-2, 2), Q...