Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [geometric-construction]

Questions on constructing geometrical figures using a limited set of tools. The compass and straightedge are almost always allowed, while other tools like angle trisectors and marked rulers (neusis) may be allowed depending on context.

The most common use of "geometric construction" refers to the "compass and straightedge" constructions in classical Euclidean geometry. The notion has been extended also to (a) compass/straightedge constructions in non-Euclidean geometries and (b) allowing different sets of tools such as a marked straightedge (neusis) or origami.

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Tools other than compass and straightedge

What other mathematical construction tools or methods do exist apart from compass and straightedge? I know of folding and neusis (incl. tomahawk), also perhaps calipers (dividers) for plastic ratio. One question mentioned "3D ruler": Are there…
curious_metazoan
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Ruler and compass construction

Given the three line segments below, of lengths a, b and 1, respectively: construct the following length using a compass and ruler: $$\frac{1}{\sqrt{b+\sqrt{a}}} \ \ \text{and} \ \ \ \sqrt[4]{a} $$ Make sure to draw the appropriate diagram(s) and…
Yahya Farooq
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Compass and ruler construction

Given the three line segments below, of lengths a, b and 1, respectively: construct the following length using a compass and ruler: $$\frac{1}{\sqrt{b+\sqrt{a}}} \ \ \text{and} \ \ \ \sqrt[4]{a} $$ Make sure to draw the appropriate diagram(s) and…
HKT
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Euclidean constructions

I have been playing with a Euclidean geometry application call euclidea. I have been completely stuck on this level for a while now. Any ideas how to solve this problem using only a compass and straight edge?
Mike
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given two concentric circles construct a particular chord

I am stumped by another Euclidea problem - Euclidea problem 9.8: Given two concentric circles $C_1$ and $C_2$ with radians $r_1$ and $r_2$, with $r_1 < r_2 < 2 r_1 $ Construct the chord $e$ of $C_2$ intersecting $C_2$ at $A$ and $B$, $C_1$ at $D$…
Willemien
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Construct a circle with straight edge and compass with some given conditions.

A line is given and two points in one half plane of the line are given. Construct a circle passing through these two points such that the given line is tangent to this circle. I have no idea how to do this. I have derived the radius of the required…
Satvik Mashkaria
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Triangle Construction being known its perimeter, height and angle

"Construct a triangle $ABC$ knowing his perimeter, the angle $\widehat{A}$ and the height relative to $BC$, i.e., $h_a$." It really looks to be an easy one, but I wasn't able to do it... :( Any hint? (I only done two paralel lines with distance…
Derso
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Construct a triangle given an angle and two medians

Construct, with ruler and compass, a triangle $ABC$ knowing the angle $\widehat{A}$ and $m_a$ and $m_b$, where $m_a$ and $m_b$ are the medians relative to the vertices $A$ and $B$, respectively.
Derso
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Construction of pentagon with all sides and alternative two angles given.

All sides of a pentagon ABCDE are given. Angles A & C are given. Can such pentagon be created by straightedge and compass?
Satvik Mashkaria
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Constructing "strange" sets by removing elements: Is there any comparison?

Recently I had a thought about some sets with special properties that are constructed from a starting set $A$ and successively removing elements from it. I am not an expert in set theory but perhaps someone who is can enlighten me. To be more…
Georgy
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Could $2^{1/n}$ be straightedge-and-compass constructible for some $n \in \mathbb{N}$ that is NOT a power of 2?

I understand that the square root of an integer is constructible using straightedge and compass; but are they the only constructible radicals? Any hint would be greatly appreciated.
Dick Grayson
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Multiplication of variables with a compass when a segment of length 1 is not given.

"Suppose that length a and b are given. Construct sqrt(ab) (Not that a segment of length 1 is not given)." I know how to multiply ab together and then take the square root of ab if a length of segment 1 is given but not when it is not.
eric zhou
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What does "$\cos(\pi/17)$ is an algebraic number of degree $8$" mean? (Heptadecagon, Wolfram MathWorld)

In Heptadecagon page: The trigonometric functions $\cos(\pi/17)$ and $\cos(2\pi/17)$ are both algebraic numbers of degree 8 given respectively by: $\cos(\pi/17) = (256x^8-128x^7-448x^6+192x^5+240x^4-80x^3-40x^2+8x+1)_8\\ \cos(2\pi/17) =…
auntyellow
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Constructing to locate V from U

Two undirected red line segments are placed diametrically opposite along diameter on a unit circle of radius OF such that the product $$ Uu\cdot Vv= OF^2 $$ remains a constant thus mapping U to V. If the position of U is given then what geometric…
Narasimham
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Construction of a line segment having length $x^2$, where $x$ is the length of a given line segment

Suppose that we have a line segment of length $8.4$ units. Is it possible to draw another line segment of length $8.4^2$ units, using only an unmarked straight edge and compass? I have no clue about how to approach this problem. I could think of…
Vansh Saini
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