Fattah Method
Draw the segment SR. Revolve the segment SR around the point S using compasses. A circle will be created with S as its center and SR as its radius. Draw the diameter GT perpendicular to the radius SR. Now, remove the 90-degree arc RT. There will remain two lines, a curved line and a straight line. The segment GT will be twice the segment SR and the arc GT will be twice the arc RG. The 2:1 ratio is clearly seen in either of the aforesaid pairs of lines. Now revolve the radius GS at an angle of 60 degrees around the centers G using compasses so that the hypotenuse GB is resulted. Draw the hypotenuse BT. The segment BT should be drawn; it is not automatically created. Therefore, the right angle triangle GBT with its acute angles of 30 degrees and 60 degrees will be inscribed in the semi-circle. With a 60-degree revolution the right-angle triangle GBT will be turned into the right-angle triangle ASG. The side GB will conform to the radius GS. TB is converted into AS and it will be located along SR. The hypotenuse GT is converted into the hypotenuse AG and intersect the circumference of the circle at the point (K). with such a 60-degree revolution, the inscribed right-angle triangle will change position from an inscribed status. Now, draw the hypotenuse KT with a rule and by hand. The segment AR will be cut at L. The right-angle triangle TSL will be created and it is identical to the right-angle triangle GKT. Now, draw hypotenuse RT. The right-angle triangle RST will be created with two 45º angles The two right-angle triangles TSL and RST have the side ST in common and they create together, the indefinite triangle LTR with 60, 75 and 45 degree angles. Now, rotate the triangle LTR around the center R at 90 degrees. The side RL will be tangent to the circle and perpendicular to AR. The hypotenuse TR will be turned into the hypotenuse GR.
The elevation TS is turned into the elevation GM and the side TL will be located along the hypotenuse AG in the form of the segment GL. Therefore, the right-angle triangle ARL will be created with 30-degree and 60-degree angles. The 90-degree arc GR has been inscribed in this triangle. In case the right-angle triangle ARL is rotated around the side AR, an equilateral triangle is created in which the semi-circle GRT is inscribed in the triangle with its single inscribed equilateral triangle. The length of each of the sides of this triangle is equal to that of the half-plane arc. Using the lines from the circle you will observe that the product of AL divided by divided by SR is 3.154700538000, Geometrics is the area of measurable elements. Make a circle and measure its diameter and circumference. Don’t insist on wrong reasoning. Be reasonable to consider anything with the power of a sound mind. Defend the knowledge that is based on reasoning and accept the idea that is reasonable even if it is against the wrong teachings that have already been offered to you as reasonable principles. A wise man follows reasoning and knowledge.