What is PI (refering to circle)?

Answer 1

Pi is the ratio of circumfarence of circle to the diameter. It is irrational and approximated by 22/7

This can be defined as 4(tan ^-1 1)

Answer 2

Hi:

To answer your question you need to know what pi is : It is the name of the ratio of a circle's circumference to it's diameter. it a constant number that never changes no matter how big or small the diameter of the circle you make. Start by cut some paper circles of varying diameters say 1 inch , 2 inch and 3 inch take a ruler and mark a spot on the edge of the paper circle and position that spot on the zero mark on the ruler. Then carefully roll the paper circle along the ruler and see where you end up as that point return to the bottom of the circle . This is the circumference now divide that number by the circle diameter, you should get a close value for pi. of about 3.1 or 3.2 . To make a circle that about equal the value of pi to the first 6 places. By using this method would need a circle about 1,000,000 inches or 15.7828... miles in diameter obviously no one is going to make a circle that big. Fortunately mathematics gives us others way to to find the value which you can read about in it history below


Back about three thousand years ago the ancient Egyptians estimated Pi to be about 3 units (you have to remember that their Mathematics were quite primitive and they had no algebra to help them at this time). Later the ancient Greeks developed and used the area of triangles filling a circle method to estimate pi to be between 22/7 and 3 10/71

{pi= sin ( (360/N)/2)*N

pi = tan(360/N)/2)*N { N= the number of triangles try the numbers between 100,000 to 1*10^50) for good results}

This is the modern day formula for the filling the circle method used by the Greek }

around 240 B.C. However this was good enough for building things and such, but is was not good enough for mathematicans however. So a quest was started to find the true value for pi and various mehods were used to get a better and better estimate for the value of pi. In about the 15th and 16 th centry A.D. Various discovery where made about Pi:

1) Pi is irrational { Meaning it does not repeat itself ever ; like 1/3} and it's transcendental { Meaning that powers of and combination of powers of pi will not give finite whole numbers } So all formulae for computing pi will be infinitely long.

2) with the devolpment of Algbera and Calculus, certain series were found to give the approximate value of pi

Pi= sqr ( 6*(1 + 1/(2^2)+ 1/(3^2)+ 1/ (4^2) + 1/(5^2).....) { sqr means Square root}

or

Pi = 4*( 1- (1/3)+(1/5)-(1/7)+(1/9)- (1/11)......)

Those series take a long time to come to the value of Pi that we know Pi to be today. Which bring us to our era, when electronic computers where built, and as soon as they became avialable. Mathematican were able to confirm those series to be the appoximate value of Pi , which are still in use today. it has been calulated the about 15 billion decimal places and is so well known that it is use to gauged the speed and power of all supercomputers and computers that made today and in the future to come. and it being surpassed in the number of decimal places to be counted in. and it pop up in some interesting places.

Here Pi to a few hundred decimal places I got off the Internet:

3.

1415926535 8979323846 2643383279 5028841971 6939937510
5820974944 5923078164 0628620899 8628034825 3421170679
8214808651 3282306647 0938446095 5058223172 5359408128
4811174502 8410270193 8521105559 6446229489 5493038196
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7245870066 0631558817 4881520920 9628292540 9171536436
7892590360 0113305305 4882046652 1384146951 9415116094
3305727036 5759591953 0921861173 8193261179 3105118548
0744623799 6274956735 1885752724 8912279381 8301194912
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0005681271 4526356082 7785771342 7577896091 7363717872
1468440901 2249534301 4654958537 1050792279 6892589235
4201995611 2129021960 8640344181 5981362977 4771309960
5187072113 4999999837 2978049951 0597317328 1609631859
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7101000313 7838752886 5875332083 8142061717 7669147303
5982534904 2875546873 1159562863 8823537875 9375195778
1857780532 1712268066 1300192787 6611195909 2164201989

3809525720 1065485863 2788659361 5338182796 8230301952
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6711136990 8658516398 3150197016 5151168517 1437657618
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6549859461 6371802709 8199430992 4488957571 2828905923
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5836041428 1388303203 8249037589 8524374417 0291327656
1809377344 4030707469 2112019130 2033038019 7621101100
4492932151 6084244485 9637669838 9522868478 3123552658
2131449576 8572624334 4189303968 6426243410 7732269780
2807318915 4411010446 8232527162 0105265227 2111660396

6655730925 4711055785 3763466820 6531098965 2691862056
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3348850346 1136576867 5324944166 8039626579 7877185560
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7002378776 5913440171 2749470420 5622305389 9456131407
1127000407 8547332699 3908145466 4645880797 2708266830
6343285878 5698305235 8089330657 5740679545 7163775254
2021149557 6158140025 0126228594 1302164715 5097925923
0990796547 3761255176 5675135751 7829666454 7791745011
2996148903 0463994713 2962107340 4375189573 5961458901
9389713111 7904297828 5647503203 1986915140 2870808599
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4252308177 0367515906 7350235072 8354056704 0386743513
6222247715 8915049530 9844489333 0963408780 7693259939
7805419341 4473774418 4263129860 8099888687 4132604721

