In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain (or polygonal circuit). The bounded plane region, the bounding circuit, or the two together, may be called a polygon.
The segments of a polygonal circuit are called its edges or sides. The points where two edges meet are the polygon's vertices (singular: vertex) or corners. The interior of a solid polygon is sometimes called its body. An n-gon is a polygon with n sides; for example, a triangle is a 3-gon.
A simple polygon is one which does not intersect itself. Mathematicians are often concerned only with the bounding polygonal chains of simple polygons and they often define a polygon accordingly. A polygonal boundary may be allowed to cross over itself, creating star polygons and other self-intersecting polygons.
A polygon is a 2-dimensional example of the more general polytope in any number of dimensions. There are many more generalizations of polygons defined for different purposes.
How does a polygon shaped body's toppling shifts from one edge to next adjacent edge when the object is already in motion without any sliding and no external force is applied ? Explain it with the case of hexagon or octagon both ways, with and without including CoM.
For a shape to qualify as a polygon does it have to be closed. I was just introduced to frequency polygons and was surprised to see each one was a shape that wasn't closed. The definitions of polygon that I've come across go something like, a closed shape consisting of three or more lines.
Hello, I'm new to the forum, I want to ask help on this problem here, above is a press mechanism and I'm tasked to draw a velocity polygon based on this mechanism. The point of contact between the two gears is A and consider it as a swivel hinge (rotating but stay still), so I guess it's O2...
I’m wondering if there is a formula for calculating the coordinate points of a polygon given the following
- Center point is known
- area is known
- Point A is known
- Points B, C, and D are UNKNOWN
I am NOT a math pro - this is for a puzzle I’m trying to solve and I can’t remember if this...
Summary:: Questions about finding largest ellipse in polygon
Was wondering if someone could help me understand two concepts involved with finding largest ellipse in a polygon? Some background:
First, I set up a set of half-plane representations for the example polygon below and as you can...
Hi I made an attempt at this problem but have got the wrong answer
The correct answer is actually resultant force = 21.767 N at 61.34 degrees (or 151.34 degrees bearing), but I don't know how they got that?
Any help would be appreciated! Thanks
An ##n##-sided regular polygon is rolling down a frictional ramp at angle ##\theta## to the horizontal. I define ##\beta := \frac{2\pi}{n}## as the angle at the top of each of the ##n## isosceles triangles that make up the polygon. Let ##\omega_{k, 1}## be the angular velocity just after the...
Suppose that I have the coordinates of x and y on a plane.
I am writing a piece of software where the user can select a polygon of 3, 4, 5, 6 or 8 sides. All of the polygon points are equidistant from the x, y point. In other words, if you drew a circle where the center was the x, y point, all...
Hello everyone!
I have been looking for a general equation for any regular polygon and I have arrived at this equation:
$$\frac{nx^{2}}{4}tan(90-\frac{180}{n})$$
Where x is the side length and n the number of sides.
So I thought to myself "if the number of sides is increased as to almost look...
Hello, I'm wondering if anyone has a formula for determining whether a line intersects a polygon. I would define the line with a starting latitude/longitude and ending latitude/longitude, and I would define the polygon with a series of latitude/longitude coordinates. Many thanks in advance...
I'm trying to draw a quadrilateral in matlab. I has 4 line equations.
Can i draw that polygon, using line equations ? I knew MATLAB can draw polygon from coordinates, but i don't want to use it.
Let's say we have a somewhat complex polygon shape.
We know the list of 2d vectors that make up its border loop.
Now let's say i want to create a list of points within this polygon. Currently i am using ray traces to create a grid of points that fall within the polygon. I'm certain there is...
The original problem for anyone that can read Chinese:
https://zerojudge.tw/ShowProblem?problemid=b221
The problem defines a convex polygon with multiple points located in the first quadrant and the required task is to find a linear function y = ax that can spilt the polygon into two parts each...
In the link:
https://www.maa.org/external_archive/joma/Volume7/Aktumen/Polygon.html
Why the law of sines is permitted here? What are the goals of the author to use it?
Homework Statement
Suppose we have a regular n-gon with identical charges at each vertex. What force would a charge ##Q## at the centre feel? What would the force on the charge ##Q## be if one of the charges at the vertices were removed? [/B]Homework Equations
Principle of Superposition, the...
Hello.
Please, take a look at the screenshot from the textbook. They say in the textbook that there are in total 48 data observations, 20 of which lie in the interval 0 - 2, and 6 lie in the interval 2 - 4. Yes, both 20 and 6 are more or less clear on the graph, but how did they come up with 48...
Homework Statement
How many sides does a polygon have if the measure of each interior angle is 8 times the measure of each exterior angle?
Homework Equations
Interior angle of a polygon: ((n-2) * 180)/n
Exterior angle of a polygon: (360)/n
The Attempt at a Solution
((n-2) * 180)/n = 8 *...
I am trying to find the most efficient way to select points on a 2d plane from a set that maximizes the area of the of the shape they define when joined together.
The points are all paired (sharing the same A->B vector), with these pairs also appearing mirrored about the origin. Here is an...
I'm working on a school project and my goal is to recognize objects. I started with taking pictures, applying various filters and doing boundary tracing. Fourier descriptors are to high for me, so I started approximating polygons from my List of Points. Now I have to match those polygons, which...
Homework Statement
The problem statement is in the attached picture file and this thread will focus on question 7
Homework Equations
The length of a curve formula given in the problem statement
Take a polygon in R^n as an n-tuple of vectors (a0,...,ak) where we imagine the vectors, ai, as the...
Bert and Ernie are running around a regular polygon with x sides, all of length 12m. They start from the same point and run in opposite directions. If Bert is twice as fast as Ernie, how far will Ernie have traveled when they meet?
