Polygon Definition and 115 Threads

Homework Statement In a convex polygon of 6 sides, 2 diagonals are selected at random. The probability that they intersect in the interior of the polygon isHomework Equations The Attempt at a Solution There are 9 diagonals in a polygon of 6 sides. Therefore the total cases are 9C2. But how...

Hi, I've run into a problem with expanding algebraic functions via Newton polygons. Consider the function: f(z,w)=a_0(z)+a_1(z)w+a_2(z^2)w^2+\cdots+a_{10}(z)w^{10}=0 and say the degree of each a_i(z) is ten. Now suppose I wish to expand the function around some ramification point of the...

Imagine you have a regular 13 sided polygon with charges distributed on every corner of the polygon. What would a test charge experience in the center? The answer to that was a 0 net force (which makes some intuitive sense to me due to the symmetry of the polygon). I understand that if we...

Find the area of the polygon formed by the points (3,5), (5,11), (14,7), (8,3), and (6,6). I can find the area of the polygon by dividing it into 3 triangles and then finding area of each triangle separately. I want to know if there is any simpler way of doing this.

Suppose you look at all of the equilateral (non-self-intersecting) polygons** with an odd number of sides, and each side length is equal to 1 unit. For examples, the polygon with the fewest number of sides in this group is the equilateral triangle, and then the next one is an equilateral...

Hello, I'm a civil engineering student. I learned how to contruct a funicular polygon and bending moment diagrams in two different subjects and I realized how close looking the two are, so I wondered if there was a good explanation to relate the two. I can feel it's kind of the same as the...

So any help would be really appreciated! I really have no idea where to start, and I can use any help. So essentially the problem is we have a regular polygon P inscribed in a unit circle. This regular polygon has n vertices. Fix one vertex and take the product of the lengths of diagonals...

Let say I have a triangle(polygon). I know all the co-ordinates of all points(x1,x2,x3,y1,y2,y3). Let say the polygon is inclined(at x3,y3) and it's angle is 30 degree. How to get the point x4, y4?

Hi can anyone help me out with finding the interior angles of a pentagon on a sphere. I know two of the interior angles already and I know all the angles that correspond with the arc lengths of the sides of the pentagon. How do I find the other three interior angles? Thanks

Homework Statement Show that it is possible to cut any convex polygon into 4 pieces of equal areas by using two cuts perpendicular to each other. Homework Equations None, it's just a proof I found on the back of my book. The relevant chapter is Continuity, the maximum principle, and...

Hello everybody, I have a shape (polygon) made up from pixels (squares) similar to the image below. I need an algorithm to cut it into "lines" i.e. shapes of 1x[1..20] pixels. The lines should not be necessarily straight, but they should fill the entire area. Any ideas on where to start...

Homework Statement Let C be the line segment connecting the points (x1,y1) and (x2,y2). More over let the line integral over C of (x dy - y dx) = x1y2 - x2y1. Suppose the vertices of a polygon, listed in counter-clockwise order, are (x1y1), (x2y2), ... , (xnyn). Show that the area of the...

I have a 3D shape described by a triangulation map i.e. a map between the vertices to the faces of the shape which are all triangles. I then sliced the shape by a plane and computed the intersections of the plane and the triangle faces. Each triangle face that intersects the plane, will have...

Prove that the area of the polygon with vertices at (-1,0), (-1+2^(-n), 1-(-1+2^(-n))^2), (-1+2(2)^(-n), 1-(-1+2(2)^(-n))^2),..., (1,0) is 1 + 4^(-1) + 4^(-2) + ... + 4^(-n). I tried using the formula for the area of a polygon but could not get the answer. Now sure how to prove this.

Homework Statement 1. In an equilateral triangle ABC, a line segment is drawn from each vertex to a point of the opposite side so that the segment divides the side in the ratio 1:2, creating another triangle DEF. a. What is the ratio of the area of the two equilateral triangles? b. Check the...

