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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Why can't we write an equation for a polygon?

You can write an equation for a circle, but why can't you write an equation for a triangle or any other polygon? By equation I mean an equation that is not just a piecewise equation of lines.
Tdonut
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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 efficient manner to find the vertices (corners)…
Ian Douglas
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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?
Alexander Trauzzi
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How do I write my reference for a polygon

Given a regular pentagon ABCDE. Angle EAB = x + y I have this formula: x + y = (1/5)(180)(5-2) But how do I write the reference of that?
Jamie
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COM of a polygon

The COM of a point is the point itself. With another point you can construct a line. The COM of a line is 1/2 the distance between the COM the old point and the new measured form the former, with another point you can construct a triangle. The COM…
Sean
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Sum of interior angles of a rectilinear

For a Rectilinear (concave polygon having all sides parallel to either X or Y axis), how do we find the "sum of all the interior angles" given total number of convex corners (corner whose internal angle is 90 degrees). For example - what will be…
Chintan S.
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What is the optimal way of placing a square such that, the corners touch a set of points, and some set of points are outside the surface area?

Consider a 2D square of $16 cm^2$ should be placed inside a bounded region of width=12cm and height=12cm. A square $s_i$ is positioned at the center $(x,y,\theta_z)$, has four corners $c_0^{s_i} \cdots c_3^{s_i}$. Now, the square should be…
goldfinch
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Calculating the area of a hexagon (6-sided entity) alternative

I am kinda curious in something. When looking at a hexagon (6-sided entity) and wanting to calculate the area, could you in theory treat the hexagon as 4 triangles and one square in the middle like this? Here is my calculations, if this can be…
Nemanja Vuksanovic
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Regular polygon with 2K sides/vertices; colours and rotations

We have a regular polygon with $2K$ vertices that are coloured in $2K$ different colours(one vertex - one colour). There is another regular polygon with $2K$ vertices that are coloured in $2K$ different colours that overlaps the previous one…
King Crimson
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Which are the interior angles of a crossed rectangle?

I'm implementing an algorithm to dertermine if a polygon is convex. I believe(correct me if I'm wrong) this algorithm here(Loren Pechtel answer) will determine if a polygon, self intersecting or not, is convex. To test this I'm using a crossed…
Lead Vaxeral
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Will $n$ segments form a polygon IFF the sum of $n-1$ sides is greater than the remaining side?

I know the IFF condition holds for a triangle, but does the IFF condition hold true for any $n$-sided polygon? The IFF condition is clear in the forward direction in that it's intuitive why any $n$-sided polygon would require that the sum of any…
roulette01
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How to calculate how long each side of an regular polygon should be to fit on a grid of x*x size?

I found this formula (see link) that's supposed to calculate the length of each side of my polygon. But I end up with an negative size, my polygon has 16 sides and an radius of 24 cm. So how do I calculate how long each side should actually…
AceKiron
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Number of diagonals that cut the center of a regular polygon

An $n$-sided regular polygon ($n \geq 3$) has, as we know, $\dfrac{n(n-3)}{2}$ diagonals. If $n$ is odd, then none of those diagonals pass through the center of it. If $n$ is even, then $\dfrac{n}{2}$ diagonal passes through its center. That's the…
Feripinho
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Is it possible to divide an equilateral triangle into 16 congruent triangles?

The 16 triangles must all be congruent, and must not have overlapping sides.
idk
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In a convex 1897-sided polygon distances from chosen point to all sides independent of the choice of the point

Prove that in a convex 1897-sided polygon, in which all internal angles are equal, for any point inside this polygon, the sum of the distances from this point to all sides of the polygon is independent of the choice of the point. I tried to solve…
Mouvre
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