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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To cut a line in two so that the squares of ... (geometric construction)

Cut a given straight line so that the sum of the square of one part and twice the square of the other part equals a given size. Given a line of length $L$ which is cut in two pieces, lengths $x$ and $L-x$, I first thought of constructing the…
mf67
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Can pentagons that are known to tile the plane be ruler and compass construction?

There are 15 types of convex pentagons are known to tile the plane monohedrally. https://en.wikipedia.org/wiki/Pentagonal_tiling I am wondering if all these 15 types pentagons are ruler and compass construction. If not, which of them can be (or not…
John
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Find all $a,b \in {\mathbb Q}$ such that $a + b \sqrt[3]{4}$ is constructible.

Find all $a,b \in {\mathbb Q}$ such that $a + b \sqrt[3]{4}$ is constructible. For this question, clearly, since every rational number is constructible, the sum of two constructible numbers is constructible and if $a$ and $b$ are constructible…
WaterBro
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Doubling the cube neusis

Can anyone explain me in simple maths the neusis construction at http://en.wikipedia.org/wiki/Doubling_the_cube#Using_a_marked_ruler? Why and how does it produce the $\root 3 \of 2$?
Sawarnik
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Ruler-and-Compass metric: draw a line from any point to separate the area of a triangle?

Given a triangle $ABC$ and a point $X$, is it possible to only use Ruler and Compass, to draw a line $l$ through $X$, such that $l$ will split $ABC$ to two parts with equal area?
athos
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Is this curve defined by an envelope construction known?

Consider the following construction. Start with the standard envelope construction of a cardioid: on a circle, join each point $\theta$ to $2\theta$. Only, instead of joining with a line, join with an arc. Of course, there are many such arcs so…
Andrew Stacey
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Division of a line segment in the given ration internally

Before I state my problem description, would like to describe problem which was stated before my problem. So it is like this Given a line segment $AB$. You are required to divide it internally in the ratio $2 : 3$. steps for this problem…
dato datuashvili
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Constructing the reciprocal of a segment

How can one construct the reciprocal length of a line segment? For example, given any line segment a, how can $\frac{1}{a}$ be constructed? I was told that it can be solved by creating similar triangles, but I do not get it.
Rex
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Construction of a point with resprect to a triangle

For a given triangle $ABC$, how to construct a point $P$ such that $PA \colon PB \colon PC = 1 \colon 2 \colon4$?
hola
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Why does a geometric construction exercise has a unique solution, when two similar triangles are the answers of the exercise?

Exercise: Construct a right triangle by the hypotenuse and the leg with a compass and a ruler without graduations. The solution figures: Note: The text book that I learn math with is on the Ukrainian language, that is the part of cyrillic. So…
curioushuman
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A doubt about what is straightedge and compass construction

The doubt comes from a try. To bisect a segment, I wonder whether I can first choose an arbitrary degree of opening for the compass, then use the compass to measure the segment until I can measure it with two times of use of the compass. It seems…
CHEN WONG
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Scaling a parallelogram to fit a triangle

How do I, with straightedge and compass, scale the red parallelogram to the green one, given the blue triangle so that both top corners of the green parallelogram touches the triangle?
mf67
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Geometric construction (problem from Swedish 12th grade ‘Student Exam’ from 1932)

The following problem is taken from a Swedish 12th grade ‘Student Exam’ from 1932. Inscribe in a given circle a quadrangle in which de two diagonals have given lengths and, in addition, where the ratio between two adjacent sides are equal to a…
mf67
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Draw a parallel line with only a straightedge

I'm trying to draw a line through point P, parallel to given line l, with only a blank ruler (a straightedge of a certain length). I know this is easy with a compass, but I don't know how to do it without anything else. Is this even…
user202112
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Construction of 145 degree angle

I've tried doing it but I end up only constructing 135 degree angle.I have to use ruler without divisions and compass.It must be done with system of isosceles and equilateral triangle and their properties ,e.g external angle and etc. and the…
randomwebdev
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