That ratio, which is about 3. We memorized these and similar formulas for the S. Is it some kind of weird circle fixation? The beauty of pi, in part, is that it puts infinity within reach. Even young children get this. The digits of pi never end and never show a pattern. This tension between order and randomness is one of the most tantalizing aspects of pi. Pi touches infinity in other ways.
For example, there are astonishing formulas in which an endless procession of smaller and smaller numbers adds up to pi. The appearance of this formula alone is cause for celebration. It connects all odd numbers to pi, thereby also linking number theory to circles and geometry.
In this way, pi joins two seemingly separate mathematical universes, like a cosmic wormhole. After all, other famous irrational numbers, like e the base of natural logarithms and the square root of two, bridge different areas of mathematics, and they, too, have never-ending, seemingly random sequences of digits.
And in , self-taught British mathematics teacher William Jones introduced the use of the Greek letter to represent the constant in his book A New Introduction to the Mathematics. In more recent times, the advent of computers has allowed pi aficionados to calculate the number to astronomically high levels of accuracy, far beyond anything Archimedes and his ilk could ever have imagined. For example, in November , Peter Trueb successfully calculated the constant to a world-record 22,,,, twenty-two trillion, four hundred fifty-nine billion, one hundred fifty-seven million, seven hundred eighteen thousand, three hundred sixty-one figures using a special program called y-cruncher.
The computer he used to run the program contained 24 hard drives and 6 terabytes of memory to store the huge quantity of data required to process the numbers. Calculating pi to this level of accuracy has few practical uses, though—other than for testing supercomputers and high-tech algorithms—as most scientific applications require only hundreds of digits or fewer. For example, NASA uses a maximum of 15 digits in its calculations for sending spacecraft to other planets. And with 39 digits, you would be able to calculate the circumference of the known universe to within the width of a single hydrogen atom, according to mathematician James Grime.
Despite this, pi itself is incredibly useful because it relates to the circle and so is found in many formulae in fields such as trigonometry a branch of mathematics which examines the relationship between the lengths and angles of triangles and geometry the field of mathematics concerned with shapes, size, relative positions and the properties of space —which are essential to sectors like architecture and robotics, among others.
But pi also has countless applications beyond geometry and trigonometry. For example, it can help scientists to understand objects and phenomena in nature which contain circular shapes, such as the orbit of the planets or the concentric waves created by a stone falling into a pond. Whether or not humans and gods grasp the irrational number, pi seems to crop up everywhere, even in places that have no ostensible connection to circles.
Strange, no? But pi's ubiquity goes beyond math. The number crops up in the natural world, too. It appears everywhere there's a circle, of course, such as the disk of the sun, the spiral of the DNA double helix, the pupil of the eye, the concentric rings that travel outward from splashes in ponds.
Pi also appears in the physics that describes waves, such as ripples of light and sound. It even enters into the equation that defines how precisely we can know the state of the universe, known as Heisenberg's uncertainty principle.
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