Answer to Question #6407 in Geometry for Danielle
In the Rhind papyrus area of a circle is taken as equal to that of a square on 8/9 of the circles diameter. Show that this is equivalent to taking π=3.1604
The formula given in the Rhind papyrus is
S = (8d/9)².
We know that the true formula is
St = π(d/2)².
Let's consider equality S = St:
(8d/9)² = π(d/2)²& ==> π = (8d/9)² / (d/2)² = ((8d/9) / (d/2))² = ((8d/9) * (2/d))² = (8/9 * 2)² = (16/9)² ≈ 3.1604938.
So, formula given in the Rhind papyrus uses π ≈ 3.1604.