# Tagged Questions

Questions on the construction of geometrical figures using a limited set of "tools".

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), ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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, ...
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 ...
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