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I chose to make 2 segments of the unit, each of area a
quarter of the unit circle, and the remained part of the circle to
be divided into two equal parts, as shown in the figure.
Let x be the central angle determined by the segment. The
area of the segment is: {1\over 2}\left(x - \sin x\right).
And
it must be a quarter the area of the circle so: {1\over 2}\left(x
- \sin x\right)= {\pi \over 4} . |
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To find a better approximation I used this graph.
Plot \left[x - \sin [x]- {\pi \over 2}, {x, 2.309,
2.31}\right]
So x \approx 2.3099.
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A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?
By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?