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3.
1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224...
Pi has an infinite number of non-repeating digits.
One of the more accurate fractions for pi is 104348/33215. ; It is accurate to 0.00000001056%.
In the first one million digits of pi there are:
99,959 zeros
99,758 ones
100,026 twos
100,229 threes
100,230 fours
100,359 fives
99,548 sixes
99,800 sevens
99,985 eights
100,106 nines
But the first ten digits (3.141592654) that are built into most scientific calculators are sufficient for nearly any real-world calculation
Formulae involving π in Geometry:
- Circumference of circle or sphere of radius r: C = 2 π r
- Area of circle of radius r: A = π r2
- Area of ellipse with semiaxes a and b: A = π ab
(The size and shape of an ellipse are determined by two constants, conventionally denoted a and b. The constant a equals the length of the semimajor axis; The constant b equals the length of the semiminor axis.)
- Volume of sphere of radius r: V = (4/3) π r3
- Surface area of sphere of radius r: A = 4 π r2
- Angles: 180 degrees is equivalent to π radians
Circumference
The circumference is the distance around a closed curve. The circumference of a circle can be calculated using the formulae:
* circumference = 2 π r
or
* circumference = π d
where r is the radius and d is the diameter of the circle. (2 • r = d)
Area
For a two dimensional object the area and surface area are the same:
* square or rectangle: l • w
(where l is the length and w is the width; in the case of a square, l = w.)
* circle: π • r2
(where r is the radius)
Some basic formulas for calculating surface areas of three dimensional objects are:
* cube: 6 • (s2)
(where s is the length of any side)
* rectangular box: 2 • ((l • w) + (l • h) + (w • h))
(where l, w, and h are the length, width, and height of the box)
* sphere: 4 • π • (r2)
(where π is the ratio of circumference to diameter of a circle, 3.14159..., and r is the radius of the sphere
* cylinder: 2 • π • r • (h + r)
(where r is the radius of the circular base, and h is the height)
* cone: π • r • (r + √(r2 + h2))
(where r is the radius of the circular base, and h is the height.)
Units for measuring surface area include:
square metre - SI derived unit
are - 100 square metres
hectare - 10,000 square metres
square kilometre - 1,000,000 square metres
square megametre - 1012 square metres
Volume
* A cube: s3
(where s is the length of a side)
* A rectangular prism: l • w • h
(length, width, height)
* A cylinder: π • r2 h
(r = radius of circular face, h = distance between faces)
* A sphere: 4 • π r3 / 3
(r = radius of sphere)
* A cone: π • r2 • h / 3
(r = radius of circle at base, h = distance from base to tip)
Volume measures: SI
A commonly used SI unit for volume is the liter, and one thousand liters is the volume of a cubic meter, which was formerly termed a stere. A cubic centimeter is the same volume as a milliliter.
Pi is the constant ratio between the diameter of a circle and the circumference of that circle. Although a small minority of people still try to prove that pi is a rational, essentially all mathematicians agree that pi is an irrational number.
Half of the circumference of a circle with a diameter of 2 is pi. The area inside the circle is also pi.
Archimedes
Archimedes was the first to give a scientific method for calculating to arbitrary accuracy. He realized that the perimeter of a regular polygon of n sides inscribed in a circle is smaller than the circumference of that circle, and that the perimeter of a regular polygon of n sides circumscribed around a circle is greater than the circumference of that circle. As n approaches infinity, the two perimeters approach the circumference. In fact, one can think of a circle as a regular polygon with infinitely many sides.
Through his method he was able to make accurate calculations for a 12, 24, 48, and ultimately a 96-sided polygons. With the regular 96-gon, Archimedes was able show that:
3.140845 < Pi < 3.142858
By Archimedes; Pi =
3 10/71 < Pi < 3 1/7
or:
3,14084507 < Pi < 3,142857143
or?
223/71 < Pi < 22/7
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