Questions on the construction of geometrical figures using a limited set of "tools".
12
votes
2answers
427 views
Representing the multiplication of two numbers on the real line
There is a simple way to graphically represent positive numbers $x$ and $y$ multiplied using only a ruler and a compass: Just draw the rectangle with height $y$ in top of it side $x$ (or vice versa), ...
1
vote
2answers
481 views
construct inverse point with respect to the circle by the use of the compass alone
If the given point P lies inside a circle C ，with center O，the circle of radius OP about P intersects C in two points.
How to construct point P' inverse to point P with respect to the circle C
by ...
2
votes
3answers
394 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 ...
5
votes
2answers
5k 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 ...
20
votes
8answers
4k views
What is the (mathematical) point of geometric 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 ...
45
votes
1answer
2k views
Direct proof that $\pi$ is not constructible
Is there a direct proof that $\pi$ is not constructible, that is, that squaring the circle cannot be done by rule and compass?
Of course, $\pi$ is not constructible because it is transcendental and ...
12
votes
2answers
504 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 ...
4
votes
4answers
448 views
Constructing a triangle given three concurrent cevians?
Well, I've been taught how to construct triangles given the $3$ sides, the $3$ angles and etc. This question came up and the first thing I wondered was if the three altitudes (medians, ...
4
votes
3answers
725 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 ...
