Squaring the Circle

STEP 4: Construct point R such that line OR is equal to the reciprocal of line OS. 4a: Construct line D parallel to line SU through N(1). 4b: Mark point R at the intersection of line D and line X.

STEP 5: Construct point B(i) such that OB(i) = OB(i-1) + R. 5a: Draw circle E with centerpoint B(i-1) and radius equal to OR. 5b. Mark point B(i) at the intersection of circle E and line X, furthest from point O.

STEP 6: Calculate point P, such that OP / OU = π. 6a: Repeat Steps 2-5 for n iterations. 6b: Construct line F through points N(1) and B(n). 6c: Construct line G parallel to line F through point N(6). 6d: Construct point H at the intersection of line G and line X. 6e: Construct point J at the intersection of line X and circle OU. 6f: Construct point K at the midpoint between point H and point J. 6g: Construct point P at the intersection between line X and circle KJ.

STEP 7: Construct a square with the same area as a unit circle. 7a: Mark point P' at the intersection of line X and circle OP, near to point U. 7b: Mark point Q at the midpoint between point U' and point P'. 7c: Mark point S at the intersection of line Y and circle QZ. 7d: Mark point T at the intersection of line X and circle OS. 7e: Mark point V at the intersection of line Y and circle OS. 7f: Construct line T parallel to line Y and passing through point T. 7g: Construct line W, reflecting line T over line Y. 7h: Construct line V parallel to line X and passing through point V. 7i: Construct line Z, reflecting line U over line X. 7j The four intersections between the lines T, V, Q, and Z form a square with area equal to that of a unit circle.