The letter πThe letter π

The constant is named "π" because it The constant is named "π" because it is the first letter of the Greek words:is the first letter of the Greek words:

περιφέρεια = peripheryπεριφέρεια = periphery περίμετρος = perimeterπερίμετρος = perimeter

DefinitionDefinition

In Euclidean plane geometry, π is In Euclidean plane geometry, π is defined as the ratio of a circle's defined as the ratio of a circle's circumference to its diameter.circumference to its diameter.

π = c/d = c/2rπ = c/d = c/2r

Calculating πCalculating π

π can be empirically measured by π can be empirically measured by drawing a large circle, then drawing a large circle, then measuring its diameter and measuring its diameter and circumference, since the circumference, since the circumference of a circle is always π circumference of a circle is always π times its diameter.times its diameter.

π can also be calculated using purely π can also be calculated using purely mathematical methods mathematical methods

Principle of Archimedes' Principle of Archimedes' method to approximate πmethod to approximate π

n=5 n=6 n=8

n inscribed polygon described polygon3 2,598076211 5,196152423

4 2,828427125 4

5 2,938926261 3,63271264

6 3 3,464101615

7 3,037186174 3,371022332

8 3,061467459 3,313708499

9 3,07818129 3,275732108

10 3,090169944 3,249196962

11 3,099058125 3,229891422

12 3,105828541 3,215390309

13 3,111103636 3,204212219

14 3,115293075 3,195408641

15 3,118675362 3,188348425

16 3,121445152 3,182597878

17 3,123741803 3,177850751

18 3,125667198 3,173885653

19 3,127297215 3,170539238

20 3,128689301 3,167688806

21 3,12988759 3,165240713

22 3,130926442 3,163122468

. . .

. . .

. . .

Infinite π π

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16 18

inscribed polygon described polygon π

a few excitements...a few excitements...

In 2002 Kanada and fellow researchers at Japan's Information In 2002 Kanada and fellow researchers at Japan's Information Technology Center set a new record for finding the number of Technology Center set a new record for finding the number of digits of π 1.24 trillion decimal places. This calculation took digits of π 1.24 trillion decimal places. This calculation took about 602 hours. about 602 hours.

Chao Lu of China recited π on 67,890 decimal places on 20 Chao Lu of China recited π on 67,890 decimal places on 20 November 2005.November 2005.

Rose Hare is the youngest person to make the Pi World Rose Hare is the youngest person to make the Pi World Ranking List (age: 3 years 356 days)Ranking List (age: 3 years 356 days)

Math lovers celebrate March 14 (or "3-14") as Pi Day. Math lovers celebrate March 14 (or "3-14") as Pi Day.

The theory of elliptic curves and complex multiplication The theory of elliptic curves and complex multiplication derives the approximationderives the approximation

which is valid to about 30 digits. which is valid to about 30 digits.