Questions tagged [polygons]
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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How Archimedes estimated Pi, if sin is related to Pi
As far as I understood, in order to estimate Pi by Archimedes method with polygons, one may use sin function.
Now, in order to calculate sin by "hand", one need to use Pi value.
Then how he ...
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Pieces of a regular octagon [closed]
Given regular octagon ABCDEFGH, is it always true that AD||BC||HE||GF?
In order to prove this, it also needs to be proven that the diagonals of an even sided polygon bisect each angle.
These two ...
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Circular random walk to generate a Polygon
I am trying to generate a set of points distributed in such a way as to give a "rough circle" sort of shape. The points should not deviate too far from neighboring points, with larger jumps ...
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EdExcel iGCSE Higher Maths PAPER 2, Q24 - possible mistake?
I believe there is a mistake in the following question which was asked at the end of this year's iGCSE maths paper 2 in the UK. Please read through my solution or attempt it yourself and see if you ...
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Mismatching Euler characteristic of the Torus
Why is it that when I try to compute the Euler characteristic for the Torus using a drawing like the following , then the number that I get is not the number that the Torus should have? Which is $0$?
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Create a regular n-gon from sides and bounds width [closed]
I am trying to create a regular polygon with an arbitrarily number of sides with the starting parameters:
number of sides,
width of bounding box.
And the polygon should have an edge at the base.
For ...
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Prove that the Hausdorff distance and Area metric are not equivalent on the set of all bounded plane polygons.
Prove that the area metric, $d_{\Delta}$, is not equivalent to the Hausdorff distance between two sets. The book and definitions are here [1] (4.Dx & 4.Ex). The approaches I’ve tried are here:
Let ...
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What is the full symmetry group of a tile in the shape of a regular n–gon?
I am trying to answer the question on exercise 4.5.6 from the book "Algebra: Abstract and concrete" by Goodman. The chapter is on the symmetries of polyhedra and in this exercise he asks me ...
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Algorithm / equations to position a point just outside or inside the edge of a regular polygon?
Here is a polygon with a dot inside an edge, and a dot outside another edge.
How do you calculate the $x$ and $y$ position of any dot (whether it's inside or outside of the line's edge) positioned ...
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What is the maximum area that can be enclosed in a polygon formed by n wires? [duplicate]
The problem is that we have n wires of different lengths, i.e. $w_1,w_2,...,w_n$. The wires are aligned in a way such that they enclose the maximum area. What is that maximum area, or its best ...
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Necessary and sufficient conditions of the set of interior angles of a polygon
Question
Can we find a set of conditions such that for any set $A$ satisfying these conditions, a polygon can be constructed whose set of interior angles is equal to $A$, and for any polygon $P$, the ...
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Maximal irregular polygon inside a regular polygon
Problem:
We have a regular $n$-gon. We want to choose some of it's vertices ($A_1, A_2, \ldots, A_m$), so these vertices form a completely irregular $m$-gon. Meaning that all of it's sides have ...
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Is it always possible to cross two opposite pairs of adjacent sides of a convex 2n-gon by two parallel lines, not crossing through vertex?
We are given a convex polygon with even number of vertexes ($ABCDEF$ in my picture). We want to prove that it is always possible to find two pairs of adjacent sides that have the same amount of ...
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Area of Cyclic polygons
Can we generalize /extend Brahmagupta's formula to find the area of cyclic pentagons, hexagons, $n$ sided polygons $n>3$ ? For example
$$ 2s= (a+b+c+d+e), \Delta=\sqrt{s (s-a)(s-b)(s-c)(s-d)(s-e)};...
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Circular Array - Incoming Wave angle for a Polygon
I am trying to calculate the angle of a plane sound wave arriving at a circular array. A circular array has $M$ receiving elements that are lying on a circle with radius R and the distance between ...
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