That solution is refering to the ancient problem of squaring the circle and refers to a square with an area equal to that of the circle.
The solution given " If we take this solution as a general formula, then in modern notation we obtain the “formula” for the area A of a circle of diameter d as: A = d−d 9 2 = 64 81 d2. From this we deduce (since A = π d2/4) that the ancient Egyptians implicitly used the value π = 256/81 = (4/3)4 = 3.160493827..."
However there are 2 questions in this problem. 1. to find a square equal in area to that of the circle and 2. to find a square with perimeter equal to the circumference. Many think 1 square solves both questions however not so.
By the way it's not possible to do this with the exact value for pi and Rind 50 is using 3.1604.
I first published one solution on this in 1995.
For example your number 897.6 has a diameter of 284.00625 using the Egyptian value for pi.
If you wanted to 'square the circle' using the Egyptian value for pi 3.1604 then simply do this.
Take the number 897.6 make the diameter of a circle 284.00625 then divide it by construction into 9 even spaces / 9 = 31.55625 then measure to the 8th space.
31.55625 x 8 = 252.45 this then is the side of a square the area of which equals that of the circle using the Egyptian value for pi 3.1604 63731.00251 square feet
The diameter / 2 and squared and multiplied by 3.1604 or 284.00625 / 2 = 142.003125
142.003125 squared = 20,164.88751 x 3.160493827 = 63731.00251 same number arrived at by simply dividing by 9 and multiplying by 8 then squaring.
The next problem is to find a square equal in perimeter to that of the circles circumference.
Your number as diameter 284.00625
Begin where we left off and repeat process 252.45 / 9 = 28.05 x 8 = 224.4 this then is the side of a square the perimeter of which equals that of the circle. 224.4 x 4 = 897.6 or 284.00625 x 3.16049... = 897.6
The Egyptians were indeed squaring a circle and interesting how your number 897.6 worked out so neatly with diameter 284.00625. Hope I havnt made a mistake.