Pi

Animation o the act o unrollin a circle's circumference, illustratin the ratio π.

Pi, kent as Ludolph's nummer or Archimedes' constant an aw, is an irraitional nummer that's gey uissfu in mathematics an naitural philosophy. The seembol uised for it comes frae the 16t letter o the Greek ABC, π

Defineition

π can be defined aither as the ratio atween the perimeter an the diameter o a circle, or as the area o a circle that's radius equals 1 (the unit circle).

Vailyie

Acause π is an irraitional nummer, it canna be written wi a finite nummer o decimal places. It's kent that π is a transcendental nummer an aw; houaniver, the hypothesis that it is a ordinar nummer, haesna yet been pruiven the tae wey or the tither. Calculation o the vailyie o π tae sae monie decimal places as is possible haes become a popular task tae set gey swith computers. An approximate vailyie o π wis aareadies kent in the 20t C ACE in Babylon. Archimedes, in the 3d C ACE, fund the weel-kent approxmiation 22/7. In ther 17t C Ludolph Van Ceulen wis successfu in calculatin the vailyie o π tae 35 decimal places. In 1949 a computer (Eniac) wis uised for the first time, an calculatit the first 2 037 decimals. In 2003 the first 1 241 100 000 000 (1.241 billion) digits o π wis calculate.

The vailyie o π roondit tae the first 64 digits (sequence A000796 Archived 2001-07-15 at the Wayback Machine in the OEIS) is thon:

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 5923

Ye can hae a keek at e'en mair digits o π: pi tae 1 000 digits, 10 000 digits, 100 000 digits, 1 000 000 digits.

Fremmit airtins

Rake π Archived 2005-10-18 at the Wayback Machine (in Inglis)
Pi-memory Archived 2008-03-19 at the Wayback Machine (in Inglis)