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

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1answer
30 views

Finding vertices of regular polygon

I am trying to find the vertices of a regular polygon using just the number of sides and 2 vertices. After the second vertex, I will make left turns to find each subsequent vertex that follows. For ...
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0answers
19 views

Finding vertices of a hexagon or pentagon

I have a grid of 150000 x 150000 points, and I have a list of points corresponding the x,y coordinates of a shape that make up a slightly imperfect hexagon or pentagon. I'm trying to figure out a more ...
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1answer
16 views

Regular polygon Interior angles

I am to find if any given angle(say x)can be interior angle of regular polygon.In other words,is there a regular polygon which angles are equal to X. I know the formula for sum of interior angles of ...
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0answers
6 views

How to clean Self intersecting Polygon ( remove the intersecting points ) [Multipolygon to single polygon]

I have been googling it almost for a week, my problem is that, I have a polygon which is made up of Latitude and Longitude points, I have used Douglus Pecker Algorithm to Decimate the polylines to ...
2
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1answer
17 views

Check if convex polygon is completely contained completely within another convex polygon.

How can I determine if a convex polygon is completely contained within another convex polygon where speed is critical? I've thought about doing this, which will only use inequalities: pcp = ...
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0answers
21 views

Specific polygons in \R^{3} [closed]

Find all (convex) polyhedra P in $\mathbb{R}^{3}$ with following property: for every two vertices $v, u \in P$: $[u,v] \in \partial P$ . Here $[u, v] = \{w \; \vert \; w = tv + (1-t)u, \; t \in ...
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2answers
27 views

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?
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0answers
37 views

On the centroid of a triangle

There's three different ways to see a triangle in the Euclidean plane: as three non-collinear points, say $A$, $B$, $C$; as the line segments connecting the three points, that we can parametrize as a ...
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1answer
19 views

Reference request: Topological space of polygonal chains and its properties

I'm interested in approximations of $C^1([a,b])$-functions by polygonal chains: image File:NURBstatic.svg by User:WulfTheSaxon licensed under GNU Free Documentation License A polygonal chain can be ...
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2answers
627 views

Find the area of this irregular octagon inscribed in a circle [closed]

Find the area of the octagon pictured here I do have some ideas how to solve it, but do not want to write them down here, because I'm hoping to find some different approaches. Also, see 1978 ...
0
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1answer
40 views

Given the set of all polygons with m sides and perimeter 1, why is there an element with maximal area?

The set of all polygons with $m$ sides and perimeter $1$ has an element with maximal area. I read this fact in a book, and the reference was in German. Does anyone here know? I know how to ...
2
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1answer
36 views

Area of Spherical Polygon

It appears to me that after repeated applications of Girard's theorem on the area of spherical triangles that we can obtain the surface area of a spherical polygon with interior angles ...
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0answers
35 views

Decomposition of ball in Banach Tarski paradox and covering a soccer ball

Banach Tarski paradox says that it's possible to decompose a ball in $R^3$ into a finite number of disjoint subsets, which can be then reassembled into 2 identical copies of the original ball. ...
0
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1answer
29 views

Parallel sides in regular polygons

So I've noticed a couple of things about regular polygons with an even number of sides but I'm having a hard time proving them, these are all very obvious, and I think perhaps induction is the best ...
0
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1answer
27 views

drawing the polygon

I want to draw the polygon, its sides and area is provided. e.g. number of sides : 4 length of 1st side : 1 length of 2nd side : 2 length of 3rd side : 3 length of 4th side : 4 ...
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0answers
26 views

Parameterizing equilateral polygons

I'm not exactly sure how to describe what I want, so if I butcher terms, please forgive me :) I want to "parameterize" the space of simple irregular equilateral polygons with n sides, or at least a ...
0
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1answer
20 views

ratio of “diameter” of a n-gon to perimeter

So say I have a regular polygon with n sides, and I bisect the an angle E such and the line (EF). Assume line segment EF has length b, while the polygons side length is s. What is $b/(n*s)$, and as n ...
4
votes
1answer
40 views

What is the name for a rectangular figure of many sides?

