By Keith Ball
How does arithmetic let us to ship photos from house again to Earth? the place does the bell-shaped curve come from? Why do you want merely 23 humans in a room for a 50/50 probability of 2 of them sharing a similar birthday? In unusual Curves, Counting Rabbits, and different Mathematical Explorations, Keith Ball highlights how principles, commonly from natural math, can solution those questions and plenty of extra. Drawing on components of arithmetic from likelihood idea, quantity idea, and geometry, he explores a variety of suggestions, a few extra light-hearted, others critical to the improvement of the sector and used day-by-day via mathematicians, physicists, and engineers.
Each of the book's ten chapters starts via outlining key suggestions and is going directly to speak about, with the minimal of technical aspect, the foundations that underlie them. each one contains puzzles and difficulties of various hassle. whereas the chapters are self-contained, in addition they demonstrate the hyperlinks among possible unrelated themes. for instance, the matter of ways to layout codes for satellite tv for pc conversation offers upward thrust to an analogous notion of uncertainty because the challenge of screening blood samples for disease.
Accessible to a person accustomed to uncomplicated calculus, this e-book is a treasure trove of principles that may entertain, amuse, and bemuse scholars, lecturers, and math enthusiasts of every age.
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Extra resources for Strange Curves, Counting Rabbits, & Other Mathematical Explorations
Once you have identiﬁed which rules are violated by the string, you know which column to look for in the paritycheck matrix. Since there is only one way to decode each string, there cannot be two diﬀerent codewords adjacent to the same string. 1. These shapes were always polygons and their corners were points in the plane whose coordinates were whole numbers: ‘lattice points’. The idea was that we had to cut the regions up into rectangles and triangles, or else surround them with rectangles and triangles, so as to ﬁnd the area.
The magical argument by which the Coprimality Theorem establishes the Fundamental Theorem of Arithmetic was in essence known to Euclid. The fact that each whole number has a unique prime factorization makes the prime numbers the ‘building blocks’ for the integers and explains the special role of the primes in mathematics. 2. Spirographtm . mental Theorem can turn up in surprising places. The following problem is an example. 3. When I was a child there was a popular toy on the market called Spirographtm .
It will reappear in Chapter 7, where the idea of uncertainty is explored in more depth. 7 Further Reading There are several excellent text books on coding theory. I personally like the one by van Lint, which is referenced below. Most of them assume some knowledge of university-level mathematics; in particular linear algebra and group theory. uk. 21 CHAPTER 1 As was explained in the text, the codes discussed in this chapter have nothing to do with cryptography (the art of communicating information secretly).