Area of a circle taken as equal to that of a square

I just picked up this book Intro to foundations and fundamental concepts of math (Howard Eves/Carroll Newsom)

Practice problem: In the Rhind papyrus area pf 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 $\pi=3.1604$

What does equal to that of a square on 8/9 mean?

ty!

--I'm not sure if I used the correct tag

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All caps is the Net equivalent of shouting. Please don't shout. – Arturo Magidin Oct 31 '11 at 19:57

The author just means that the Rhind papyrus said a circle of diameter $d$ has area equal to that of a square of side $\frac{8}{9}d$.

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is that through an inscribed square? – jxtux23 Oct 31 '11 at 20:09
No, an inscribed square would have an area visibly less than the full circle. This is simply a square whose dimensions are related to that of the circle by the given formula. – AMPerrine Oct 31 '11 at 20:13

first draw a circle with center o whose diameter is less than 10 them bisect the radius now extend the bisected line at the point at which it cuts the perimeter of the circle let that point name be A and B now measure the length of A and B and this would the side of the square whose area ia equal to that of circle.

now for the circle whose diameter is more than or equal to 10.

1)draw a circle with center o with diameter more than 10

3)at what point the bisected line segment cut the radius line let it be p

4)now bisect p and o

5)let the bisected point between p and o be q

6) now bisect q and p

7)let the point be r

8)extend the line segment r

9)now at the points at which it cuts the circle measure the length of line segment

10)this length would be equal to side of the square whose area is equal to the circle

                                 ........ research by **AV**

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Use Mathjax to format your equations. – SchrodingersCat Dec 30 '15 at 13:26