Mathematics Stack Exchange
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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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Representing the multiplication of two numbers on the real line

There is a simple way to graphically represent positive numbers $x$ and $y$ multiplied using only a ruler and a compass: Just draw the rectangle with height $y$ in top of it side $x$ (or vice versa), like this But is there a way to draw the number…
temo
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How can I construct a square using a compass and straight edge in only 8 moves?

I'm playing this addictive little compass and straight edge game: http://www.sciencevsmagic.net/geo/ I've been able to beat most of the challenges, but I can't construct a square in 8 moves. To clarify a move is: Drawing a line Drawing a…
fredley
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What makes a difference if the ruler is marked?

The classical straightedge and compass construction problems, i.e. squaring the circle, devising a trisecting algorithm for a generic angle, doubling the cube, are they indeed answered in the positive, should the ruler be marked? Why, a marked ruler…
Tony Marshle
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Geometric construction of logarithms

Can you draw a logarithmic scale just using some clever geometric construction? Or can it only be done using an actual table of logarithms? (It's obviously trivial to draw a linear scale. It isn't hard to draw a scale where the spaces between tick…
MathematicalOrchid
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Construction of square root of 3

I came up with this construction for $\sqrt{3}$, and want to know if it's valid. Start with a unit segment $AB$. At points $A$ and $B$, draw two circles with radius 1 like so: Then, mark the points where these circles intersect as $C$ and $D$. Draw…
zenzicubic
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what name for a shape made from two intersecting circles of different sizes?

what is the name of a shape made from two circles with different radii that intersect each other? Sort of like a snowman shape, made of a big and a small ball of snow, melted together a bit! :-) Thanks
lucy
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Construct a triangle, given its angle at the vertex, and the altitude and the median drawn to the base.

The problem is from a book. Also it gives a hint: "Double the median extending it past the base, connect the endpoint the with the vertices at the base, and consider the parallelogram thus formed.". The image below is my interpretation of the…
tighten
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construct triangle given angle and centroid

I am stumped by Euclidea problem 8.11: From a triangle are given angle A and the centroid G Construct the points B and C. Please only a hint
Willemien
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Angle bisector on a piece of paper?

Let's draw $\overline{AB}$ and $\overline{CD}$ (not parallel) on a piece of paper (rectangular). The intersection of the lines AB and CD is off the paper. Is it possible to construct the section of the angle bisector falling on the piece of paper…
chx
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how do the conic sections add to the possibilities of geometric construction?

If we are limited by what we can construct with compass and straight edge, then what becomes possible by expanding our toolkit to include all conic sections? The tools would be based on already constructed points, lines and circles. I'm aware that…
Honest Abe
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Angle Quintisection

Angle trisection famously cannot be accomplished by straightedge and compass. But it can be accomplished by compass and a straightedge with two marks, or by conic sections. However, none of these devices are adequate to quintisect an arbitrary…
C Monsour
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Cube root of a line

Well this may be simple but I am not getting it. Give a line segment (of length $l$)(and a segment of unit length if you require) how to construct a line of length $l^{1/3}$ with only a straight edge and compass? I know how to draw a line with…
Qwerty
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Is there any construction method that yields all algebraic numbers?

Compass and Straightedge = rationals and square roots Origami = rationals, square roots and cube roots (I think) How far can we get if we use other tools, like rulers, protractors, pieces of string, etc? Can we cover all the algebraic numbers?
Eriek
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Regular Polyspiral (Geometry)

Criteria: -Each side of every polygon has to be the same length. -Every successive polygon has to have one more side. -Each additional polygon has to start on the opposite right side (assuming the bottom is where the polygon meets preceding polygon,…
Joe
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Construct a triangle ABC when angle A, length of angle bisector from A and circumradius are given.

Construct a triangle ABC when angle A, length of angle bisector from A and circumradius are given. Since angle A and circumradius are given, we can find out the length of BC. I can elaborate on the same further if you're interested... This seems…
Rama
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