Question #6407

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

Expert's answer

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.

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.

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