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The length of the curved part of a unit semicircle is π. We can approximate π by using t...

The length of the curved part of a unit semicircle is π. We can approximate π by using triangles and elementary mathematics. Consider the semicircle with the arc bisected as in Figure (a). The hypotenuse of the right triangle is √ 2. Hence, a rough approximation to π is given by 2 √ 2 ≈ 2.8284. In Figure (b), we consider an angle θthat is a fraction 1/k of the semicircle. The secant shown has length 2 sin(θ/2), and so an approximation to π is 2k sin(θ/2). From trigonometry, we have

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Solutions For Problems in Chapter 1.2

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