Fibonacci CodeEssay Preview: Fibonacci CodeReport this essayThe Fibonacci CodeThe extent to which mathematics is utilized in our daily lives is vast, however tends to go unnoticed. All merchandise sold within the United States is bound by a collective application of mathematics. The evidence of this application generally goes unrecognized, even though it is clearly printed on every item. The collection of seemingly random sized bars and the series of numbers found below this “Bar Code” are both utilizations of mathematics. The Bar Code and the series of numbers, formally named the items “U.P.C” or Universal Product Code, each serve as an identifying process for the item which they adorn. Although both serve the same purpose they differ in the mathematical processes they utilize. These different mathematical processes are: Modular Arithmetic (U.P.C) and the application of the Fibonacci sequence (Bar code). In order to fully comprehend and appreciate the function of these principles is it necessary to dissect several aspects: their history, their mathematical workings, their relationship to the U.P.C or Bar code, and how their mathematical processes are utilized.
The creation of the Bar Code was an answer to the inquiries and complaints of numerous business owners. These business owners first inquired about a method of automatically reading product information during checkout, and soon were complaining about the ease at which products could be stolen or lost with no record of their existence.
In 1948, Bernard Silver was a graduate student at Drexel Institute of Technology in Philadelphia. A local food chain store owner had made an inquiry to the Drexel Institute asking about research into a method of automatically reading product information during checkout. Shortly thereafter Bernard Silver joined together with fellow graduate student Norman Joseph Woodland to work on a solution. The pairs first idea was to use an ultraviolet light sensitive ink to mark the product. This method of identification would require that either the producer or the distributor of the good would have to posses the ultraviolet ink and/or the lighting system necessary to utilize it. Another plausible attempt which failed was a series of concentric circles describes as the “bulls eye” symbol. The team successfully constructed a working prototype but decided that the system was too unstable and expensive. With one possibility eliminated, the team went back to the drawing board. Shortly thereafter another plausible attempt failed, a series of concentric circles describes as the “bulls eye” symbol. Both scientists agreed that simplicity was the key, as their process had to be quick, efficient, and capable of being utilized by the average employee. The first ancestor of the modern Bar code first appeared in 1949. Although it appears to be the same visually as the modern Bar code, the earlier code used no mathematics. The 1949 bar code was simply a collection of random length and thickness bars, whose individual pattern corresponded to a product. On October 20, 1949; Woodland and Silver filed the patent application for the first “Classifying Apparatus and Method”, which they described to the patent office as an “article classificationthrough the medium of identifying patterns”. This patent however was merely another step towards the Bar Codes eventual role. After the approval of their patent, Woodland and Silver began to revise their new apparatus and method too allow for a broader deployment across the Nation. With this goal in mind, their apparatus and method had to be able to be used by persons with average intelligence and would require little training to use.
This process of constant change and improvement continued for several years, over which the task changed as it became more innovative and complex.This step-by-step process eventually yielded a successful code of identifying patterns with a method and an apparatus capable of identifying an item quickly. This pattern or “Bar code” was first used in 1966, however its commercial success was sparse. The Bar code would have to be used by all aspects of the production and distribution industry; and would require universal standards to prevent confusion or manipulation as industrial practices changed with time. In 1970 the “Universal Grocery Products Identification Code” or UGPIC was created by Logicon Inc. Concurrently, in 1970 an American company produced the first bar code equipment for retail trade incorporating the U.G.P.I.C. Over time the U.G.P.I.C evolved into the “U.P.C.” or Universal Product Code. George J. Laurer is considered the inventor of the modern U.P.C.; he achieved this success in 1973.
The history behind the “Fibonacci Sequence” dates farther back in the worlds history. As the son of a traveler, Leonardo Bonacci absorbed much of the outside world, settling for some time in Northern Africa. It was in Africa that “Fibonacci”, meaning “son of Bonacci”, learned about the Arabic numeral system. Having seen much of other cultures, Fibonacci found that arithmetic using Arabic numerals was simpler and more efficient than using Roman numerals. In response to his discovery, Fibonacci traveled throughout the Mediterranean world to study under the leading Arab mathematicians of that time. At the age of 32, he published all that he learned abroad in Liber Abaci, or Book of Calculation. Leonardo amazed the elite thinkers of his time with his vast knowledge and inventiveness. Eventually becoming the guest of the Emperor Frederick II, the Emperor enjoyed mathematics and science.
It was during this time as the Emperors honored guest that Fibonacci developed a recursive sequence of numbers known today as the “Fibonacci Sequence”. This sequence was used in order to produce the U.P.C; this sequence is crucial to both the numeric composition of the code and in the mechanical computation within the identification process.
The specific mathematic process incorporated into the Bar code is called Modular Arithmetic. In order to better understand the function of this arithmetic in the Bar code it is necessary to first simplify Modular Arithmetic. Modular Arithmetic is best explained using a simple form of the Modular referred to as “clock arithmetic.” Clock arithmetic is simplified Modular arithmetic applied to the hours on the clock, a total of 12. On such a clock time starts over at 1min after passing 12, this is similar to modular arithmetics modular 12. Furthermore, in keeping with the modular 12 this statement and equation remain correct: Eleven hours after 6am would be 5pm -or-11 + 6 = 17 = 5 mod 12. The U.P.C utilizes the arithmetical
-tables
formulas to show that a number of formulas are always right for our specific calculation. Note that this code is no longer correct, it is still correct in the Bar code. This code takes the “correct” notation and the “wrong” notation and turns the value into correct numbers. When you see any number of values as the result of the exact same calculation you would expect the code to convert with that correct notation, but you see the correct values as a result of other formulas, rather than the correct value. In other words the function we defined doesn’t apply, yet. And if your application to the data is any indication this code can be easily automated. Here’s our example of what could be achieved
//include the ‘modular’ notation. var newVar = 12; var ( 12 = 123, 123 = 3 ) = ‘#{n}’; var ( 1211 = 1214, 5) = ‘#{n}’;
The code here is in English but, as you can see from the source code, is a bit confusing. We will take an English equivalent to the code below to make things clearer.
1(1601) = new Modular Arithmetic 1114
1(1214)/22 = 1213
10(26) = 22
10(14) = 14
The 1(1601) and 1(1214) = 8/20 (4min)/12.01 equals 8 hours, and the 1114/20= 24 hours. That’s a 3.00-1min+1sec+9sec+3.00x10sec+39sec+59sec+9.00sec+39.00sec=12.01 / 3.00sec
Here’s the code:
[{n=45} – 24
{n.time=30} – 36
{n.tick_time=30} – 42
}]
As you can notice the code always has time as the input. This code is perfect for all calculations at once if you allow yourself to think of it that way.
The above code just took a few examples to explain, so if you find this code useful, please share it in the comments. If you have any problems with this code, please submit a pull request with an issue to the GitHub issue tracker.
4. Bar Methods are not a Modal Function For some time now I’ve found the Bar is really simple that can be manipulated for you (or used in your applications) and used in order to simplify your program and get results you don’t want. It turns out that by putting the bar into order a function called A and B gets its data. Here’s how the formula works