The Hidden Numerical Code that Underpins Nature and the Universe
The Code is a three-part TV series about maths in the world around us,
presented by the Oxford University Maths lecturer Marcus du Sautoy.
A mysterious code underpins the world. But what does it mean and what can we learn from it? Marcus du Sautoy takes us on an odyssey to uncover the code and reveal its meaning.
du Sautoy explores the hidden numerical code that underpins nature,
going in search of the numbers, shapes and patterns in everything from
human veins to the night sky.
He begins by revealing how 12th-century
medieval clergy used simple number ratios to create cathedrals that they
felt mirrored God's creation, uses pi to predict a Brighton fisherman's
biggest-ever catch and explores the bizarre world of imaginary numbers,
claiming that the radar used by air-traffic controllers is only made
possible because of a figure that does not exist.
A code is a rule for converting a piece of information (for example, a letter, word, phrase, or gesture) into another form or representation (one sign into another sign), not necessarily of the same type.
In communications and information processing, encoding is the process by which information from a source is converted into symbols to be communicated.
Decoding is the reverse process, converting these code symbols back into information understandable by a receiver.
One reason for coding is to enable communication in places where ordinary spoken or written language is difficult or impossible.
For example, semaphore, where the configuration of flags held signaller or the arms of a semaphore tower encodes parts of the message, typically individual letters and numbers. Another person standing a great distance away can interpret the flags and reproduce the words sent.
An imaginary number is defined as any number that, when squared, results in a real number less than zero. When any real number is squared, the result is never negative, however, the square of an imaginary number is always negative. Imaginary numbers have the form bi where b is a non-zero real number and i is the imaginary unit, defined such that i 2 = −1.
An imaginary number bi can be added to a real number a to form a complex number of the form a+bi, where a and b are called, respectively, the "real part" and the "imaginary part" of the complex number. Imaginary numbers can therefore be thought of as non-zero complex numbers where the real part is zero.
The name "imaginary number" was originally coined in the 17th century as a derogatory term as such numbers were regarded by some as fictitious or useless, but today they have essential, concrete applications in a variety of scientific, engineering, and related areas.
An irrational number is defined to be any number that is the part of the real number system that cannot be written as a complete ratio of two integers.
Pi or π is the ratio of the distance around a circle to the circle's diameter. This produces a number, and that number is always the same.
However, the number is rather strange. The number starts 3.14159265... and continues without end. Such numbers are called irrational.
An irrational number cannot be fully written down in decimal form. It would have an infinite number of digits after the decimal point. These digits would also not repeat.
Irrational numbers often occur in geometry. For instance, if we have a square which has sides of 1 meter, the distance between opposite corners is the square root of two meters.
This is an irrational number. In decimal for it is written as 1.414213... Mathematicians have proved that the square root of every natural number is either an integer or an irrational number.
π (sometimes written pi) is a mathematical constant whose value is the ratio of any circle's circumference to its diameter; this is the same value as the ratio of a circle's area to the square of its radius. π is approximately equal to 3.14159 in the usual decimal positional notation.
Many formulae from mathematics, science, and engineering involve π, which makes it one of the most important mathematical constants. π is an irrational number, which means that its value cannot be expressed exactly as a fraction, the numerator and denominator of which are integers.
Consequently, its decimal representation never ends or repeats. π is also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can be equal to its value; proving this was a late achievement in mathematical history and a significant result of 19th century German mathematics.
Throughout the history of mathematics, there has been much effort to determine π more accurately and to understand its nature; fascination with the number has even carried over into non-mathematical culture.