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.

14
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1answer
2k views

Construction of a regular pentagon

In Robert Dixon's Mathographics, a regular pentagon is constructed with straightedge and compass only. It is the pentagon $ABCDE$ pictured below. I am having trouble seeing why the central angles ...
18
votes
2answers
4k views

Can a regular heptagon be constructed using a compass, straightedge, and angle trisector?

Euclid has a magical compass with which he can trisect any angle. Together with a regular compass and a straightedge, can he construct a regular heptagon?
0
votes
1answer
129 views

circle that touch quadrantal internally

I want to know how to construct circle that touch quadrantal(1/4 part of circle) internally. I spend several hours for solving this problem but I have no luck. I attached the picture what I've ...
10
votes
6answers
7k views

Find the maximum area possible of equilateral triangle that inside the given square

How can I find the maximum area possible of equilateral triangle that inside a square whose sides have length a. And how does that triangle look like? Can we construct it (with compass and ...
1
vote
0answers
100 views

How to determine the center of a circle with pen and straightedge [duplicate]

Possible Duplicate: Determine the centre of a circle My buddy draws a circle then he erase its center. He quiz me how can find the center with only pen and straightedge (no compass). Do you ...
2
votes
2answers
857 views

The angle trisection problem

You have an angle and you have a pen, paper, compass and a straight edge. You don't know how big the angle is, divide this angle into three equal part using only the material that is listed here? If ...
5
votes
3answers
3k views

Can a circle's circumference be divided into arbitrary number of equal parts using straight edge and compass only?

Can a circle's circumference be divided into arbitrary number of equal parts using straight edge and compass only? In other words, are all the $\frac{2\pi}{k} , k \in \mathbb N^+$ angles constructible?...
3
votes
3answers
1k views

Determine the centre of a circle

Given a circle $O$ on a paper, we do not know the centre point. Can we draw the centre only using a ruler (by which we can only draw straight lines)? One fact I know: we can draw the tangent line at ...
7
votes
1answer
312 views

Triangle from lengths of angle bisectors

According to http://www.cut-the-knot.org/triangle/TriangleFromBisectors.shtml it is impossible to construct a triangle from the lengths of its angle bisectors. Is there a more comprehensive account of ...
8
votes
1answer
674 views

Is there any (nontrivial) constructible rational angle?

Yesterday, I talked with a friend about a problem where the solution would be an angle of $2$ radians (about $114.6°$). Then somehow the question arose whether such an angle would be constructible (...
4
votes
2answers
2k views

Why can't we construct a square with area equal to a given equilateral triangle?

In modern geometry, given an equilateral triangle, one can't construct a square with the same area with the use of Hilbert tools. Why is this? The claim seems untrue to me, so there must be something ...
2
votes
1answer
350 views

geometric construction of a given angle

Given any angle how can you say that it is constructable or not?
4
votes
1answer
2k views

what name for a shape made from two intersecting circles of different sizes?

what is the name of a shape made from two circles with different radii that intersect each other? Sort of like a snowman shape, made of a big and a small ball of snow, melted together a bit! :-) ...
6
votes
3answers
8k views

Constructing a circle through a given point, tangent to a given line, and tangent to a given circle

While browsing around about problems similar to the problem of Apollonius, I have found references to constructions of all types of circles. For example, not only is it possible to construct a circle ...
12
votes
1answer
839 views

How to divide a pizza into $n$ parts?

Let's say you have invited $(n-1)$ people for dinner. You decide that the main course consists of one pizza for each guest, so you order $n$ pizzas. Unfortunately, the pizza guy on the scooter trips ...
2
votes
3answers
7k views

Construction of 145 degree angle

I've tried doing it but I end up only constructing 135 degree angle.I have to use ruler without divisions and compass.It must be done with system of isosceles and equilateral triangle and their ...
5
votes
1answer
1k views

Doubling the cube with the help of a parabola

Looking into the intersection of abstract algebra and geometry, it's well known that it is impossible to double the cube with ruler and compass, since $\sqrt[3]{2}$ is not constructible. However, I ...
15
votes
2answers
6k views

Finding the circles passing through two points and touching a circle

Given two points and a circle, construct a/the circle through the two points and touching the given circle. I came across this problem in History of Numerical Analysis by H. Goldstein. I spent some ...
1
vote
0answers
196 views

Motivation for studying compass and straightedge constructions? [duplicate]

Possible Duplicate: What is the (mathematical) point of geometric constructions? Are there good motivations to study compass and straightedge constructions? More specifically I want to know: 1)...
34
votes
10answers
14k views

What is the (mathematical) point of straightedge and compass constructions?

The ancient discipline of construction by straightedge and compass is both fascinating and entertaining. But what is its significance in a mathematical sense? It is still taught in high school ...
17
votes
2answers
5k views

Trisect unknown angle using pencil, straight edge & compass; Prove validity of technique

This question was posed by my high school geometry teacher, for extra credit: Is it possible, using only a pencil, a straightedge (not a ruler) and a compass to trisect an angle of unknown value? ...
2
votes
2answers
1k views

What is the difference in radii of two concentric circles given an angle and length of a triangle that is inscribed in the annulus?

In relation to this geometric construction: where D is the center of both circles, if the inner radius (x = length of line segments DA and DE), the angle φ = ∠CAB, and the length Δg of line segment ...
25
votes
3answers
51k views

Compass-and-straightedge construction of the square root of a given line?

Given A straight line of arbitrary length The ability to construct a straight line in any direction from any starting point with the "unit length", or the length whose square root of its magnitude ...
5
votes
4answers
926 views

What transformations of the plane are geometrically constructable (compass & straight edge)?

Congruence transformations (isometries) and similarity transformations (isometries + dilations) should be constructable. What about other affine transformations? Other conformal mappings? edit: by ...