Before I commence with my mathematical meanderings, let me firstly confess to a most dismal loss in soccer last week. I think the score was 14-2 or something along those lines. And while I'm about it, Jesamine's Gems lost on Saturday, as did Suzy's Gems on Thursday.
Now, on to my personal challenge.
It seems from my admittedly cursory research that there is no intuitive mathematical formula from which to calculate Pi. By intuitive, I mean a formula of which, with a basic grasp of logic, you can understand the why-for. For example, the formula for the area of a square, length by width, can be understood by picturing a grid of 1-unit by 1-unit squares filling the area. I had anticipated some similarly logical reasoning would lie behind a formula for calculating Pi - and I was sadly mistaken.
'Twould appear that for some time Pi was only known by measurement. If you draw a large enough circle and measure the circumference and the diameter accurately enough, you can determine Pi to, well, around 3-4 decimal places. Not much really is it - but for most people using pencil and paper a 1 meter diameter circle and a 1 millimetre is about the practical limit, so that's a 3 decimal place limit.
Wikipedia tells me that with a circle the size of the observable universe, and a measurement precision of 1 hydrogen atom - you can still only calculate Pi to 39 decimal places. And in case you're not aware, the observable universe is very large, and a hydrogen atom considerably less so. If you imagine a teapot, you couldn't fit the observable universe in it - whereas you could easily fit two hydrogen atoms within a teacup - and still have room for milk and sugar.
I just did a quick calculation, and by my reconing, if a hydrogen atom is around 25 picametres, and the obervable universe is around 1000 billion trillion kms, then I can't see how you'd get beyond 38 decimals.
Anyway, so it seems that calculating Pi was all about drawing circles until people started stumbling across mathematical series that approach Pi. Still, these are non-intuitive, but they do work.
For example, the series (4/1)-(4/3)+(4/5)-(4/7)+(4/9) .... where the denominator increase by 2 in each term, converges towards Pi ... very slowly. You get up to (4/13) before it even gets to "3", and you're up to (4/49) before you've found Pi to one decimal place. At (4/1017), which is all that I could do using all the columns in Excel with two terms per column, I still hadn't resolved Pi to 2 decimal places.
Whe I first read about this, I thought, if that's the way it works, how do people know how many places they've calculated Pi to? You've got a raft of decimals after each result, but how do you know which ones are right?
Then I thought to myself, obviously you keep adding terms until a decimal stops changing. But they don't change with each calculation. For the first six terms you'd be convinced that Pi = 2 point something. For the next 18 terms you'd think the first decimal is 0.
So, at the moment I remain a little confused. But by gosh by golly hasn't this been educational. I shall continue my investigations a little further.
Toodle-oo
Monday, May 26, 2008
Sunday, May 18, 2008
THE ENDS OF MANY ERAS
The FOB United dream run has come to an end. We went down by 1 goal last Wednesday.
The Gems nightmare run has also come to an end. To clarify, this is Suzy's Thursday night netball, not Jesamine's Saturday morning netball - both teams are called the Gems. Two whole seasons without a win, and finally they won 29-23. Better than Jesamine's Gems on Saturday, who lost 23-3.
The era of Jesamine not having a blog has also come to an end. Might I suggest you make your virtual way to Fabulous Jesamine 3 to check it out.
The era of the kids not both doing Auskick on a Sunday morning has come to an end - as has the era of me sleeping in on a Sunday.
One era that hasn't come to an end is me losing at Puerto Rico. We has another Puerto Rico night with Lee and Brian on Friday night, but I lost again. I did roll the highest number to start the game again though - which is rather curiously emerging as quite a hidden talent of mine.
BOOK UPDATE
I have finished Billy Bathgate. It was a struggle at the beginning, because the first full-stop didn't appear until half-way down the first page. I don't mind writers taking liberties with grammar - broken sentences are often a great way to establish tempo. In this case I found the sentence structure was often detracting from the story.
This comes from the perspective of an auditory reader - meaning that I hear the words in my head (and sometimes in the voice of Fred Flintstone - which is a whole other issue). The writing may serve very well for people who "process" written information in other ways.
Billy Bathgate is a story of a young boy becoming a gangster. I know that I saw the movie many years ago - but I can remember nothing of it.
