Yes, the Egyptians calculated an approximate value for pi.
While the Egyptians didn't explicitly recognize pi as a distinct mathematical constant as we do today, they employed a method for calculating the area of a circle that effectively yielded an approximation for pi. This approximation is evident in the Rhind Papyrus, a mathematical document dating back to around 1650 BC.
The Rhind Papyrus and Area of a Circle
The Rhind Papyrus describes how to find the area of a circle. Their method involved subtracting 1/9th of the circle's diameter and then squaring the result. This can be expressed as:
Area ≈ ((8/9) * d)2
Where 'd' represents the diameter of the circle.
Calculating the Egyptian Approximation of Pi
We know that the area of a circle is also given by the formula:
Area = π (r2) = π (d/2)2 = π * (d2)/4
If we equate the Egyptian approximation with the modern formula and solve for pi, we get:
((8/9) d)2 = π (d2)/4
(64/81) d2 = π (d2)/4
π ≈ (64/81) * 4
π ≈ 256/81
π ≈ 3.1605
Conclusion
Therefore, based on the formula used in the Rhind Papyrus for calculating the area of a circle, the Egyptians effectively approximated pi to be around 3.1605. This is a reasonable approximation, although not as accurate as later calculations by other civilizations.
