March 14th is Pi Day. Pi is the Greek letter used to name the

ratio of two special lengths: the length around the circle's

edge, the circumference, and the length of the diameter of a

circle. That is, Pi is the ratio you get when you divide the

circumference length by the diameter length.

(Geeks may skip ahead, here.) That length, that ratio, is an

irrational number -- meaning that there is no fraction with an

integer on top and an integer on the bottom that will equal that

ratio. The ancient Greek only liked ratios of integers. (An

integer is, for our purposes, a counting number: 1, 2, 3...)

They liked ratios like 1/2 or 43/295, or even 22/7.

Because they liked these integer ratios so much, the Greeks tried

to come up with an integer ratio that they thought would be equal

to Pi. They used 22/7, which is good to four hundredths of one

percent (0.04%). It's good enough for most construction work.

Later people also tried to use integer fractions, and came up

with 355/113 -- which is 10,000 times more accurate than 22/7

(good to 0.000008%).

These days, we use a decimal point, rather than an integer ratio,

to show Pi. For construction engineers, usually 3.14 is

adequate. It's about as good as 22/7. By the way, this form is

why March 14th is called Pi Day: 3.14 treated as a month and day.

If you compute more digits of Pi you will better come understand

that you never get to a place where a sequence of digits starts

repeating over and over. That is the mark of an irrational

number -- no repetition. The integer fractions you're used to

seeing are different. One half, 1/2, is 0.5000... One third,

1/3, is 0.333... One fourth is 0.25000... One fifth, 1/5, is

0.2000... One sixth, 1/6,is 0.1666... And one seventh, 1/7, is

0.142857142857142857..., where the "142857" pattern repeats forever.

There are a lot of other weird things about Pi. While some are

more advanced than others, let's end with an oddball weirdity.

The first and second decimal places of Pi are the digits "1" and

"4", the digits that make up the "14th" for Pi Day. There is a

spot where Pi has six 9s in a row, in decimal places 762 through

767. Pi doesn't start repeating after this, it never repeats.

The start of this repetition of six 9s is called the Feynman

Point.*[Click on the title above, or date stamp below, to see the full post.]*

Feynman,

being the practical joker he is, wanted to memorize the decimal

digit sequence Pi up to this point so that he could recite and

say "...2 1 1 3 4 9 9 9 9 9 9 and so on" -- acting as if Pi

really *did* repeat 9s forever.

## Friday, March 14, 2008

### Happy Pi Day

Subscribe to:
Post Comments (Atom)

## No comments:

## Post a Comment

We reserve the right to delete comments, but the failure to delete any particular comment should not be interpreted as an endorsement thereof.

In general, we expect comments to be relevant to the story, or to a prior comment that is relevant; and we expect some minimal level of civility. Defining that line is inherently subjective, so try to stay clear of insulting remarks. If you respond to a comment that is later deleted, we may take your response with it. Deleting your comment isn't a personal knock on you, so don't take it as such.

We allow a variety of ways for commenters to identify themselves; those who choose not to do so should take extra care. Absent any prior context in which they may be understood, ironic comments may be misinterpreted. Once you've earned a reputation for contributing to a conversation, we are likely to be more tolerant in those gray areas, as we'll understand where you're coming from.