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.

134 questions
982 views

Minimal number of moves to construct the challenges (circle packings and regular polygons) in Ancient Greek Geometry?

In the web game Ancient Greek Geometry, there are challenges to construct regular polygons and circle packings using ruler and compass constructions. The game measures the number of line and circles ...
180 views

Optimal Compass and Straightedge Constructions

I was recently looking over some Islamic geometry patterns, and was struck by the complexity of the constructions needed to create seeming simple patterns. This got me wondering regarding optimal ...
141 views

What makes a geometric construction more or less stable?

As anyone who's actually done geometric construction of n-gons knows, not all construction methods are made equal. Some are very stable (the shape you get is always close to ideal even if you're not ...
307 views

Can one trisect $\arccos(6/7)$?

Is this proof correct? Proof: Here $\theta = \arccos(6/7)$. Now to show we can't trisect $\theta$, we show that $\theta/3$ is not constructible by finding the irreducible polynomial in $\mathbb Q[x]$,...
71 views

Constraints on conical coffee cup constructions of cardioids & catacaustics

The Mathologer video Times Tables, Mandelbrot and the Heart of Mathematics discusses several relationships. For the n=2 and 3 cases, the cardiod and catacaustic (or nephroid per @Rahul's comment) ...
299 views

Find the intersection of two lines entirely outside the given sheet of paper by straightedge alone

This is a problem from Courant:"Two straight lines entirely outside the given sheet of paper are each given by two pairs of straight lines intersecting at points of the lines outside the paper. ...
Why $\pi$ is not Constructible with Circumference Length
If we use a compass to draw a circle with a diameter of length 1, then the circumference is $\pi$. From the definition given here (http://en.wikipedia.org/wiki/Constructible_number), it seems to me \$\...