By Alfred S. Posamentier
All of us discovered that the ratio of the circumference of a circle to its diameter is named pi and that the price of this algebraic image is approximately 3.14. What we were not informed, even though, is that in the back of this possible mundane truth is a global of puzzle, which has involved mathematicians from precedent days to the current. easily placed, pi is bizarre. Mathematicians name it a "transcendental quantity" simply because its price can't be calculated through any mix of addition, subtraction, multiplication, department, and sq. root extraction.
In this pleasant layperson's advent to at least one of math's best phenomena, Drs. Posamentier and Lehmann evaluate pi's historical past from prebiblical occasions to the twenty first century, the various fun and mind-boggling methods of estimating pi over the centuries, quirky examples of obsessing approximately pi (including an try and legislate its precise value), and priceless functions of pi in way of life, together with statistics.
This enlightening and stimulating method of arithmetic will entertain lay readers whereas enhancing their mathematical literacy.
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Additional resources for Pi: A Biography of the World's Most Mysterious Number
Let us take a quick look at how Archimedes actually came to this conclusion. ) What Archimedes did was to inscribe a regular hexagon13 in a given circle and circumscribe a regular hexagon about this same circle. He was able tofindthe areas of the two hexagons and then knew that the area of the circle had to be somewhere between these two areas. Inscribed and circumscribed hexagons Fig. 2-9 He then repeated this with regular dodecagons (twelve-sided regular polygons) and again calculated the area of each, realizing that the circle's area had to be between these values, and more closely "sandwiched in," to use a modern analogy.
We can easily calculate these with our current knowledge about the formulas for these various figures. The formula for the volume of a sphere is -nr\15 The volume of the cylinder is obtained by taking the area of the base and mul tiplying it by the height: (;rr 2 )(2r) = 2/rr3 = -/rr 3 (we wrote 2 as the fraction - to make the comparison easier). Thus the ratio of the volumes of the sphere to the cylinder is — /rr3 ~ 3 = 2 6 ^3 3 3 15 This formula was first published by Archimedes in his book On the Sphere and the Cylinder.
If you are unfamiliar with continued fractions, then see page 146 for a simple introduction 26. William Lord Viscount Brouncker (ca. 1620-1684), who found this continued fraction, was cofounder and the first president of the Royal Society (1660) 27 The bar over the digits means that the pattern continues indefinitely.