Pie value is 22/7. Tell me 22 stands for and 7 stands for.?

Question

We are all aware that in maths we have several times used the 22/7 as a Pie value; but I do not know that how this term arrived. Is there anybody to explain this term.

Answer 1

The correct spelling is Pi.
The real source of 22/7 is unknown as it is stated that the Eqyptians used the value 0f 22/7.
www.jimloy.com/geometry/pi.htm

Archimedes (A greek mathmatician) made an approximation of Pi by increasing the number of sides of a regular polygon until it looked like a circle.
http://en.wikipedia.org/wiki/Pi#Early_approximations
Here you can see a pentagon (5 sides) and then a hexagon (6 sides). Archimedes increased the number of sides to 96! to get a value of Pi between 223/71 and 22/7.

22/7 is just easier to remember.

Answer 2

The way that Archimedes and others up to the end of the Middle Ages
used to compute Pi was to approximate it using a regular polygon of
n sides and its inscribed and circumscribed circles. The inscribed
circle has circumference smaller than the perimeter of the polygon,
which is in turn smaller than the circumference of the circumscribed
circle. That gave inequalities of the form

P/(2*r) > Pi > P/(2*R)

By using very large values of n, the first and last of these can be
made very close together, which gives a very good estimate of Pi.

These inequalities can be rewritten in terms of n, the number of
sides,using trigonometric functions, as

n*tan(180/n degrees) > Pi > n*sin(180/n degrees)

Archimedes started with a regular hexagon, n = 6. Then 180/6 = 30
degrees is the pertinent angle, and this gives

tan(30 degrees) = 1/sqrt(3),
sin(30 degrees) = 1/2.

This produces the inequalities

2*sqrt(3) > Pi > 3
3.464 > Pi > 3

If you double the number of sides to 12, you will cut the angle in
half. You can find the tangent and sine of 15 degrees by using the
formulas

tan(x/2) = (sqrt[1+tan^2(x)]-1)/tan(x)
sin(x/2) = sqrt[(1-sqrt[1-sin^2(x)])/2]

That will give you the values

tan(15 degrees) = 2 - sqrt(3) = 0.267949...
sin(15 degrees) = sqrt[2-sqrt(3)]/2 = 0.258819...

so

3.21539 > Pi > 3.105829

Doubling the number of sides to 24, you get

tan(7.5 degrees) = 0.13165250
sin(7.5 degrees) = 0.13052619
3.15966 > Pi > 3.13263

Doubling again to 48 sides, you get

tan(3.75 degrees) = 0.06540313
sin(3.75 degrees) = 0.06554346
3.14609 > Pi > 3.13935

Doubling again to 96 sides, you get

tan(1.875 degrees) = 0.03273661
sin(1.875 degrees) = 0.03271908
3.14271 > Pi > 3.14103

This already shows that the first three significant figures of Pi are
3.14. This can be continued to get more and more significant figures
of Pi. Ludolph Van Ceulen used this method to compute 17 decimal
places of Pi in the early 1600s, which was a record at the time.
To 20 decimal places, you get

Pi = 3.14159265358979323846...

Modern methods of computing Pi are somewhat different. This is a very
complicated and interesting subject, about which I can't go into much
more detail here.

Answer 3

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!

Answer 4

22 and 7 don't "stand" for anything. They are just numbers. 22/7 is a ratio; you can read it as "twenty-two sevenths" or "twenty-two divided by seven." Since pi is defined as the ratio of a circle's circumference to its diameter, you could say that 22 is the circumference of a circle and 7 is its diameter, approximately.

22/7 is approximation for pi (note spelling) based on measurements of the diameters and circumferences of circles, and it was derived before more precise methods of calculation were developed. 22/7 was calculated independently by the famous Greek scientist Archimedes in the 3rd century BCE and by the Chinese mathematician Zu Chongzhi in the 5th century CE. Archimedes used geometry to construct 96-sided polygons incribed and circumscribed by a given circle in order to formulate his approximation.

Answer 5

pi is 3.1415926535897932384626433832795

22/7 (i.e. 22 divided by 7) is 3.1428571428571428571428571428571

Thus, 22/7 is a pretty decent, easy to remember approximation.

BTW Happy pi day for tomorrow (3-14!)

Answer 6

Pi (not PIE) is a ratio of the circle's circumference to it's diameter. 22/7 is an approximation of that.

Since it's a ratio, the top number (22) is the circumference and the bottom number (7) is the diameter.

Answer 7

22/7 is just a fractional approximation of pi. The numerator and denominator have no other significance than that.

Answer 8

22 pieces per seven pies. U know just like 24/7. 24hrs. 7 days a week.

Answer 9

It is an approximation for pi. A more accurate value for pi would be 3.14159265359. Pie value is usually about $2.50 at the grocery store.

Answer 10

3.14....

They're just saying it in fractional terms. basicly, if you divide 22 into 7 you get the numbers of pi.