# Questions tagged [geometric-constructions]

The tag has no usage guidance.

41 questions
Filter by
Sorted by
Tagged with
1 vote
73 views

### Obstruction for a manifold to admit a periodic Ricci flow

Let M be a (compact) smooth manifold. What kind of obstruction exist for M to admit a metric whose Ricci flow is a t-periodic flow?
27 views

### Alternative equivalence results for the constructibility of real numbers

Everyone is aware of the standard result from undergraduate field theory that a real number $\alpha$ is constructible by straightedge and compass if and only if there exists a finite sequence of field ...
1 vote
102 views

### Reconstructing an ellipse from an arc, synthetically

Given only an arc of a circle, we can easily reconstruct it fully without any use of analytic geometry - indeed using only compass and straightedge. Note that by "given only an arc", we mean ...
108 views

46 views

### A construction of Weyl-equivariant maps from the space of regular Cartan triples to the space of tuples of complex polynomials (up to scalar factors)

Let $G$ be a compact semisimple Lie group and let $T$ be a maximal torus in $G$. On the Lie algebra level, we have a real Lie algebra $\mathfrak{g}$ and a (particular) real slice, say $\mathfrak{t}$, ...
2k views

### How can we determine the center of a circle using a straightedge?

Given a circle with diameter AB, how can we determine the center of the circle with a straightedge (we cannot measure lengths, cannot measure angles, or draw parallel lines,... We can only draw ...
2k views

### Is the hierarchy of relative geometric constructibility by straightedge and compass a dense order?

Consider the hierarchy of relative geometric constructibility by straightedge and compass. Namely, given a geometric figure $B$, a set of points in the plane, we define that geometric figure $A$ is ...
113 views

### Geometric construction exercises

Many of you know dynamic geometry exercises in Euclidea; if not, here is one example. It lets you do a geometric construction and sends a message once you achieve the result. I am looking for a way to ...
79 views

### The power of Archimedean spirals: is there an algebraic characterization of Archimedean numbers?

I asked this question over a year ago on Math.StackExchange but I didn't get an answer. In his famous treatise On spirals, Archimedean used a spiral to square the circle and trisect an angle. There ...
Gauss–Wantzel theorem states that A regular n-gon is constructible with straightedge and compass if and only if $n = 2^kp_1p_2...p_t$, where $p_i$'s are distinct Fermat primes (A Fermat prime is a ...