March 14, 2014

March 14 marks an important date, from a whimsically mathematical perspective at least. The numerical designation of the date–3/14–coincides with the first digits of the number pi, the ratio of a circle’s circumference to its diameter. Pi, also written as the Greek letter of the same name, π, is approximately equal to 3.14. It’s even more approximately equal to 3.14159265359. Mathematicians have approximated pi for trillions of digits after the decimal point. But those digits keep on going forever, with no apparent pattern or repetition, which makes pi an irrational number–that is, a number that cannot be represented exactly by a fraction or a decimal.

Mathematicians call pi a constant. It seems to be a fundamentally important number in mathematics, and in our universe. Without pi, mathematicians could not find the areas of circles or the volumes of spheres and cones. Without pi, physicists could not accurately describe such phenomena as electricity, gravity, and quantum mechanics.

Archimedes was a mathematician and inventor of ancient Greece. He approximated pi as the fraction 22/7. (Granger Collection)

Albert Einstein was a German-born physicist. He used pi in his famous equations for general relativity. (© Hulton/Archive)

The ancients, notably the Greeks, had some idea that the ratio of a circle’s circumference to its diameter was a special quantity. The Greek mathematician Archimedes used geometry to approximate pi as the fraction 22/7.  In the 1700′s, the Swiss mathematician Leonhard Euler discovered a famous formula that features pi:

e^πi + 1 = 0

This formula relates five of the most important numbers in mathematics, pi included. The number e is another irrational number (named after the e in Euler’s name), approximately equal to 2.718281, that features prominently in calculus. The number i, called the imaginary unit, equals the square root of –1. Some mathematicians have called this formula one of the most beautiful expressions in mathematics.

Pi Day has its roots in the San Francisco Exploratorium museum, which has celebrated the holiday since 1988. As it happens, March 14 is also the birthday of the German-born American physicist Albert Einstein, who used pi in his famous equations for general relativity. Some people celebrate Pi Day by baking pies, which, of course, all feature the number pi in the ratio of their circumferences to their diameters.

Some people enjoy memorizing the digits in pi. According to the Guiness Book of World Records, the current champion is Chao Lu of China, who recited pi from memory to 67,890 places. This feat took 24 hours and 4 minutes.

Additional World Book articles:

• Aryabhatta
• Rational number

Websites:

• Pi Day
• The Exploratorium

Nov. 29, 2011

Incredibly tiny subatomic particles called neutrinos may travel faster than light, according to a series of experiments conducted in Europe. The results were first announced in September and repeated in a refined experiment announced in November. The particles were produced at the CERN laboratory on the German-Swiss border. They then traveled about 450 miles (730 kilometers) through the ground to a giant detector in Italy. The neutrinos reportedly arrived a 0.000000058 second faster than a light beam would have.

In the early 1900′s, the physicist Albert Einstein concluded that nothing could travel faster than the speed of light–about 186,282 miles (299,792 kilometers) per second in empty space. The idea was part of a larger concept called the theory of relativity. The theory has been a cornerstone of modern physics ever since. Many of the ideas in the theory have been proven through different experiments over the years.

The Sudbury Neutrino Observatory consists of a large spherical water tank surrounded by sensors. The sensors detect flashes of light that occur when neutrinos interact with the water. Sudbury Neutrino Observatory.

If it is true that the speed of light is not a dead end, the most widely accepted theories of modern physics may need to be revised. However, neutrinos are rather unusual in nature. They probably have some mass. But this mass is so small that scientists have not yet been able to measure it directly. Neutrinos do not interact with ordinary matter easily. Many millions produced by the sun pass through our body everyday. The ghostly nature of neutrinos or a simple error in the experiment may yet undo these controversial results.

Additional World Book articles:

• Astronomy (Neutrino astronomy)
• Observatory (Neutrino observatories)
• On the Trail of the Elusive Neutrino (a Special Report)