PIE/Pi is perhaps one of the most well known and culturally discussed math concepts. Apart from the high technical applications, this concept has frequently crossed into mainstream consciousness. Perhaps everyone must have heard of Pi, even if one has slept through high school math. However, most do not really know that importance of this seemingly mystical value.
A Piece of Pi
The symbol of Pi is the Greek alphabet counterpart of the letter P. The most basic definition of this value is that it is the ratio of the circumference of any circle to its diameter. This applies no matter how big or small the circle is. The value is usually approximated to 2 decimal places with 3.14 is its accepted decimal approximation.
To better understand the concept of Pi in circles, try to draw a small circle using a compass or any other object similar in size and shape. Take a piece of string and trace it around the circle, covering the whole length. This measure is the circumference. Try to get the number by measuring the string against a ruler. Now to get the diameter, simply measure one point of the circle straight through the center, ending at the exact opposite side of the first point. The diameter is the length between any point of a circle, across the center of the circle to another point on the opposite side. (The radius is the measure of any point of the circle to its center and is thus half the measure of a circle’s diameter). If you divide the value of the circumference with the diameter, you will get an approximated value of 3.14. Try drawing a bigger circle and you will still get the same value.
Another intriguing characteristic of Pi is that it is an irrational number. This means that the decimal value of Pi does not end, such as seen in fractions like (1/5 = 0.2), and it does not repeat, like the fraction (1/6 = 0.166666…).
The Origin of Pi
The symbol used for PIE/Pi was first popularized in a published work back in 1748 by Leonhard Euler. Pi is written in the Greek letter “π” and is pronounced “pie” in the English language. However, the value of Pi has repeatedly emerged even in the ancient world. Some believe the Egyptians may have used it in building the pyramids. Artifacts from the Babylonian period also show what may have been a simple fraction that denoted the value Pi.
William Jones was the first known mathematician to ever make use of this value as a representation of the ratio between circumference and diameter. In a published work he released back in 1706, Pi first appeared in the mathematical phrase “1/2 Periphery (π)” with regards to the radius of the circle. Many believe that the term Pi came from the convenient use of the letter P with regards to the word periphery. However, Jones had repeatedly stated in his work that his use of π was inspired by John Machin, leading many to believe that Machin may have been the first one to associate the Greek letter with the value of Pi. It was only until Euler used the symbol to denote the value we know today that it received mainstream acceptance.
Modern Day Applications of Pi
The use of Pi goes just beyond measuring simple circles. In truth, modern geometry would not be what it is without Pi. Pi is used for calculating shapes derived from circles such as spheres and cones. Furthermore, Pi can emerge from different other areas of math. In the field of trigonometry, Circles are just as important in measuring the angles of a triangle making the value an essential in this field of math.
Some of the most fundamental equations used to describe different phenomena and principles in our known universe use the value of PIE/Pi. In quantum mechanics for example, which studies the behavior of particles smaller than the atom, Pi has been routinely used in several principles to predict and measure the activity of little particles. Even Einstein’s theory on the nature of gravity with relation to matter and energy affecting space-time incorporated the value of Pi.
Probability and Statistics
There are many practical applications for statistical calculations today. A statistical model can help predict trends and test hypotheses in research studies. The use of Pi is commonly seen in a statistical formula using the Gaussian function.
The various modern structures and machinery today all incorporate crucial concepts from engineering and the value of Pi is ever present in several calculations that deal with structural studies. Furthermore, a few formulae associated with fluid dynamics also incorporate the value of Pi to measure efficient systems utilizing fluids.
Breaking the Limits of Pi
One of the more interesting endeavors when talking about PIE/Pi is calculating for the decimal digits. A majority of the calculations used today use only a few decimal places for the value of Pi. However, depending on the field of study, the number of places used can vary.
The dawn of high powered computing machines gave rise to more precise calculations using Pi. One area that requires a minimum of 40 decimal places for Pi is cosmology or the study of the various aspects of the universe as a whole. This calculated Pi value is usually enough for measuring volume of the universe. However, many individuals today are tirelessly striving to expand pie down to a trillion decimal digits. World records for the value of Pi are actually headlined by various mainstream media around the globe. As of late last year, the highest known number of decimal digits for Pi has reached 10 trillion.
Pi in Everyday Life
So how does this seemingly endless numerical value affect the common man? In many ways we may not be aware of how PIE/Pi benefits us. However, taking a closer look at the applications of the formulae in various fields and realizing the implications that these calculations can bring to our lives can give a new found significance to this number. The development and testing of supercomputers we have today owe some of the work to the value of Pi. In technologies that arise from various fields of engineering, Pi is also ever apparent. Undeniably, the numerical and practical value of PIE/Pi has gone beyond the circle. With more and more fields of math and science incorporating the value in practical calculations, our modern world, with its fast computers and high rising structures, owes some debt to this irrational, unending but ultimately beneficial number.