Pi!
Time for my favorite topic: pi.
Pi is an irrational number. Its decimal trail extends to infinity, meaning that the complete number will never be calculated (See the infinity post). Pi is generally seen as equaling 3.1415926353…, but is actually far more complex than that. Other than simply using it in area and volume equations, it seems useless. However, pi is extremely valuable to math, and has a rather simple origin.
Pi is derived from the ratio of a circle’s area to its radius squared. For example, imagine a circle with a radius of two units. The area would thus be πr^2, or 4π. This divided by 4, or r^2, equals π. Another method to finding π is through inscribing a polygon with many sides into a circle, taking its area, and dividing it by the radius. This produces a close value to π, but not the actual number.
π cannot be found through any series of integer operations, meaning it is trancendental. The letter π is Greek and origin, and is likely derived from the Greek word for perimeter, περίμετρος. The term was popularized by William Jones and Leonhard Euler, and also has origins in Archimedes work. Pi has been said to be equal to 22/7, but this has been proven untrue. Actually, 22/7 is equal to 3.142857, not π. The attempt to discover and analyze π has lasted since very early times, in Arabic and Greek societies. Its mystery extends to present day, where computers are being used to calulate the most expansive versions of π ever seen.
Pi has a strong presence in modern culture. Pi day, a celebration of the number and its origins, falls on March 14th, or 3/14. Contests to recite the most digits of π have spawned many new records and stories, where some are rumored to know 100,000 digits.
Pi is used in most branches of math. In trigonometry, it is used on the unit circle to find sine, cosine, and other values. It is also used in the radian system, where π represents 180 degrees. In calculus, π is used to find the volume of revolution of a function. In physics, π is often utilized whenever the spherical coordinate systems are present.
Pi is extremely interesting, and is the theme of much mathematical work. For pi to 4 million digits, see http://zenwerx.com/pi.php .