What is a polygon where each edge is at a 90 degree or 270 degree angle to the prior edge (giving both concave and convex vertices) called? Here is one example of such a shape: ...
2
votes
1answer
46 views

Regular polygons.

$1.)$ What is the minimum measure of exterior angle possible for a regular polygon. $2.)$ What is the maximum measure of interior angle possible for a regular polygon.? $3.)$ And how many sides ...
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1answer
38 views

Polygon center which always lies inside the polygon (with no hole)

Is there is any type of centre (of polygon) which always lies inside the polygon (with no hole)? Note: Here our polygon may be any type of polygon (convex or concave) but ...
3
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0answers
23 views

Do side-rational triangles of the same area admit side-rational dissections?

Call a polygon side-rational if the lengths of all its sides are rational. Call a dissection of a polygon side-rational if all of the polygons within the dissection are side-rational. Then my ...
0
votes
2answers
79 views

How many sides can a polygon have before it is “considered” a circle?

Good day, my family had a dinner discussion about polygons and how many sides a polygon has in relation to the angle measurement you'll get when you measure an "arc" encompassing a "side" of the ...
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0answers
20 views

Number of grid points in a polygon

Following problem: I want to approximate the number of grid points in a polygon, based on the condition that the distance of the grid points are variable. What i need is an approximation, i am aware ...
3
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2answers
27 views

is a line of symmetry going through the center of an octagon parallel to the ground it is on?

I came across this question recently, It wanted me to find angle EDG assuming the line crossing between the octagon/polygon is it's line of symmetry. My answer was 25 degrees, but A few friends ...
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0answers
19 views

Is there an efficient algorithm to extract the farthest ends of a thin contour?

Let's say you have pixel bitmaps that look something like this: From this I can easily extract a contour, which will be a concave polygon defined by a set of 2D points. The question is what is the ...
3
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0answers
23 views

Centroids of a polygon

Obviously, for any polygon we can define at least 3 different centroids: C1: mass center of the lamina; C2: mass center of vertices with equal masses; C3: mass center of the perimeter. For the ...
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1answer
79 views

What is a composition of two binary relations geometrically?

the composition was defined as follow: (a,b) \in (R;S) <=> there is c | (a,c) \in R and (c,b) \in S . If our two relations R and S are two convex polygon ...
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2answers
77 views

How to draw an irregular polygon given all the side lengths and total area, but no angles?

I need to draw a sketch of an irregular piece of land where I know the 8 side-lengths and the total area, but I have no information on the interior angles. The description of the terrain is as ...
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0answers
12 views

Polygonal approximation of simple, closed smooth curve.

I was wondering if you could help me with the following problem: Suppose $\gamma : [0, L] \to \mathbb{R}^2$ is an arc-length parametrisation of a simple, closed, smooth curve. If for each $n \in ...
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0answers
18 views

What is the term to define a single point in a polychoron?

I'm looking for any correct term used to define a point in 4 dimensional space. IE: What does a polychoron compose?
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1answer
34 views

Why simple polygons in plane have this property?

If we are given a simple polygon $P$ in the plane by the points $A_1, A_2, \dots, A_n$. How can we prove that there are $3$ consecutive points $A_i, A_{i+1}, A_{i+2}$ (if $i = n$, for $A_{i + 1}$ and ...
0
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1answer
242 views

Drawing ellipse as google.maps.Polygon with 8 points

In a web page using Google Maps JavaScript API v3 (including Geometry library) I currently draw an ellipse as a "diamond" with 4 corner points by the following JavaScript code: ...
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0answers
15 views

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?
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1answer
30 views

Regular polygon finding the circumference

Area of the 10 regular polygon is 770cm^2 and the gap between the parallel line is 30,8cm. Find its circumference. Yeah, I'm going to fail on this subject.
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4answers
648 views

