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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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Construct two circles tangent to each other and to a line, and a circle tangent to all three

I saw a question that was nearly the same as this, but I couldn't understand the answers. Assume that everything that seems to be tangent should be tangent, and that everything that appears to be a radius is a radius. This question is based on a…
Rex
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smallest set of curves for constructing any real number and angle

If we are limited by what we can construct with compass and straight edge, then what are the fundamental curves required for constructing any real number? In other words, what is the smallest collection of geometric objects for constructing a line…
Honest Abe
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construction of the rectangle with the highest area

I have 2 times a square with side length 2, 2 times a square with side length 3, 1 times a square with side length 4 and 1 times a square with side length 5. I have to create the rectangle with the biggest area with some or all of the squares. I…
Nick Podowalski
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Tangent Circumference Construction

"Construct a circumference that is tangent to a given circumference and tangent to a line $r$ through a point $A$ of this line." I've done the line perpendicular to $r$ through $A$, cause we know that the center of the circumference must lie in…
Derso
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Is it possible to construct a precise regular pentagon with just a straightedge (no compass)? If yes, then how?

Regular polygon = all angles have the same measure AND all sides have equal length. So, is there a possibility to draw a regular pentagon with just a straightedge? (I think you may also call it a ruler.) If the answer is "yes", then how? No compass…
Alexander
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Constructions: A straight line segment of length pi units.

A line segment of length 22/7 units or 3.14 units can be drawn. But how can a line segment be drawn of exactly pi units?
Asit Srivastava
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