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Mysteries of Pi |
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(Original source http://www.pithemovie.com )
Pi is both the sixteenth letter of the Greek alphabet and
the symbol which represents the world's oldest mathematical mystery: the ratio
of a circle's circumference to its diameter.
The earliest known written record of the ratio comes from 1650 BCE Egypt,
where a scribe calculated the value to be 3.16 (a mere 1% off the true value).
Although now, we have methods to calculate the digits of pi (3.1415...) its
exact value remains a mystery.
Since 1794, when it was proven that Pi was both irrational and infinite,
people have been searching for a pattern in the endless string of numbers.
As it turns out, Pi can be found everywhere, from astronomy to probability to
the physics of sound and light. To date it has been calculated to over 51
billion digits, so far with no discernible pattern emerging from its numbers.
In fact, the first time that the sequence 123456789 appears, it is over 500
million digits into the ratio. Calculating the digits to millions of decimal
places is now used to test computers for bugs in hardware and software (which
is how Intel's Pentium found a chip bug a few years ago).
If you prefer to calculate Pi the old fashioned way, you're not alone.
Hundreds of clubs have been formed to celebrate and calculate the ratio, many
of which require a good deal of sequence memorization in order to join. The
current world record for pi memorization was made in 1995, when a Japanese man
recited 42,000 digits from memory in just over nine hours.
pi=Circumference/Diameter
Pi is the ratio between the circumference and diameter of a
circle.
It seems that all people with a written language, no matter at what point in
history, had at least a fundamental knowledge of pi. Degrees of accuracy have
changed over time, but little else about pi has.
Pi can also be rendered as 22/7 or 377/120, but is most commonly considered
3.14. Making the number more mysterious is that no one has ever been able to
locate a repeating pattern in the decimal sequence. Most decimals repeat a
pattern eventually (8.2349574623879879879879, for example), but despite having
taken pi out to literally hundreds and thousands of places, no pattern has
emerged -- indeed, it is thought to be a truly infinite number.
Through Pi we can thus witness the Macrocosm in the Microcosm; the Infinite
within the Finite. It also adds mathematical substance to the role of the
circle as a symbol of Infinity.
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Mysterious relation between PI, Gregorian and
Islamic calendars
(Original source
http://fakir60.tripod.com/calendar.htm
The year is the period taken by the Earth to complete an orbit around the Sun
and, again, there are a number of ways in which this can be measured. But for
calculating a calendar that is to remain in step with the seasons, it is most
convenient to use the tropical year, since this refers directly to the Sun's
apparent annual motion. The tropical year is defined as the interval between
successive passages of the Sun through the vernal equinox (i.e., when it
crosses the celestial equator late in March) and amounts to 365.242199 mean
solar days.
The tropical year and the synodic month (lunar month) are incommensurable, 12
synodic months amounting to 354.36706 days, almost 11 days shorter than the
tropical year.
The Muslim Era is computed from the starting point of the year of the
emigration (Hegira); that is, from the year in which Muhammad, the prophet of
Islam, emigrated from Mecca to Medina, AD 622. The second caliph, 'Umar I, who
reigned 634-644, set the first day of the month Muharram as the beginning of
the year; that is, July 16, 622.
The years of the Muslim calendar are lunar and always consist of 12 (lunar)
months, each month beginning approximately at the time of the New Moon. The
months are alternately 30 and 29 days long except for the 12th, Dhu al-Hijjah,
the length of which is varied in a 30-year cycle intended to keep the calendar
in step with the true phases of the Moon. In 11 years of this cycle, Dhu al-Hijjah
has 30 days, and in the other 19 years it has 29. Thus the year has either 354
or 355 days. No months are intercalated, so that the named months do not
remain in the same seasons but retrogress through the entire solar, or
seasonal, year (of about 365.25 days) every 32.5 solar years.
Now the following equation shows the in time relation between the Islamic
year, the Gregorian year and the transcendent magical number Pi =3,1415....
It's to say that also history and dates are mathematically linked to each
other. The conversion is usually made by special software. Try the below
equation to see the accuracy of the results and control the precision with a
Hegira/Gregorian converter.
622 AD is the year of Hegira. If you are in the second half of the year use
622.
Use 622,5 if you are in the first half.
Pi = 3,14159265.....
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Buffon's Needle Test
1. What you need: a. A needle or toothpick (call the length one unit). b. A piece of paper with several parallel lines one unit apart from each other. 2. What to do: Drop the needle onto the piece of paper lots of times (the more the better, try at least twenty). Count the number of times you drop it and the number of times the needle comes to rest touching one of the lines on the paper. Multiply the number of drops by two and divide the total by the number of hits. What is your result? 3. Explanation: The probability of a hit is . Therefore = (# of Hits)/(# of Drops). Rearranging, we get: Pi = 2(# of Drops)/(# of Hits) |
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