What polyhedron has 11 vertices and 17 edges

On my math test it asked me how many polygons it takes to create a polyhedron that has $11$ vertices and $17$ edges. I'd just like to see what the shape would look like and I can figure out the ...
0
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2answers
47 views

How to connect a line between 4 randomly placed points on a plane such that the line does not cross itself

You get 4 coordinates of points on a plain. You need to connect them all with a line. The line must not cross itself. What's your strategy?
0
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1answer
9 views

Regular $n$-gons and Linear Tranformations

Let $P$ be a regular $n$-gon and let $Q$ be an another convex polygon with the same number of vertices. Is there always a linear transformation $M\colon \mathbb{R}^2 \to \mathbb{R}^2$ such that $M(P) ...
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vote
1answer
45 views

Discrete Gauß and geodesic curvature

Imagine that you have an n-polygon $S$ and you wanted to calculated the discrete Gaussian or gedoesic curvature. How are they defined? If $p$ is a vertex of $S$ then Gauß-Bonnet suggests that the ...
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0answers
21 views

Do generalizations of the golden/silver ratios have geometric representations in corresponding polygons?

A silver mean of order n is $N_n=\frac{N+\sqrt{N^2+4}}{2}$. For N=1 we get $\phi$, which is found in a regular pentagon. For N=2 we get the silver ratio, which is found in a regular octagon. Will ...
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1answer
44 views

Find a segment inside a polygon

Let $P = A_1 A_2 \dots A_n$ be a polygon in the plane, with $n \geq 4$. That is, it is a closed broken line with no self-intersections. Then $P$ determines an interior and an exterior, by the Jordan ...
2
votes
1answer
58 views

Interior angles of a polygon.

I was solving problems from Paul Zeitz's book "The Art and Craft of Problem Solving." There is a problem which states 3.2.11 Fix the proof in Example 2.3.5 on page 45. Show that even a concave ...
9
votes
3answers
283 views

Scaling and rotating a square so that it is inscribed in the original square

I have a square with a side length of 100 cm. I then want to rotate a square clockwise by ten degrees so that it is scaled and contained inside the existing square. The image below is what I'm ...
4
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0answers
58 views

Polygons with coincident area and perimeter centroids

Let $P$ be a simple, planar polygon. Define $c_a$ as the area centroid of $P$, i.e., the center of gravity of the closed shape $P$. Define $c_p$ as the perimeter centroid of $P$, the center of gravity ...
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2answers
81 views

Number of $r$-sided polygons in $P$ with no common edges

We have a $n$-sided convex polygon $P$. How many $r$-sided polygons $(r<n)$, with its vertices among those of $P$, can be formed such that it has no sides (edges) in common with $P$? I tried ...
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votes
2answers
111 views

Transform polygons into one another?

I am aware that there must be no standard way to achieve this, but I don't know what has been done so far. I feel like I'm missing keywords to investigate further. I have any two 2D polygons $a$ and ...
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1answer
39 views

How to calculate the center of a regular polygon?

What is the formula for the center of an n-edge regular polygon that has the given segment as its edge? So, given a segment AB, ...
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0answers
58 views

How do I detect if two polygons overlap each other or not?

I'm developing a game engine. Currently I'm writing the collision detection part. I have to write down an algorithm which detects if two given polygons are overlapping each other or they are separated ...
0
votes
1answer
55 views

Fattest scalene quadrilateral

What angles of a plane scalene quadrilateral maximize its area? By 'scalene' I mean the four lengths are unequal. It is known that if a quadrilateral has opposite sides equal and parallel as a ...
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0answers
27 views

Projection of a Triangle into a Tetrahedron

I was referring to a paper to implement an algorithm in which one of the step was to project the triangle into the ...
0
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1answer
33 views

Calculating rectangle having 2 coordinates and 1 length

How could I calculate the other 2 points if I have a rectangle with 2 points and 1 length given? ...