Homework Statement Use the polygon of forces to demonstrate that a 200 kg crate on a 25o incline is in equilibrium on the slope. Homework Equations See attached The Attempt at a Solution Please see attached for my attempt, I think I am in the right ball park, just need to know what...

Homework Statement I want to calculate the magnetic field with Biot Savart in the given drawing in the point P=(0,0,0) Homework Equations Biot Savart The Attempt at a Solution I have already problems in parametrizising the conducter loop. Can anyone give me some hints on...

Sorry if this seems elementary but what shapes are the opposite of polygons (closed by line segments) and what do you call them? Sorry if my question is phrased weird.

Here's an interesting problem: How can you find the area of any normal polygon with x sides (or corners) that is inscribed in a circle of radius 1? No trig functions, or things like e or π (Pi), or infinite series, are allowed. If possible, try to avoid summation notation as well, but that might...

If any number of forces acting on a point is in equilibrium then the forces does not necessarily form a polygon of forces? How can we prove it?

Homework Statement Evaluate Integral y^2 dx + (xy - x^2) dy over the given path C (0,0) to (2,4) the polygonal path (0,0), (2,0), (2,4) (All one question) Homework Equations integral of h (dot product) dr over C The Attempt at a Solution I realize I have to parametrize the...

Homework Statement Quadrilaterals are formed by using the vertices of a convex polygon of 24 sides. The number of quadrilaterals having atleast one side of the quadrilateral in common with the side of the polygon is ? The Attempt at a Solution We can find out the total no. of...

equation, square of resultant, R2 = Rx2 + Ry2 [b] interior angle of a polygon = (n-2)* 180°/n = (30 - 2)* 180°/30 = 168° components on X axis: Ax1 = 20* cos 168° Ax2 = 20* cos (168°+168°) . . . . Ax30 = 20* cos...

1. I have a problem like this: I. As you see (in the attachment) each of the closed polygons (as in the attachment) is called a BAY II. The logic I need is: The user of my program will select a bay (with a mouse). And after selection he would want the program to draw some vertical (or...

Homework Statement I am reading this trig book and it is saying that if both are reg polygons ( I am assuming they would have to have the same sides) that they are ratios of one another... I would like to read more on this so I understand it better... is there a link anywhere that someone can...

Homework Statement Use the polygon of forces to demonstrate that the crate is in equilibrium on the slope Homework Equations No friction 1962 N crate sitting on a inclined plane 25 degree angle. The Attempt at a Solution I have drawn four forces mg = 1962 N ( 200 kg * 9.81)...

The number of sides of two regular polygons are in the ratio 5:4 and the difference between their interior angles is 6 degrees.Find the number of sides of the two polygons. I forgot the relation between interior angles and the number of sides of a regular polygon.Can anyone help me to figure...

I don't know exactly how to explain this, but I'll try my best: Let's say I have a set of points (P1, P2, P3...Pn), that are the vertexes of a n-sided polygon. As would be expected, the polygon is drawn simply by connecting the points in order (P1 to P2, P2 to P3, Pn to P1). This is the...

Hello. Nice to be here. If I may, I would like to inquire about the enclosed area of complex polygons. Is there a general formula that will work for these and reduce/cancel out partly for simple/non self-intersecting polygons for a correct enclosed area of theirs as well? I need to compute...

polygon problem (?!) Hi there!:smile: I have got an problem here.It's a simple one.Not much to think about "The ratio between the numbers of sides of two regular polygons is 1:2 and the ratio between the sum of their 3:4.Find the number of sides in each polygon" It appears easy and is too...

how to prove that the symmetry group of a regular polygon has only 1 and 2 dim irreducible representations?

Hello everyone. While I was waiting for my computer program to run, I occupied myself with this little problem. For a fixed perimeter, which regular polygon (or any closed shape in the plane) has the largest area? The answer is the circle (I guess), if we regard it as an infinite-sided...

I am trying to code a 2D rigid body physics engine in Java, and I am having some trouble figuring out how an object will move and rotate if the force is off-center. Basically, what I can't seem to figure out is a way to find out the x, y, and rotational acceleration when a force is applied at...

