The Life of Pi!

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has a long and interesting history!

The ratio of the circumference to the diameter of a circle is constant (namely, pi) has been recognized for as long as we have written records.

A ratio of 3:1 appears in the following biblical verse:

And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about. (I Kings 7, 23; II Chronicles 4, 2.)

The ancient Babylonians generally calculated the area of a circle by taking 3 times the square of its radius (=3), but one Old Babylonian tablet (from ca. 1900-1680 BCE) indicates a value of 3.125 for pi.
Ancient Egyptians calculated the area of a circle by the following formula (where d is the diameter of the circle):

This yields an approximate value of 3.1605 for pi.

The first theoretical calculation of a value of pi was that of Archimedes of Syracuse (287-212 BCE), one of the most brilliant mathematicians of the ancient world. Archimedes worked out that 223/71 < < 22/7. Archimedes's results rested upon approximating the area of a circle based on the area of a regular polygon inscribed within the circle and the area of a regular polygon within which the circle was circumscribed.

Beginning with a hexagon, he worked all the way up to a ploygon with 96 sides!



Archimedes's method for approximating the value of pi.
The approximate area of the circle lies between the areas of the circumscribed and the inscribed hexagons.

More pi history:
European mathematicians in the early modern period developed new arithmetical formulae to approximate the value of pi, such as that of James Gregory (1638-1675), which was taken up by Leibniz:

/4 = 1 - 1/3 + 1/5 - 1/7 + . . . . . . . . . . .

One problem with using this formula to calculate the value of pi is that you would have to add 5 million terms to work out a value of /4 that extends to 6 or 7 decimal places!

In 1706, another mathematician named John Machin developed a refinement on Gregory's formula, yielding the formula still used today by computer programmers to compute pi:

Using this formula, an Englishman named William Shanks calculated pi to 707 places, a labor of many years, which he published in 1873. (Only 527 places were correct, however!)

A novel way to compute pi:
An eighteenth-century French mathematician named Georges Buffon devised a way to calculate pi based on probability. Buffon's method begins with a uniform grid of parallel lines, a unit distance apart. If you drop a needle of length k < 1 on the grid, the probability that the needle falls across a line is 2k/. Various people have tried to calculate pi by throwing needles. Depending on when you stop the experiment, you can obtain a reasonably accurate estimate of pi.
You can try Buffon's needle experiment for yourself (virtually) at http://www.angelfire.com/wa/hurben/buff.html
Some ants apparently actually use this algorithm to measure the size of potential nest sites!

The symbol for pi:
was introduced by the English mathematician William Jones in 1706, who wrote:

3.14159 =

This symbol was adopted by Euler in 1737 and became the standard symbol for pi.



Having fun with pi:
Some people are just crazy about pi!
There are pi poems . . .
There are pieces of music based on the digits of pi . . .
There is a web site where you can find your birthday in pi . . .
There are people who have memorized 1000+ digits of pi . . .
Pi has earned a spot in "The Useless Pages" . . .

Pi Day 

March 14th is Pi Day

Pi Day is a holiday held to celbrate the number Pi. Since 3.14 is a rough approximation of the constant Pi and the American date format for March 14th is 3/14 it was only logical to choose March 14th as the perfect date for Pi Day.
The Pi Day tradition started in 1988. The founder of Pi Day is physicist Larry Shaw also known by his prolific nickname: the "Prince of Pi."

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Fruits and Vegetables are humans too!

Ever wondered why somebody called you a cabbage man! the following post make you acquainted with some fruity and veggie metaphors so that you can become an apple in the eye of big banana peachy daughter!
Starting with fruit and vegetable; the two generic words which you may have already known; yet so contrast in meaning.. 
1.Fruit: Fruit and fruitcake (as well as many variations) are sexual terms which have various origins but modern usages tend to primarily refer to gay men and sometimes other LGBT people. Usually used as pejoratives, the terms have also been re-appropriated as insider terms of endearment within LGBT communities.
Add the term forbidden and we get forbidden fruit which is the term the term most generally refers to any indulgence or pleasure that is considered illegal or immoral and potentially dangerous or harmful, particularly relating to human sexuality.

2.Vegetable: this term is equal in degree of pejorativeness alongside fruit. It usages tend to primarily refer to a unconscious or quadriplegic person who cannot do anything. though nowadays someone lazy and stupid who does nothing of physical activity or who does not make use of brain is decorated with this term.

3.Cabbage: Feel proud if someone calls you that. Cabbage generally refers to dollar bills and if you are called cabbage that signifies others think you have a lot of money!

4.Apple or apple of the eye, noun  According to the Oxford English Dictionary, at least since the ninth century, English-speaking people have referred to the black dot in the middle of the iris at the center of the eye as the apple.  Apple was a generic term for many fruits of similar shape, in much the same way that corn was the generic term for many types of edible grain.  Apparently people thought that what we now call the pupil was a globular solid, like an apple.  From a very early period, the apple of the eye also served as a metaphor identifying the person on whom the eye gazed with pleasure.

            At about the time that people in England realized that the black center of the eye was not a solid but an opening, they began using the word pupil, from the Latin pupilla, meaning a little girl.  (The word pupil indicating a student comes from the same Latin root, pupillus in the masculine, which could be used for an orphan who was a minor and consequently a ward.)

5.Pumpkin:It is basically a term of endearment to a cute child; remember how girls called their boyfriends as you are my pumpkin chumpkin:D.Though if somebody calls you a great pumpkin that means they have a firm belief in your potential yet you have not done anything to show the world what kind of potential you have!

6. Peach: Peaches are sweet so are pretty girls!..I didnt find any sweet or perhaps pretty girls are quite bitter on me thats other story but if your girlfriend is peach you are lucky! it directly means the sweetness and prettiness that she possesses1

7.Banana: invariably this innocent fruit bore the burnt of sex related stories. Think what kind of sex emotions generate when you see your hyper boss.Zilch..so that contradicts the sex relation of banana,a big banana usually means a boss who goes bananas(means overly excited and hyper now and then)! a banana republic on the other hand denotes a politically unstable country.

8.  Cherry: as the fruit so the term.The fruit that evokes pleasure(purely stomach related i am not going below that)..relates to a extremely sweet girl who is virgin too!

9.   Potato:  See the shape guess the meaning: refers to someone who does nothing!..if it sits on couch...couch potato!..though hot potato generally refers to a topic too hot to handle.