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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Geometric proof of existence of irrational numbers.

It is easy, using only straightedge and compass, to construct irrational lengths, is there a way to prove, using only straightedge and compass, that there are constructible lengths which are irrational? Ie a geometric proof. And is it possible to…
TROLLHUNTER
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Thinking outside of the box

You want to draw a circle with a 4 inch radius. A trivial task for you and your trusty compass. When you go to grab your compass which has not had much love for a while you find it is rusted shut; stuck at 5 inches. Is it still possible to…
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Pair of compasses drawing a square (from children's fiction)

I have read a children's book where alien race of "square people" used a pair of compasses that drafted a perfect square when used. Now I wanted to explain to the child that it is not possible to have such a pair of compasses, but then I was not…
MartinTeeVarga
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How to divide a pizza into $n$ parts?

Let's say you have invited $(n-1)$ people for dinner. You decide that the main course consists of one pizza for each guest, so you order $n$ pizzas. Unfortunately, the pizza guy on the scooter trips on his way to your house and loses all but one…
Max Muller
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For compass and straightedge problems, are you allowed to use the compass as a ruler?

For compass and straightedge problems, you could have a line between two points A and B, and want to make a line the same size between C and line DE. If you placed the two points of the compass between A and B, and made a circle around C with the…
Piomicron
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same distance from a point to 2 non-parallel lines

There are 2 nonparallel lines $a,b$ and point $E$ which doesn't belong to any of them and lies anywhere between them. EDIT: Task is to find two couples of points F, G and H, I $\in$ y such that $|EF|=|FG|$ and $|EH|=|HI|$. (where $|FG|$ and $|HI|$…
T. Böhm
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History of Compass/Straight Edge Construction

I'm interested in learning the origin of compass/straight-edge constructions. In particular, I am interested in the historical interplay between Euclid's axioms for plane geometry, and compass/straightedge constructions: Were the axioms designed to…
Dan M. Katz
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How to construct a square equal to a given triangle.

I have a triangle $ABC$ and I want to construct a square of the same area as that of the triangle using ruler and compass. Consider the following image. I first locate the mid-points of $AB$ and $BC$ and draw a line parallel to $AB$ passing through…
caffeinemachine
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On The Construction Of An Ellipse

You know how when you construct an ellipse, you take a rope, fix it to 2 points, and stretch that rope? When the rope is being stretched, let's call the part of the string attached to the first point d1, and the part of the string attached to the…
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Geometric notion of addition for the real projective line

The real projective line $\mathbb{RP}^1 = \mathbb{R} \cup {\infty}$ is usually identified with (or defined as) the set of lines passing through the origin in $\mathbb{R}^2$. Thus, the number $m\in \mathbb{R}$ corresponds to the unique line with…
pregunton
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Construction of a right triangle

It's a high school level question which we can't seem to solve. Here it is: Given $2$ lines, one of the length of the hypotenuse and the other with the length of the sum of the $2$ legs, construct with straightedge and compass the corresponding…
Amihai Zivan
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Graphically locate the axes or foci of an ellipse from 5 arbitrary points on its perimeter.

Five distinct non-collinear points are required to define an ellipse similar to the way that three non-collinear points define a circle and can be used to determine the center point of that circle. I have found many mechanical explanations showing…
David
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What is the reflection across a parabola?

Reflection across a line is well familiar, reflection across a circle is the inversion, the point at a distance $d$ from the center is reflected into a point on the same ray through the center, but at the distance $R^2/d$, where $R$ is the radius.…
Conifold
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Did anyone ever build a mechanical device to take fifth roots, or solve general quintics?

This question is from a post from John Baez's blog on, among other things, geometrical constructions. I was hoping someone here might know the answer. In his post, Baez writes that Nowadays we realize that if you only have a straightedge, you can…
Will
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How to construct three mutually orthogonal circles in stereographic projection?

I'm new to spherical geometry and I enjoy doing ruler-and-compass constructions, so I'm trying to teach myself to do them in stereographic projection. I'm finding it challenging, to put it mildly. The following picture shows three mutually…
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