Hi all! I develop an application in computer science that shows the execution of an Algorithm that triangulates a simple polygon. The first thing I have to do is to transform the given Polygon into monotone pieces, in order to do that I have to figure out the interior angles of the simple...

Homework Statement Show that the complement of the set S = {all (x, y) with x and y rational numbers} is a polygon connected set. Is it an open set? Homework Equations The Attempt at a Solution The complement of S = {all (x, y) with x not rational or y not rational} Let the...

Homework Statement A floor tile has the shape of a regular polygon. If the tile is removed from the floor and rotated through 50◦ it will fit back exactly into its original place in the floor. The least number of sides that the polygon can have is? I don't know what are the theories that i...

Homework Statement I want to plot a Regular Polygon of many sides on a X-Y graph where I know the number of sides and the radius. I would like a method to calculate the position of the corners of this shape without using compass/ruler. If there was an algorithm that goes all the way around...

Homework Statement Recall that the area enclosed by the polygon with vertices z1,z2,z3,...,zn is 1/2I(z1conguatez2+z2congugatez3+...+zncongugatez1) Show that the area enclosed =1/2I\Sigmazkcongugate(zsub(k+1)-zk). Interpret this sum as part of the approximating sum in the definition of...

Homework Statement http://i41.tinypic.com/35mno6v.jpg 2. The attempt at a solution So far, I found out that angle 4 and 5 is 55, because angle D is 110.. but I don't know if that's right. Please help!

I'm working on an engine right now, and I'm having trouble calculating the moment of inertia for a polygon. Is there any way to easily do this without decomposing the polygon into triangles? edit: I've looked at the wikipedia page with examples on the subject...

Hi, I am working on a simulation code that simulates the deformation of sand grains in 2D. The sand grains are modeled as simple polygons. However, during the simulation the grains can deform to create non-convex vertices. Further more, when deformation becomes extreme, there is a possibility...

Hi all, I want to know whether it is correct that every convex polygon has an inner-circle (& hence an inner-radius). I think it is only possible for triangle and for regular polygon. Am I right? If there is any convex N-gon having sides a_1,a_2,...,a_N which has an incircle, then...

1. Find the resultant of two forces of 40 lbs. and 50 lbs. acting at an angle of 60○ between them. 2. Three forces of 30 gms, 50 gms, and 60 gms respectively act at an angle of 120○ from each other. Find the resultant by rectangular-resolution (a) by making the 30-gm force lie on the x-axis...

Geometry is arguably my weakest link in mathematics. The answers just don't "hit me" in geometry like some other sections of math do. When trying to prove something in a polygon, such as congruence of triangles made by segments etc. I find it difficult since the equal sides/angles aren't...

I'm doing some programing and I am wondering how I can find the length of a Polygon's side (variable number of sides) from the radius (distance between center and one corner). Thank you _Zachariah

Hi all, I have this math problem where an equilateral triangle has each of its sides divided into ratio 2:1, and a smaller equilateral drawn within it from the intersecting lines. There is also a similar problem, but relating to a square. My objective is to figure out a relationship between...

[SOLVED] Moment of inertia for Concave Polygon While working on a simulation I ran into this problem. I'm trying to calculate the moment of inertia for a concave polygon. The polygon is made of N vertices (Also the edges are straight lines). I've done a bit of researching however I've only...

So i began reading up on some group theory and I came across an interesting question, what is the order of the group of symmetries on of a n-sided regular polygon? with a square it's 8, triangle it's 4. I feel like I'm missing something with the pentagon because I'm only finding these: the 5...

Hi all, I am a little confused with a supposedly simple statics concept. The topic was on vector forces and the polygon of forces with respect to a static mechanics problem. The text i was reading was a little confusing: The text also shows a diagram both spatial and a 2D polygon of...

http://www.physorg.com/news66924222.html%22 Why does the fluid act like this? I'm truly stumped... I would read the published results paper, but I can't pay for it.