math

问题 I am stuck at this problem. I think it is equivalent to show 2m choose m is big theta of 4 to the power n, but still find difficult to prove it. Thanks of @LutzL's suggestion. I thought of stirling's approximation before. 回答1: The O -part should be easy. Choosing exactly n /2 elements out of n is a special case of choosing arbitrary combinations out of n elements, i.e. deciding for each of these n elements whether to choose it or not. The Ω -part is harder. In fact, plotting 4n / binomial(2 n

问题 I am stuck at this problem. I think it is equivalent to show 2m choose m is big theta of 4 to the power n, but still find difficult to prove it. Thanks of @LutzL's suggestion. I thought of stirling's approximation before. 回答1: The O -part should be easy. Choosing exactly n /2 elements out of n is a special case of choosing arbitrary combinations out of n elements, i.e. deciding for each of these n elements whether to choose it or not. The Ω -part is harder. In fact, plotting 4n / binomial(2 n

问题 I'm attempting to write a program in C which finds the numeric value of the second derivative of f(x) where x is given. When I use my function to find the first derivative, everything seems to be working okay, but the recursive second derivative part always gives me 0.0. Here's my function: double derivative(double (*f)(double), double x0, int order) { if(order == 1){ const double delta = 1.0e-6; double x1 = x0-delta; double x2 = x0+delta; double y1 = f(x1); double y2 = f(x2); return (y2 - y1

问题 Sorry for my language since English is my second language. I am trying to convert a straight line into a fractal known as Koch curve. The 2 points of the straight line are given and then I need to create the Koch curve where I divide the line to 3 segments and then make the second segment an equilateral triangle. See http://www.tgmdev.be/curvevonkoch.php. So far we convert the straight line to 4 equally segments, and I need to figure out all the coordinates of the Koch curve. I have thought

问题 I am trying to calculate my location with help of 3 stations (p1,p2,p3) with radius (r1,r2,r3). Stations are in 3D space. Example 1: P1=(2,2,0), P2=(3,3,0), P3=(1,4,0) r1=1 r2=1 r3=1.4142 Result should be: P=(2,3,0) Example 2: P1=(2,1,0), P2=(4,3,0), P3=(4,4,1) r1=2, r2=2, r3=2.449 Result should be: P=(2,3,0) My code: private void button1_Click(object sender, EventArgs e) { double x1, x2, x3, y1, y2, y3, z1, z2, z3; double.TryParse(textBox1.Text, out x1); double.TryParse(textBox2.Text, out x2

问题 I want to get the angle between two lines with respect to direction of the line. A normal dot product of the 2 vectors of the lines always returns the lowest angle between the two lines, which is not what I'm looking for. Example image: Blue lines: The lines I have Red lines: indication of the direction Green lines: failed attempt at a curving line that indicates the direction of the rotation I want. p0~p3: the x, y coordinates of the points of the lines. a: The angle I am looking to get. I

问题 I want to get the angle between two lines with respect to direction of the line. A normal dot product of the 2 vectors of the lines always returns the lowest angle between the two lines, which is not what I'm looking for. Example image: Blue lines: The lines I have Red lines: indication of the direction Green lines: failed attempt at a curving line that indicates the direction of the rotation I want. p0~p3: the x, y coordinates of the points of the lines. a: The angle I am looking to get. I

问题 I know this sounds like a homework assignment, but it isn't. Lately I've been interested in algorithms used to perform certain mathematical operations, such as sine, square root, etc. At the moment, I'm trying to write the Babylonian method of computing square roots in C#. So far, I have this: public static double SquareRoot(double x) { if (x == 0) return 0; double r = x / 2; // this is inefficient, but I can't find a better way // to get a close estimate for the starting value of r double

问题 Let us suppose we have a number circle, that ranges from -180 to 180, looking something like this: 180/-180 *** *** *** 90 *** *** -90 *** *** *** 0 A section of the circle is always swept in a clockwise direction. How can you tell if a number is inside or outside of the interval swept? In the following sample I/O, the first two numbers represent the interval and the third number is the number being checked. Output is true if the point is (inclusively) inside the interval, false otherwise. 2

问题 I am trying to find a user through their Bluetooth strength (RSSI value). I have 3 Raspberry PIs, each gathering the signal strength of the user. Lets say the nodes returned: node1 = 65 node2 = 70 node3 = 75 How would I find the user through triangulation and pin point them on a map, and output the RSSI value? I have researched Trilateration and Ceva's Theorem but do not know how to implement them. I am unsure on how to locate the nodes in an environment, do I give the main node a location of