Mathematics Stack Exchange
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Questions tagged [polygons]

For questions on polygons, a flat shape consisting of straight lines that are joined to form a closed chain or circuit

In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain or circuit.

A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular: vertex) or corners. An $n$-gon is a polygon with $n$ sides. The interior of the polygon is sometimes called its body. A polygon is a $2$-dimensional example of the more general polytope in any number of dimensions.

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Finding vertex weight given the center of mass

I have a problem with given polygons. I am trying to figure out the vertex (or corner) weights. I do have the center of mass and the mass. Right now i tried simplifying the problem to a simple rectangle for text purpose. The real polygons have a lot…
Franck
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is a line segment a polygon, I guess the answer is `yes`, I just need a double confirmation.

per wiki, 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. "is a line segment a polygon"? i searched this question on…
JJJohn
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Points that are quadrilaterals

When are 4 points in a plane considered quadrilaterals? Also, could you give me examples of 4 points that are not considered quadrilaterals? Thank you in advance!
De Le
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Check if latitude & longitude coordinates are inside a specific range of a latitude longitude polygon

Since I'm not a mathematician I came here to ask what the most efficient way is to check if latitude and longitude coordinates are inside a range (for example 50 meters) of multiple latitude and longitude points (polygon). I have a list of these…
SaltyPotato
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Formula for finding area for all polygons

I have a image below, kinda hard to see but was wondering if anyone has seen this formula and what its from and how to use it. thx $$A=\frac{1}{2}\sum\limits_{i=0}^{n-1}(x_iy_{i+1}-x_{i+1}y_i)$$
fox man
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How to find the top right and bottom left vertexes of a polygon?

Having the coordinates of polygon vertexes, what is the formula to find the top right and bottom left vertexes? Also, how is top right and bottom left vertex of a polygon defined?
user3132457
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Proof or law of the number of sides of a polygon

The definition of "polygon" seems to include the fact that any polygon will have the same number of sides as points. For instance: A polygon can be defined ... as a geometric object "consisting of a number of points (called vertices) and an…
StayOnTarget
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Height of a regular polygon in terms of amount of sides and length of each side

I am trying to find an explicit expression for the length of each side $L$ of a regular $N$-sided polygon if I want the total height of the polygon to equal some unknown height $H$. I want $L$ to be in terms of the unknown height $H$ and the number…
Brothersquid
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Intersection of two monotone polygons.

I am using the following definition for a monotone polygon: A simple polygon is called monotone with respect to a line l if for any line l' perpendicular to l the intersection of the polygon with l' is connected. In other words, the…
hellomates
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Drawing of a regular heptadecagon

I found a very interesting blog (Gauss: Constructibility of Heptadecagon) that provides a complete demonstration of the correctness of the geometric construction of the regular heptadecagon found by Herbert William Richmond in 1893. The…
Fabrizio Faraone
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Sum of angles in an equilateral $n$-polygon if $n$ approaches infinity

It's obvious that in the case of an equilateral polygon, the number of angles between two sides increases in number, as are the angles themselves. Now the angle between two lines from both sides of one of the $n$ sides is clearly…
Deschele Schilder
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72-gon with points (cos(k35°), sin(k35°))

This is the question I am given, and I have a model answer for it as well... but I am having difficulty understanding it. What I can see is that the points are on a unit circle. Of course I can also see that $360°$$/$$72$ $=$ $5°$. Other than that…
mangopancake
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Shortest path planning - polygons

Hi there. I am preparing to Robotics class exam. I solved all the questions from previous years exams but I have no clue how to deal with this one. I would appreciate your help very much as no one else in the class knows the answer and I can't ask…
FemaleBear
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Show that every polygon is limited.

I've already set polygon , polygonal , limited sets . But I have no idea where to start, tried by reductio ad absurdum but did not. Any idea?
Danilo Santana
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Side length of regular decagon

Ok, so here are the informations. Area: $770 \;\mathrm{cm}^2$ bottom to top: $30.8$ height: half of $30.8$ = $15.4$ Find the perimeter?
naaame
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