RMP 48 is not only concerned with the square and circle but also with the inscribed pseudo-octagon. Consider a grid of 9 by 9 royal cubits, divived into 3+3+3 by 3+3+3 cubits. The pseudo-octagon in this grid has four sides of length 3 rc each, and four longer sides (diagonals of the small squares in the corners of the grid). As you can easily find, the area of the pseudo-octagon is 63 square cubits. The pseudo-octagon is close to the circle we can inscribe into the square. A close number to 63 is 64, so let us assume that the area of the circle measures 64 square cubits, or 8 by 8 cubits. The diameter of the circle measures 9 royal cubits, the area about 8 x 8 royal cubits, and from this you get the famous rule of the Rhind Mathematical Papyrus relating square and circle: a circle of diameter 9 and a square of side 8 have practically the same area.
Now for the algebraic aspect of this practical formula.
The number of the circle is smaller than 4 but a little more than 3. Begin with 4/1 and add repeatedly 3/1 in the way that was forbidden in school: