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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Naive Understanding of Constructibility.

I am a 10th grader and recently I came to know about "Straightedge and Compass Construction". Seriously, I was stunned!!, we can actually predict that what can be constructed and what not by using "Straightedge and Compass" without actually drawing…
user234614
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Software to Explain Geometrical Construction

I would like to know about a software that will help me SHOW construction of geometrical figures. Maybe something as simple as constructing a triangle. BUT I need to see a compass and a Straight Edge/Scale/Ruler in the final video. I would then…
user72036
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Given two intersecting lines and a point, how to find a segment whose endpoints lie on each line and whose middle is the given point?

This is part of a bigger problem. We are given three points $A,B,C$ in general position. The goal is to construct a triangle $AEF$ such that the segment $AB$ is a median and $C$ is the orthogonal projection of $E$ on $AF$. We trace the line $AC$, we…
H. Potter
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Formal definition of ruler and compass constructions

I would see a formal definition of ruler and compass constructions. I have searched in internet but I haven't found a very formal definiton. Update: I founded these lectures about my question: 1 - https://www.isibang.ac.in/~jay/MC/Raghavan%201.pdf 2…
asv
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How can we divide a segment of an arbitrary length in the ratio $1:\sqrt a$, where $a$ is not a perfect square?

The question in the title is asking in general. The question given: Divide a segment of length 8cm in the ratio $1:\sqrt{12}$ How can it be done?
Novice chemist
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Divide two segments (lines)

I have two lines with length of A and B. I need to find the line with length of C where C = A/B. C=A/B For solution i can use any geometric laws (a ruler and a compass). Ultimate idea is that i can divide two real planks one into another and get a…
Арсен Кул
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Is $\cos(11^\circ)$ constructible?

I'm trying to prove whether $\cos(11^\circ)\over \sqrt{1+\sin(15^\circ)}$ is constructible. I suspect it is not, and would like to use the triple angle identity to use RRT and prove there is no constructible root, but to do this I'd need…
user665214
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proof for construction of 60 degree angle

I have a construction from the game Euclidea, puzzle 4.2: The puzzle is given point $A$ and line $\overleftrightarrow{BC}$ (just the line -- neither point is given), construct a 60 degree angle with the line through the point (shown in orange). I…
Phil Frost
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How does one verify a ruler-compass construction is valid?

I happened upon this paper by Ramanujan in which he gives an approximation for the side length of a square with area nearly equal to that of a given circle. I don't have much experience with constructions of this variety, really only that which most…
Karambwan
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Geometric construction to divide a segment

Given a segment AB, I would like to construct using only straightedge and compass, a point C on the segment AB such that $\frac{AC}{CB}$ is equal to $\frac{\phi}{2}$, where $\phi$ is the golden ratio, $\phi = 1.61803..$ . The Wikipedia article on…
Davidmath7
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Constructing a triangle between an angle with an arbitrary centroid.

Let $\overrightarrow {OA}$ and $\overrightarrow {OB}$ be two ray with common end point $O$. Let $G$ be a point lying in the interior of the $\angle AOB$. Construct a $\triangle OCD$ such that the sides $OC$ and $OD$ lie on rays $\overrightarrow…
Love Invariants
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With edge and compass construction, given cubes of volumes $a^3,b^3$, can one construct a cube of volume $a^3+b^3$?

Suppose one has cubes A and B of volumes $r_A^3$ and $r_B^3$. Using only ruler and compass constructions, I need to determine whether it is possible to construct a cube of volume $r_A^3+r_B^3$. I have already shown it is possible to take given…
Addem
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Constructing a Regular Pentagon of a Desired Length

I was working on a problem that needed to construct a regular pentagon of a desired length. I couldn’t solve it so checked the solution. The solution in the book was as follows: Draw the line $AB$ of desired length of the pentagon. Draw the…
user500668
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Construct quadrilateral $ABCD$: $AB=AD=4$, $CB=CD=5$ and $BD=6$. Construct incircle of quadrilateral $ABCD$.

Its easy to construct $ABCD$ but how can we construct incircle? As $ABCD$ is a kite is there any method? For my efforts I tried incircle as in triangle will it satisfy the question?
user402681
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Proof of construction of $30^{\circ}, 60^{\circ}, 120^{\circ}$ and $135^{\circ}$ angles

What is the proof of constructing $30^{\circ}, 60^{\circ}, 120^{\circ}$ and $135^{\circ}$ angles with ruler and compass? I can prove $90^{\circ}$ by proving that the line joining point of intersection of two circle is perpendicular to the line…
Ram Keswani
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