How to Circumscribe a Square About a Circle
Euclid is the most famous geometrician of all time. An entire field of study, Euclidean Geometry, has been named after this man who lived in Egypt more than 2,300 years ago. Euclid turned his intellect to a variety of geometrical problems, providing structured proofs for facts obvious and obscure. One of those problems was how to circumscribe a square about a circle. The method we can use today is even easier than the one he proposed.
Other People Are Reading
Instructions
-
-
1
A compass will make it easier to identify the points needed to draw a square around a circle. Draw a circle. Measure the diameter. Set the compass to the radius of the circle---half the measured diameter.
-
2
Put the point of the compass on the edge of the circle and draw an arc through the center of the circle. Move the point of the compass to a spot on the opposite side of the circle and draw another arc through the center. The two arcs intersect in the center of the circle.
-
-
3
Draw a line through the center of the circle from one edge to the other. This is a diameter.
-
4
A protractor will help with constructing a perpendicular diameter. Draw another diameter perpendicular to the existing diameter, using the protractor to make it a 90-degree angle.
-
5
Set the point of the compass at the topmost point where one of the diameters intersects the circle. Draw one arc to the right of the point and one to the left.
-
6
Move the compass point to one of the next points on the edge of the circle. Draw one arc below the point at the edge of the circle and one above.
-
7
Continue the pattern at the two remaining points on the circle. The arcs drawn in the previous three steps intersect at four points outside the circle.
-
8
Connect the four points where the arcs intersect, and the circumscribing square is complete.
-
1
References
- Photo Credit Photos.com/Photos.com/Getty Images Stockbyte/Stockbyte/Getty Images Jupiterimages/Photos.com/Getty Images
