compass and straightedge construction of square
One can construct a square with sides of a given length using compass and straightedge as follows:
-
1.
Draw a line segment of length s. Label its endpoints and .
-
2.
Extend the line segment past .
-
3.
Erect the perpendicular to at .
-
4.
Using the line drawn in the previous step, mark off a line segment of length such that one of its endpoints is . Label the other endpoint as .
-
5.
Draw an arc of the circle with center and radius .
-
6.
Draw an arc of the circle with center and radius to find the point where it intersects the arc from the previous step such that .
-
7.
Draw the square .
This construction is justified because , yielding that is a rhombus. Since is a right angle, it follows that is a square.
If you are interested in seeing the rules for compass and straightedge constructions, click on the provided.
Title | compass and straightedge construction of square |
---|---|
Canonical name | CompassAndStraightedgeConstructionOfSquare |
Date of creation | 2013-03-22 17:19:13 |
Last modified on | 2013-03-22 17:19:13 |
Owner | Wkbj79 (1863) |
Last modified by | Wkbj79 (1863) |
Numerical id | 5 |
Author | Wkbj79 (1863) |
Entry type | Algorithm |
Classification | msc 51M15 |
Classification | msc 51-00 |