Mathematics Stack Exchange
Mathematics Stack Exchange

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.

1360 questions
21
votes
2 answers

If a regular polygon has a fixed edge length, can I know how many edges it has by knowing the length from corner to its center?

So I wonder if there is a formula so that when there's a defined edge length, I can calculate a regular polygon's edges amount by knowing its length from corner to center, or vice versa. So let's say our defined edge length is 1, then by knowing…
Andrew.Wolphoe
  • 379
7
votes
4 answers

Can anyone give me x,y coordinates for an octagon?

I am looking to draw a octagon and I need $(x, y)$ coordinates.
MathGuy
  • 183
6
votes
2 answers

Number of Parallel/Not Parallel Diagonals of a Regular Polygon

This is a painfully easy problem, yet the answer continues to escape me. I am seeking a general formula that can be employed to determine the number of diagonals of a regular polygon that are parallel to at least one of its sides. A quadrilateral…
Bryson S.
  • 163
4
votes
4 answers

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 polygon part myself.
Larry
  • 41
3
votes
0 answers

Find all polygons in points in plane

I have a set of points in the plane and I want to find all convex polygons without including a point inside them. For example I want to find all triangles, all four sized polygons, all four five sized polygons and so on until is possible to find…
jessica
  • 131
3
votes
1 answer

Symmetries of a polygon, according to Grünbaum

In Are Your Polyhedra the Same as my Polyhedra? by Branko Grünbaum, the author (sort of) defines the symmetries of a polygon by saying The historically and practically most important classes are defined by symmetries, that is, by isometric…
Thamus Panmegas
  • 181
2
votes
1 answer

Symmetry center of hexagon

How to show that the figure has a symmetry center for instance if we have a convex hexagon where opposite sides are of equal lenght and parallel?
Mark
  • 403
  • 5
  • 13
2
votes
0 answers

What do you call a prism / cylinder with the bases being only a sector or semicircle?

I see some references about prisms use a example of a sector as a base in the problems. But by definitions, prisms are suppose to not have bases which aren't polygons. This is why cylinders are not considered prisms, or at least you avoid calling…
AndroidV11
  • 333
2
votes
2 answers

Angle Sum of Self-intersecting polygon

If a polygon is self intersecting, is there any way to calculate its angle sum of the interior angles perhaps in terms of the number of sides and the number of points of intersection? Note we define interior angles to be the angles you get when you…
John Marty
  • 3,650
2
votes
1 answer

Fitting a general simple polygon to a regular polygon

Is there a method for finding the best fit approximation of a general simple polygon (the coastline of metropolitan France, say) by a regular polygon with given number of sides (a hexagon, say), using any reasonable interpretation of "best fit"?
u003f
  • 169
2
votes
0 answers

Finding the centre of the largest inscribed circle in an irregular polygon

[edited title] I need to find A centre point of an irregular polygon. Being an irregular polygon, I'm aware that there can be no geometric centre. I have a very specific shape in mind, it is a pentagon with 2 long sides and 3 short. The internal…
Escribblings
  • 117
2
votes
1 answer

Non Self Intersecting Polygons?

Given a set of n points is it always possible to construct a non self intersecting polygon?
harish.venkat
  • 133
2
votes
1 answer

Solve for intersecting chords inside a 9 sided polygon

I am trying to solve for the number of intersecting points inside a sphere with 9 points. Each of the nine points has 8 chords running to adjacent points.
Captric
  • 21
2
votes
1 answer

Finding center of convex polygon

If I'm given vertices of a convex polygon (in the attached image, they are D,E,F,G and H) if we know that inside the polygon there exists a point (say O) for which each angle created by any two adjacent two vertices and the O are equal. That…
Snake Eyes
  • 63
1
vote
1 answer

Arithemic progression

All the interior angles of the polygon form A.P. The common difference is 6 degree..the greatest angle is 135 degree..find the number of sides of polygon. I try to solve by using n/2[2a+(n-1)d]=(n-2)x180 but I can't solve it. I don't know what is…
Shimin
  • 25
1
2 3 4 5