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
2 answers

Construct line segments of lengths $a/b$ and $\sqrt {a}$

Given: 3 lines (longest one a, medium one b and unit 1) How can you construct line segments of lengths $a/b$, $\sqrt {a}$ and $a/n$ with $n$ a positive integer?
WinstonCherf
  • 1,022
0
votes
1 answer

How to draw/construct the function $\frac{\sqrt{1-x^2}}{x}$

can you help me with some hints how to draw or construct the function $\frac{\sqrt{1-x^2}}{x}$ ($x \in (0,1]$) ? I really have no idea - maybe by using unit circle..?!
Vazrael
  • 2,281
0
votes
0 answers

Divide a line into $n$ parts using a rusty compass

Using a rusty compass (a compass whose distance between the two needles can't be altered) divide a given line segment ${AB}$ into $n$ equal parts. In fact, a straightedge isn't provided. I know that whenever a compass-and-straightedge construction…
Mathejunior
  • 3,344
0
votes
1 answer

Calculating Path of Motion of Two Uneven Wheels

I had this question when observing something of the same nature with precise measurements. An object has 2 circular ends (objects) joined together by a cylinder. The length of the cylinder is 5.6cm. One of the ends has a radius of 1.7cm and the…
Phease
  • 13
0
votes
1 answer

Geometry/constructions

I want to contruct a trapes and I am finding it hard to find the last point D. 1) Construct a segment AB = 6.8 cm 2) Construct an angle at 67,5 degrees at A. 3) Construct AC = 8 cm 4) CD is parallell to AB 5) The distance between D and AB is equal…
Eirik
  • 71
  • 6
0
votes
0 answers

Geometrical construction of circle and circumscription of a pentagon about it.

How would you draw a circle of a given radius and circumscribe a regular pentagon about it using a scale and a compass. I cannot figure it out. I have checked the internet but cannot find anything valuable. Most of the sites are dealing with…
MrAP
  • 3,003
0
votes
2 answers

How do we come to know that they intersect each other outside the triangle?

I read about the fallacy of isosceles triangle Incorrect figure, Correct figure, The description states that the point of intersection of the bisector of angle(A) and the perpendicular bisector of side BC intersect each other at point D outside…
CandidFlakes
  • 866
  • 3
  • 10
  • 20
0
votes
1 answer

Constructing a line with length $\sqrt{7}R$ where $R$ is the radius of a circle

I was reviewing when I came upon a problem that requires me to construct a line with length $\sqrt7R$, where $R$ is the radius of a given circle. I can do a line with a $\sqrt7$ unit length just fine but this one just confuses me. Hope you guys…
Reese
  • 1
0
votes
1 answer

Perpendicular on angle leg is bisected by angle bisector

Contruct any angle $\angle O$ and construct its angle bisector. Pick a point on the left leg of the angle and denote it $P$. Drop a perpendicular from $P$ on the angle bisector and denote the point of intersection with the right leg $Q$. Prove that…
Lundborg
  • 1,646
0
votes
1 answer

Obtain the location of point E on side AB such that ACDE is a trapezium

In the traingle ABC, AB = 4.5cm , Ac = 9cm & angle ABC=90; The point D is located on BC such that DA = DC ; Using only a straight edge with a cm/mm scale and a compass, construct and accurate diagram Obtain the location of point E on side AB such…
user360471
  • 493
0
votes
0 answers

Location of the point P

A portion of a sketch drawn by a student to obtain the location of a point P which lies at a distance of 3cm from the given straight line AB and 5cm from the point A, is shown in the figure. Complete the sketch and mark the location of the point…
user360471
  • 493
0
votes
0 answers

What equation would the greeks need to do third roots?

Imagine you have a magic compass that will draw any equation (whereas an ordinary compass draws the equation $x^2 + y^2 = r^2$). What equation(s) would you have this magic compass draw in order that you could do third roots of lengths using it, a…
diligar
  • 646
0
votes
2 answers

Multiplication of lines of irrational length

Suppose you are given two lines, each has length of an irrational number. How would one, using a straight-edge and compass, draw a line whose length is the product of the two given irrational numbers? Edit: Yes, you are also given a unit line. But…
diligar
  • 646
0
votes
1 answer

What cube roots are constructible using compass and MARKED straightedge?

DUE DILIGENCE: I have reviewed the list of questions possibly related to the one that I pose below, and I find that none of them address my particular question. Is there a formal definition for the class of non-cubic integers whose cube roots are…
Senex Ægypti Parvi
  • 2,419
0
votes
4 answers

What is the distance of the two parallel lines?

So there is: $$\begin{align} e: 5x-2y &= 10 \\ f: 5x-2y &= -19 \end{align} $$ where $e$ and $f$ are parallel lines. Question: What is the distance of the two parallel lines?
LanceBaynes
  • 103
1 2 3 4 5 6
7
8