Logbook: among the many old papers that appeared last summer when we started to do a thorough cleaning of the cabins, I get on this blog one of them brings me a nice boy image of three or four years, which, one day of those, and my proposal, submitted an essay about Ludolph van Ceulaer .
The curious life of the Ceulaer are first encountered in a textbook, in a small article a trivia section included at the end of a topic. Ludolph van Ceulaer was a German mathematician of the sixteenth and early seventeenth centuries, who emigrated to Holland for religious reasons and was appointed professor at the University of Leiden in 1600, when he was 60. The most curious, and the reason to be reminded is that he spent the last twenty years of his life calculating pi to decimal, π, and when he died had been determined with a whopping π ... 35 decimal places:
3.14159265358979323846264338327950288.
As a reminder of his exploits, the number π with thirty-five first decimal was recorded on the headstone of his grave, and in parts of Europe the number π has been called long ludolphino number (pronounced the ph as a efe: "ludolfino) .
The number π is perhaps the most famous of the math and know its history is to find a long road full of milestones by which we can get an idea of \u200b\u200bwhat they have been many aspects of arithmetic, of geometry, algebra, calculus and analysis, and how they have evolved through time. Not a story to know or understand completely in a while, but it requires patience and progressive deepening.
π's story is full of anecdotes and curious facts. We can do a minimal summary of it, and start by saying that π was known since ancient times in his definition, "the reason or ratio between the circumference of a circle to its diameter," but one thing is definite and quite another is calculated differently.
Different civilizations have different approaches to the number π, some far from their real value, other tighter, more accurate. In the Bible, the Book of Kings, was a series of instructions for building a pot, and in these instructions implicitly assumes that π is 3. The Egyptians gave a value of 3'1666 π ... and the Greeks a value of 3'125. The Chinese are very close, giving a π value of 355/113. If the division we see that π matches in the first six decimal places (see wikipedia page for details).
is said that Archimedes was the first to suggest a method or algorithm used geometric for centuries to approach the value of π. The method is very simple: it comes to making a circle of a given diameter, and calculate its length approximated by the perimeter of regular polygons. We enrolled regular polygons (polygons whose vertices are inside the circle) and circumscribed regular polygons (polygons with sides outside tangent to the circle). As we increase the number of sides of these polygons, they go looking increasingly to the circumference, and the perimeters are going closer and closer to the actual length of the circumference, that the divide between the length diameter, we will approach the number pi to the precision we want.
This method, as we said before, was in use for many centuries. But the problem is the arithmetic. Without the help of calculators, even without the support of the logs, which are not inventoried until the early seventeenth century, mathematicians of that time were faced with tedious hand calculations to get a few decimal places of π, required hours and hours of work. The Archimedes method, despite the simplicity of its approach, this method is slow, you need to be taking many-sided polygons (thousands, millions, billions of sides) to make significant progress in the calculation of the decimal digits of π. It says, for example, that to obtain the 35 digits of π, Ludolph van Ceulaer regular polygons needed to handle 2 to the 62 sides (about four and a half trillion sides trillion = one followed by eighteen zeros, 1,000. 18 = 10 000.000.000.000.000 ).
From XVII century XVIII, with the progress of the calculus and mathematical analysis, began to develop more efficient methods for calculating the decimal places the number π. Newton, Leibniz, Wallis, Euler were among the mathematicians who, through study of numerical series, they found these methods of calculation.
would be in the twentieth century when the advent of computers will enable a quantum leap in the calculation of these figures. Ferguson, in 1947, with the help of a mechanical calculator, was to calculate 808 decimals of π, but just two years later, ENIAC, the first computer, was able to compute 2037 digits of π in just seventy hours. After this event and to our days, computers have been used increasingly fast and powerful, and the number of decimal places calculated has been increasing exponentially. The latter marks the established Fabrice Bellard the December 31, 2009, the day he announced he had won a total of 2.7 trillion decimal places. In this article from El País include details.
Returning to the language that I had the boy for several years, I keep a photocopy of it and I have reread. This wording has been a disconnection paradigm that sometimes occurs between apprentices and the tasks that have to do. When the vessel matenavegantes School officials will send a task, that for them is to present something, anything That is, even without the slightest sense. And that's what I had the boy, a paper written by hand, with good lyrics, and decorated with the typical method of going slightly scorching and burning the edges of the paper to look like an old parchment, but its content had no feet or head. I reproduce below, the reader should keep in mind that the intention is to write about going Ceulaer and decimal places of pi:
would be in the twentieth century when the advent of computers will enable a quantum leap in the calculation of these figures. Ferguson, in 1947, with the help of a mechanical calculator, was to calculate 808 decimals of π, but just two years later, ENIAC, the first computer, was able to compute 2037 digits of π in just seventy hours. After this event and to our days, computers have been used increasingly fast and powerful, and the number of decimal places calculated has been increasing exponentially. The latter marks the established Fabrice Bellard the December 31, 2009, the day he announced he had won a total of 2.7 trillion decimal places. In this article from El País include details.
Returning to the language that I had the boy for several years, I keep a photocopy of it and I have reread. This wording has been a disconnection paradigm that sometimes occurs between apprentices and the tasks that have to do. When the vessel matenavegantes School officials will send a task, that for them is to present something, anything That is, even without the slightest sense. And that's what I had the boy, a paper written by hand, with good lyrics, and decorated with the typical method of going slightly scorching and burning the edges of the paper to look like an old parchment, but its content had no feet or head. I reproduce below, the reader should keep in mind that the intention is to write about going Ceulaer and decimal places of pi:
Al 1500s Spain was found to a "spiritual cleansing" also known as the "inquisition ". A non-Catholics, this meant imprisonment, torture generally, and / or execution. While that the English began to conquer Western Europe, forcing many to flee to the Dutch state security.Such is the case of Cologne, which fell to Spain in 1559. As proof of identification, the wealthy classes often joined Cologne, van Keulen van Ceulaer ("akal the suffix") to his name, which literally means "Cologne."
English Inquisition "? "Cologne? "Van Keulen? "Recognition of surnames?Eventually, the names of the "van" is recognized as surnames, and so the family of the van Keulen / van Ceulaer were created.
guess the authorship of the writing is shared between a web page in English on Cologne and an automatic translator particularly odd and unfortunate. The boy did not seem to mind the content. Simply copied it by hand (which is not without merit) and introduced him. Subsequently I have been searching the net for the source of the wording, but I have not been able to find such a combination of nonsense.
What I liked most, by far, is the translation of an Ceulaer v by van Keulen . It reminds me how well they spent reading a booklet of instructions for installing the motherboard of a computer, in the brochure, among many other outrages, the translator of the day spoke of range of motherboard, actually referring to fan, and the only thing I missed is the board imagine wearing comb, shawl, and a flower connections between chips.
What I liked most, by far, is the translation of an Ceulaer v by van Keulen . It reminds me how well they spent reading a booklet of instructions for installing the motherboard of a computer, in the brochure, among many other outrages, the translator of the day spoke of range of motherboard, actually referring to fan, and the only thing I missed is the board imagine wearing comb, shawl, and a flower connections between chips.
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