Thanks to Phil Krause for this great post to celebrate the up coming Pi Day.
Happy Pie Day. Well, not today but in a couple of weeks. Being born in Melton Mowbray, I love my Pie’s.
Pi is a number that has been around before recorded history and yet it still fascinates us. We have some of the worlds most powerful computers calculating extra digits of Pi continuously. To start with it was estimated by measurement and known to be a little over 3. Archimedes was the first known to carry out calculations and produce an approximation of 223/71 < Pi < 22/7. Cleverly using inequalities to offer a proof that Pi was bounded by these two fractions. If you take the average of these two fractions you get 3.1418 which only has an error of about 0.0002. Not a bad estimate for well over 2200 years ago. By the 16th century Roomen had calculated Pi to 16 decimal places and a little later Van Ceulen to 34 decimal places. By 1841 Rutherford had calculated it to 152 digits and by 1853 he had it to 440 digits. It wasn’t until computers came on the scene that things really took off. In 1949 a computer was used to calculate Pi to 2000 digits. By 2010 Pi had been calculated to 5 trillion digits and doubled to 10 trillion in 2011 and we haven’t finished yet.
What is Pi? Its the ratio of a circles diameter compared to its circumference. If you draw a straight line across a dinner plate that goes through the centre, mark a line on a sheet of paper and roll the plate over the paper putting another line when the plate has rotated once. You can now mark the diameter of the plate between these two lines by putting the plate against one mark and marking the other side of the plate, then moving the plate and doing the same again. You will find that the plate fits a little over 3 times between the lines, whatever the plate size that you use. If you repeat with a smaller plate you get the same ratio. Whatever the size of the circle its always the same ratio. This means that if we measure the diameter accurately we can easily calculate the circumference if we know Pi accurately. We can also calculate the area. So once we know the value of Pi we can make all sorts of calculations to find other things just by measuring the diameter.
The number Pi cannot be described exactly by a ratio of two numbers (a fraction) like 22/7 no matter how large the fraction numbers are. This means that we can never describe Pi exactly. It wasn’t until the eighteenth century that Johann Heinrich Lambert proved that Pi is irrational and cannot be described as a ratio. If only the first 5 decimals from Pi are taken (3.14159) then using the American date system Pi day is on March 14th or 03 / 14 each year at 9 minutes past 3pm. But this year in 2015 is a special Pie Day because the first 10 digits of Pi will be formed by the date on 3.14.15 9:26:53 on March 14 2015 at 9:26:53am. Which is also Einstein’s Birthday (very appropriate).
Of course, the best way to celebrate Pi day is with a Pie. It can be a meat pie or a sweet Pi. People use their imagination to celebrate Pi day.
Using Pi on a computer; use Pi = 4.0 * atan(1.0)
Because the digits of Pi go on forever randomly, then every sequence of numbers you can think of will appear in Pi somewhere. For example, your Birthdate can be found somewhere. Mine is 240855 and I found it within Pi from this website. www.facade.com/legacy/amiinpi/ Not only can any number be found within Pi, however long, but an infinite number of these numbers can be found within Pi. That’s how big infinity is; but that’s another story.
Here is another interesting website that calculates how old you are in Pi years. http://pidays.jtey.com/ I like this one because I am only 18 again. Pass that Pi please, I’m a Meltonian!