# 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.

640 questions
Filter by
Sorted by
Tagged with
56 views

### Constructing a graph with radius two.

From cycles $C_n$, $n\geq6$, I was trying to form a new graph by adding a single vertex to $C_n$ so that the added vertex has eccentricity two and rest have three. I tried for $C_6$ and $C_7$ as given....
362 views

129 views

### If $a$ and $b$ are constructible numbers and $a ≥ b > 0$, give a geometric proof that $a + b$ and $a - b$ are constructible.

This problem was taken from Joseph Gallian's "Contemporary Abstract Algebra", 8th edition. Chapter 23, Exercise 1, Page 402: If $a$ and $b$ are constructible numbers and $a ≥ b > 0$, give a ...
75 views

### Construct a perpendicular in confined space?

About 45 years ago, I learned in school how to construct perpendicular lines with straight-edge and compasses, and I remember being taught two techniques (with variations on one). I recall how to ...
50 views

### On the intersections between ellipses whose foci are the vertices of any triangle

Given any triangle $\triangle ABC$, we can draw two ellipses, one with foci in $A,B$ and passing by $C$, and one with foci in $C,B$ and passing by $A$. We always obtain the points $D,E$, where these ...
92 views

### Construction of a graph with required number of vertices.

I am trying to construct a graph using $K_3$ graph. The graph $G$, obtained by adding vertices to $K_3$, should contain only one vertex with eccentricity two and the rest of the vertices with ...
73 views

### Squaring the circle, compass-and-straightedge construction

I have to proof that is not possible with compass-and-straightedge to construct a square which has surface equal to a disk. Let $M\subset \mathbb{C}$ with $\{0, 1\} \subset M$ and let $\cal{M}$ the ...
Consider any right triangle $\triangle ABC$. We focus on one side, $AC$, and we take the midpoint $E$ of this side. Then, we draw the circle with center in $E$ and passing by $A,C$. If we take the ...