5695162396 5864573021 6315981931 9516735381 2974167729
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2168895738 3798623001 5937764716 5122893578 6015881617
5578297352 3344604281 5126272037 3431465319 7777416031
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9456127531 8134078330 3362542327 8394497538 2437205835
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0408591337 4641442822 7726346594 7047458784 7787201927
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8584783163 0577775606 8887644624 8246857926 0395352773
4803048029 0058760758 2510474709 1643961362 6760449256
2742042083 2085661190 6254543372 1315359584 5068772460

2901618766 7952406163 4252257719 5429162991 9306455377
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3503895170 2989392233 4517220138 1280696501 1784408745
1960121228 5993716231 3017114448 4640903890 6449544400
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2283345085 0486082503 9302133219 7155184306 3545500766
8282949304 1377655279 3975175461 3953984683 3936383047
4611996653 8581538420 5685338621 8672523340 2830871123
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2183564622 0134967151 8819097303 8119800497 3407239610
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0516553790 6866273337 9958511562 5784322988 2737231989
8757141595 7811196358 3300594087 3068121602 8764962867

4460477464 9159950549 7374256269 0104903778 1986835938
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5189757664 5216413767 9690314950 1910857598 4423919862
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3338945257 4239950829 6591228508 5558215725 0310712570
1266830240 2929525220 1187267675 6220415420 5161841634
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9598470356 2226293486 0034158722 9805349896 5022629174
8788202734 2092222453 3985626476 6914905562 8425039127

5771028402 7998066365 8254889264 8802545661 0172967026
6407655904 2909945681 5065265305 3718294127 0336931378
5178609040 7086671149 6558343434 7693385781 7113864558
7367812301 4587687126 6034891390 9562009939 3610310291
6161528813 8437909904 2317473363 9480457593 1493140529
7634757481 1935670911 0137751721 0080315590 2485309066
9203767192 2033229094 3346768514 2214477379 3937517034
4366199104 0337511173 5471918550 4644902636 5512816228
8244625759 1633303910 7225383742 1821408835 0865739177
1509682887 4782656995 9957449066 1758344137 5223970968
3408005355 9849175417 3818839994 4697486762 6551658276

Answer 3

Pi is the (circumference/diameter).

The fact that the ratio of the circumference to the diameter of a circle is constant has been known for so long that it is quite untraceable. The earliest values of π including the 'Biblical' value of 3, were almost certainly found by measurement.

The first theoretical calculation seems to have been carried out by Archimedes of Syracuse (287-212 BC). He obtained the approximation

223/71 < π < 22/7.

Before giving an indication of his proof, notice that very considerable sophistication involved in the use of inequalities here. Archimedes knew, what so many people to this day do not, that π does not equal 22/7, and made no claim to have discovered the exact value. If we take his best estimate as the average of his two bounds we obtain 3.1418, an error of about 0.0002.

Here is Archimedes' argument.

Consider a circle of radius 1, in which we inscribe a regular polygon of 3*(2n-1) sides, with semiperimeter b_n, and superscribe a regular polygon of 3*2^(n-1) sides, with semiperimeter a_n.


The diagram for the case n = 2 is on the right.

The effect of this procedure is to define an increasing sequence

b_1 , b_2 , b_3 , ...

and a decreasing sequence

a_1 , a_2 , a_3 , ...

such that both sequences have limit π.

Using trigonometrical notation, we see that the two semiperimeters are given by

a_n = K*tan(π/K), b_n = K*sin(π/K),

where K = 3*2^(n-1). Equally, we have

a_(n+1) = 2K*tan(π/(2K)), b_(n+1) = 2K*sin(π/(2K)),

and it is not a difficult exercise in trigonometry to show that

(1/(a_n) + 1/(b_n)) = 2/(a_(n+1)) . . . (1)

(a_(n+1))*(b_n) = (b_(n+1))^2 . . . (2)

Answer 4

Pi is half the circumference of a circle, equaling 180 degrees.

Answer 5

PI, referring to a circle, is the ratio of the perimeter of the circle to its diameter

Answer 6

Pi is the ratio of the circumference of a circle to its diameter

The character is π

Greek letter π

Archimedes Constant

Irrational Number

Used in Mathmatics, Physics and engineering

Numerical value is 3.141592654

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Click on the URL below for additional information of Pi.

mathforum.org/dr.math/faq/faq.pi.html


en.wikipedia.org/wiki/Pi


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Answer 7

Pi is defined as the area
of a circle of unit radius

Answer 8

22/7
or in decimal
3.1428571428571428571428571428571
2 x pi x r = circumference
pi x r squared = area
both of a circle

Answer 9

PI is half the circumference of a circle, or 180 degrees of that circle.

Answer 10

Pi is a specific number with an infinite amount of digits after it's decimal point. 3.1415926535, that's Pi to 10 decimal places which is more accurate that any calculator because they always round up to 3.141592654.