Mathematics Stack Exchange
Mathematics Stack Exchange

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.

1013 questions
0
votes
0 answers

How to construct isosceles triangle from these given data

How do I construct an isosceles triangle ABC (|AC| = |BC| = a), given $a-v_a$ and the angle $α$?
cchris
  • 3
0
votes
3 answers

Construct a triangle given base, inradius and exradius

The following question can be found in a geometric text: Construct triangle ABC, given BC, inradius r and exradius r1, which is opposite to vertex A. I tried making the auxiliary figure for the above construction. I was pretty much able to find…
Harshit
  • 17
0
votes
0 answers

Convert gaussian $XYZ$ into magnetic heading

OK, so I'm stuck, I've tried a combination of what I can find in terms of atan, atan2. I have a Yost Labs sensor. In the 3D Test Suite it's showing a heading of $\sim234$ magnetic degrees which seems about right. Going to terminal mode I get this…
Tobias Theland
  • 1
0
votes
1 answer

Philo's line construction

The Philo line is a line segment defined from an angle and a point inside the angle as the shortest line segment through the point that has its endpoints on the two sides of the angle. There are some properties of this line in Wikipedia. But I…
eug100
  • 47
  • 5
0
votes
0 answers

How to find out how many solutions some exercise has?

I'm passing through "geometric constructions" topic and a lot of exercises have the same question in the end of their conditions: How many solutions does the exercise have ? For example, let's assume that I found a required triangle from the next…
curioushuman
  • 445
0
votes
1 answer

Is it possible to construct $\cos\frac{\theta}{3}$ from $\{0, 1, \cos\theta\}$ if $\theta$ can be trisected using straightedge and compass?

My attempt: Given $P:=\{0, 1, \cos\theta\}$, clearly we can construct the point $\sin\theta$ on the complex plane since $\sin\theta=\sqrt{1-\cos^2\theta}$, meaning $\sin\theta\in\mathbb{Q}(P)^{py}$. Now, I want to construct the point $e^{\theta i}$,…
Dick Grayson
  • 1,359
0
votes
0 answers

Construct a circle

Circles a and b intersect at M and N. Construct a circle k orthogonal to Circles a and b and touching third given circle c. Problem is supposed to be solved using inversion and/or power of a point. Since a and b intersect at M and N and k is…
JurgenKlop
  • 183
0
votes
1 answer

Questions about the problem of squaring a circle.

It was proven algebraically in 19th century that it is impossible to construct a square with an area equal to the area of a given circle using only a compass and straight edge. However, I once came across a remark that this pertained to…
Euclid Looked On Beauty Bare
  • 109
0
votes
2 answers

Construct triangle $ABC$ given point $C$ and the lines that contain the angle bisectors of angles $A$ and $B$.

The problem is as stated in the title: Construct triangle $ABC$ given point $C$ and the lines that contain the angle bisectors of angles $A$ and $B$. I'm slightly confused about the whole constructions thing; I know we're supposed to consider the…
Maths explorer
  • 677
0
votes
1 answer

if I have a length AB, defined by points A and B, how do I construct a circle with circumference AB with a compass?

I want to construct a circle with a given linear circumference with compass and straightedge. I know that you cant construct a length ¨pi¨ if the linear distance is ¨1¨, but can you find the radius? I want to do this so I can possibly take the…
Quinn Lynch
  • 1
0
votes
2 answers

Construct center of circle without using its interior

I need to find the center of a circle using compass and ruler (or preferably just a straightedge) without using the interior of the circle. In other words, no line or point can be used which is inside the circle. All lines and points used in the…
Tyler Durden
  • 954
0
votes
0 answers

Relation between the volume and surface

Is it possible to have an infinite volume of revolution of the geometric body and in the same time its finite surface area? With Respect, Oleg Yovanovich
Oleg Jovanovic
  • 1
0
votes
0 answers

Construction of roots

Is there elementary proof that, for example, $\sqrt[3]2$, cannot be constructed using rule and compass? Also, my guess is that only roots which are powers of $2$ (2nd root, 4th root, 8th root, etc.) can be geometrically constructed, is this…
1b3b
  • 1,276
0
votes
1 answer

Constructing a circle with center belonging to a line, tangent to another line and passing through a point

Given: two nonparallel lines $a$ and $b$ and point $P$. Construct: a circle whose center belongs to $a$, passes through $P$ and is tangent to $b$.
Cleric
  • 111
0
votes
0 answers

Show that every point in the interior of one circle is the orthocentre of another triangle inscribed in another circle

Let $C_1$ and $C_2$ be two circles in the plane with radius R and 3R respectively. Show that every point in the interior of $C_2$ is the orthocentre of some triangle inscribed in $C_1$. I gave a construction as follows. Take any point, call it H in…
saisanjeev
  • 2,050
1 2 3 4 5
6
7 8