Squaring a

C I R C L E

In order to square a circle, that is constructing a square with the same area as a circle, we need to rewiew some basic math skills. The area formula for a circle is (pi)r², and the area of a square is s². Let's call the radius of the the circle 1. Then the area would be pi. The square then must have an area of pi in order to be equal. Therefore, a side of the square must be the square root of pi.

To construct the square root of a number n. First you must know the unit length of 1. For example, if the length of n=3, you would have to trisect line n to find the unit 1.
Given line AB, construct the square root of AB.
Step 1. Extend line AB and find  point C on line AB so that CA= the unit length of 1.
Step 2. Find the midpoint O of line CB and construct a circle centered at O.
Step 3. Construct a perpendicular line at point A. This line intersects circle O at D. AD is the square root of AB.

Here is Kochansky's approximation of pi.
Step 1. Draw a circle P. Choose any random point A. Draw a line through PA. At point A draw a straight line perpendicular to line PA. On this line mark off points B,C,and D so that AB=BC=CD=PA=the radius of circle P.
Step 2. At point P, construct a line PG parallel to AD intersecting circle P at G.
Step 3. Draw an arc at G with radius GP. Circle G intersects circle P at F.
Step 4. Extend line PA so that it intersects circle P at E. From E, draw a line perpendicular to EA.
Step 5. Draw a line through PF. Line PF intersects line E at H.
Step 6. Line HD is the length of pi.

Now applying all the skills above, we can finally square a circle.

© 2001-2002 Robin Hu