|Part of a series of articles on the|
Irrationality and normality
- Integers: 3
- Fractions: Approximate fractions include (in order of increasing accuracy) 22, 333, 355, 52163, 103993, and 245850922. (List is selected terms from A063674 and A063673.)
- Decimal: The first 50 decimal digits are 3.14159265358979323846264338327950288419716939937510... (see A000796)
- Binary: The base 2 approximation to 48 digits is 11.001001000011111101101010100010001000010110100011... (see A004601)
- Hexadecimal: The base 16 approximation to 20 digits is 3.243F6A8885A308D31319... (see A062964)
- Sexagesimal: A base 60 approximation to five sexagesimal digits is 3;8,29,44,0,47 (see A060707)
Complex numbers and Euler's identity
Polygon approximation era
Rate of convergence
|Infinite series for π||After 1st term||After 2nd term||After 3rd term||After 4th term||After 5th term||Converges to:|
|4.0000||2.6666...||3.4666...||2.8952...||3.3396...||π = 3.1415...|
Irrationality and transcendence
Adoption of the symbol π
Modern quest for more digits
Computer era and iterative algorithms
Motivations for computing π
Rapidly convergent series
Monte Carlo methods
Geometry and trigonometry
- The circumference of a circle with radius r is 2πr.
- The area of a circle with radius r is πr2.
- The volume of a sphere with radius r is 4πr3.
- The surface area of a sphere with radius r is 4πr2.
−1 computes the area between that half of a circle and the x axis.