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 worth of this algebraic image is approximately 3.14. What we were not informed, although, is that at the back of this possible mundane truth is an international of puzzle, which has interested mathematicians from precedent days to the current. easily positioned, pi is bizarre. Mathematicians name it a "transcendental quantity" simply because its price can't be calculated via any blend of addition, subtraction, multiplication, department, and sq. root extraction.
In this pleasant layperson's advent to 1 of math's best phenomena, Drs. Posamentier and Lehmann overview pi's background from prebiblical instances 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 to legislate its targeted value), and beneficial functions of pi in way of life, together with statistics.
This enlightening and stimulating method of arithmetic will entertain lay readers whereas bettering their mathematical literacy.
Read or Download Pi: A Biography of the World's Most Mysterious Number PDF
Similar number theory books
"Addresses modern advancements in quantity idea and coding thought, initially provided as lectures at summer season college held at Bilkent college, Ankara, Turkey. comprises many leads to ebook shape for the 1st time. "
This e-book presents a lucid exposition of the connections among non-commutative geometry and the well-known Riemann speculation, targeting the idea of one-dimensional types over a finite box. The reader will come upon many very important facets of the idea, corresponding to Bombieri's facts of the Riemann speculation for functionality fields, in addition to a proof of the connections with Nevanlinna conception and non-commutative geometry.
- Automorphic Forms and Representations
- From Cardano's Great Art to Lagrange's Reflections: Filling a Gap in the History of Algebra (Heritage of European Mathematics)
- Introduction to Diophantine Approximations: New Expanded Edition
- Polynomial identities in ring theory
- Analytic Number Theory: Proceedings
Extra info for Pi: A Biography of the World's Most Mysterious Number
There was always "something left over" when trying to compare these two types of measurement. 8 Although Hippocrates' works are lost, we shall show an example that may have been similar to his. In other words, we will show an example where a region bounded by circular arcs can be exactly equal to a region bounded by straight lines. To tackle this, let's first recall the famous Pythagorean theorem. It states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
153846153846 ^ 9 13 13 Π 2+— 2 2 25. 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.
C R Fig. 2-3 48 π Suppose we now flip semicircle Ρ over the rest of the figure (using AB as its axis). We would get a figure as shown below. Notice that the flipped-over semicircle now forms four new regions marked L p L2, Jv and JT Fig. 2-4 Let us now focus on the lunes formed by the two semicircles. * J2 L-2 Fig. 2-5 When we extended the Pythagorean theorem (above) to semicircles instead of squares, we established that Area Ρ = Area Q + Area R The History of π 49 In the figure above, keeping in mind the largest semicircle's new position—that being flipped over the triangle—that same rela tionship can be written as follows: Area Jx + Area J2 + Area Τ = Area Lx + Area Jx + Area L2 + Area J2 Take a moment to convince yourself of this relationship.
Pi: A Biography of the World's Most Mysterious Number by Alfred S. Posamentier