Homework Statement
Homework Equations
sum interior angles (n-2)*180
angles of a quadrilateral: a+b+c=d = 360
[/B]
The Attempt at a Solution
What do you do with the exterior angle?
80+130+a+x=360
I am trying to determine if a function I have is working correctly. The function computes the moment of inertia for a polygon. To test the function I created a polygon that has 4 points and represents a square of 4 units by 4 units. The answer I am getting is 32. I believe the answer should be...
I am looking for theorems/information related to the following statement: any polygon can be created by an infinite number of infinitely small "extensions" or "croppings" of any other polygon, such that the shape is always a polygon (after any amount of extensions of croppings). For example, I...
Hi,
Suppose I have a data structure that models a polygon, by storing all the nodes of the given polygon, and their connections (i.e. edges).
I understand that sorting a set of nodes that may form a concave hull is ill-defined, as there could be many polygons that can be formed with those. But...
Homework Statement
A polygon with n sides has a total of 1/p . n . (n-q) diagonals, where p and q are integers.
(i) Find the values of p and q.
Homework EquationsThe Attempt at a Solution
Can someone just help me to start on this? I know that q = 3 and p = 2 but how?
...perpendicular to its path? OK; let's say you have any charged particle moving perpendicular to a magnetic field; does it describe a gigantic polygon or a perfect circle? I think it's a polygon; the particle absorbs a "quantum of force" from the magnetic field, so to speak, and changes...
Hi!
I was wondering how I could find the equations for the bottom two functions. I understand that the amplitude is not constant like that in the circular sine function--could someone please help me out?
Thanks!
Let's say I have a 5 vertex polygon drawn on a x/y graph. Each of those vertices have an x/y coordinate.
Now let's say I want to rotate the polygon 25 degrees clockwise and calculate the new coordinates of each vertex.
How can I do that so that by knowing the original coordinate I can do a...
Hello, everyone!
My question is really simple, in fact I even feel a bit ambarrassed of asking it. :x Imagine that a car is making a constant radius turn, of a given radius R. For the purposes of this question is enough to say that the car may be thought as an isosceles trapezium, or even as a...
Sorry to bring this question up again.
@aridno provides a nice formula of the moment of inertia I about the centroid in https://www.physicsforums.com/threads/calculating-polygon-inertia.25293/ as:
$$...
I am looking for a conformal map from a "polygon" to eg the upper half plane, which consists of circle segments instead of lines. So for example, it could be a quadrilateral ABCD, but where AB is a circle segment. The closest I can find is the Schwarz-Christoffel mapping.
Anyone has any tips?
Hi,
I am wondering as to how to define the boundary condition for a shape in a unit cell. Just imagine that the shape is the hole for the unit cell. Hence, for a constant thickness on the untextured boundary, thickness is, let's say C, then for the circle, it's C+depth.
For example for...
Hi,
I need to calculate area of an irregular polygon which can be of any complex shape numerically i.e. using numerical integration techniques.
Please can anyone suggest any reference material / best way of going about this efficiently?
Akash
Suppose you have a square, and you simply start increasing the number of vertices and edges proportionally, all the way to infinity.
What, exactly, distinguishes this infinitely sided polygon from a circle?
Logically, an infinitesimal edge would be like a point on a circle, although I...
Finding the area of an irregular polygon with n side is quite easy when we are given the length of all of the n sides and the length of (n-3) specific diagonals. This way, we get (n-2) triangles whose areas can be calculated using Heron's formula and then added up.
But what if the length of...
Number of Quadrilateral that can be made using the vertex of a polygon of 10 sides as
there vertices and having Exactly $2$ sides common with the polygon
My solution:
first we will take $2$ sides common is $=10$ ways now if we take two sides as $A_{1}A_{2}$ and $A_{1}A_{3}$ then we
will...
Hi everyone,
Is there a general method for finding out the moment of inertia of an irregular convex 2D polygon given the coordinates of its vertices?
I have thought of one possible method:
Split the polygon into multiple triangles and find the moment of inertia of each triangle around the...
Hello,
I am trying to simulate collisions between polygons with opengl.
The weight, velocity (as a 2d vector), the angular velocity and the collisionpoint of the colliding polygons are provided.
How can I calculate how the angular velocity and the velocity are changed?
I do know how i...
Homework Statement
13 equal charges q are placed at the corners of a polygon and as on a clockface, what is the net force on a test charge at the center Q? I assume the charge at the center is positive and the charge on the polygon so they repel
Homework Equations
(1/4piEo)(qQ/r^2)
The...
Hey I am having a little bit of difficulty.
The classification theorem for 2 - manifolds tells me that every 2 -manifold has the following representation:
1) connect sum of n-tori
2) connect sum of n-projective planes
3) a sphere
Now, using Massey's book there is a very algorithmic...
Edgar from Facebook writes:
The sum of the measures of the interior angles of a convex polygon is ten times the sum of the measures of its exterior angles. Find the number of sides of a polygon.
Hello could you please help me to solve this problem?
In every top of a regular polygon with 2n tops there is written an integer number so the numbers written in two neighboring tops always differ by 1 ( the numbers are consecutive )
The numbers which are bigger than both of their neighbors are called ”mountains” and those which are smaller than...
I'm trying to find a reasonably fast method for testing whether or not a point (x,y euclidean coordinate system) lies inside a (preferably convex, concave or complex - though different methods for each would be OK) compound polygon with edges consisting of line segments, arcs and/or elliptical...
I was wondering if anyone knew of a common technique for parametrizing a regular polygon with an arbitrary number of sides. I figured such a problem would be easy or at least be well documented online, but that doesn't seem to be the case.
I started by assuming that the polygon was centered...
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...