Knee Chapter 1b
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"Root" rectangles obtained inside a square:
The "root" rectangles constructed below (Figure I-11) are within a square (or "unity"), by essentially the same simple geometrical method as for the outside the square. Arc AB (the dotted line) is a quadrant arc with the center D and the radius line DB. DC is a diagonal to the square ACBD, and it cuts the quadrant arc at F. A line, parallel to the top of the square, is drawn through F. This line determines an internal "root-two" rectangle and DE forms its diagonal.
Next, the diagonal to the internal "root-two" rectangle cuts the quadrant arc at H. Then, DG becomes a "root-three" rectangle, the diagonal of which cuts the quadrant arc at J. DI is a "root-four' rectangle and its diagonal cuts the quadrant arc at L. DK is a "root-five" rectangle and its diagonal cuts the quadrant arc at M. All the "root" rectangles may be thus obtained within a square.