Anyway, I'd call it a good book, even a very good book - but not a great book.
Since then I read Chocky, by John Wyndham. I love John Wyndham's writing - and I'm always amazed at just how much story he's able to build into pretty short books, and without them feeling dense.
Chocky is a voice within the head of a young boy, and it's hard to say much more without spoiling the plot. I'd have to say I hate the name though.
I'm now onto another John Wyndham - The Kraken Wakes.
THE PI CHALLENGE
I'm somewhat enamoured with the number Pi (3.14 etc). I even have the Pi symbol on the back of my soccer shirt.
Most people know that Pi is believed to have an infinite number of decimal places, with no repetition. What I've never understood, however, is how people go about calculating Pi to a given precision. So, I've decided to find out. Call it my personal challenge. I'll blog about the answer when I find it.
P.S.
I can't remember if I mentioned, but we sold that kids play set they I spent so long assembling a few weeks back. We also sold the kids old swing set to someone else who called about the ad in the paper after it was sold.
The Gems nightmare run has also come to an end. To clarify, this is Suzy's Thursday night netball, not Jesamine's Saturday morning netball - both teams are called the Gems. Two whole seasons without a win, and finally they won 29-23. Better than Jesamine's Gems on Saturday, who lost 23-3.
The era of Jesamine not having a blog has also come to an end. Might I suggest you make your virtual way to Fabulous Jesamine 3 to check it out.
The era of the kids not both doing Auskick on a Sunday morning has come to an end - as has the era of me sleeping in on a Sunday.
One era that hasn't come to an end is me losing at Puerto Rico. We has another Puerto Rico night with Lee and Brian on Friday night, but I lost again. I did roll the highest number to start the game again though - which is rather curiously emerging as quite a hidden talent of mine.
BOOK UPDATE
I have finished Billy Bathgate. It was a struggle at the beginning, because the first full-stop didn't appear until half-way down the first page. I don't mind writers taking liberties with grammar - broken sentences are often a great way to establish tempo. In this case I found the sentence structure was often detracting from the story.
This comes from the perspective of an auditory reader - meaning that I hear the words in my head (and sometimes in the voice of Fred Flintstone - which is a whole other issue). The writing may serve very well for people who "process" written information in other ways.
Billy Bathgate is a story of a young boy becoming a gangster. I know that I saw the movie many years ago - but I can remember nothing of it.
Anyway, I'd call it a good book, even a very good book - but not a great book.
Since then I read Chocky, by John Wyndham. I love John Wyndham's writing - and I'm always amazed at just how much story he's able to build into pretty short books, and without them feeling dense.
Chocky is a voice within the head of a young boy, and it's hard to say much more without spoiling the plot. I'd have to say I hate the name though.
I'm now onto another John Wyndham - The Kraken Wakes.
THE PI CHALLENGE
I'm somewhat enamoured with the number Pi (3.14 etc). I even have the Pi symbol on the back of my soccer shirt.
Most people know that Pi is believed to have an infinite number of decimal places, with no repetition. What I've never understood, however, is how people go about calculating Pi to a given precision. So, I've decided to find out. Call it my personal challenge. I'll blog about the answer when I find it.
P.S.
I can't remember if I mentioned, but we sold that kids play set they I spent so long assembling a few weeks back. We also sold the kids old swing set to someone else who called about the ad in the paper after it was sold.
Wednesday, May 7, 2008
UNDEFEATED!!!!!!! (And a movie review)
That's right - you heard right.
FOB United have jolly-well done it again. 4 wins. No losses.
From one all at half time, we finished up winning by 8-1.
Egad!!!!
Also forgot to mention in my recent updates that we saw Iron Man on the weekend - and enjoyed it. It's the best of the Marvel franchise (you have to use the word franchise these days, it's some manner of by-law as I understand it.) Robert Downey Jr is excellent. The plot and structure are certainly predictable and formulaic -and it's always that bit harder to suspend disbelief when the premise tries to be believable. It's somehow easier to accept a Kryptonian with super powers, or human becoming spider-esque after being bitten by a radioactive spider, than to believe that artificially intelligent robots would resort to sarcasm. It's worth the effort though, because with disbelief suspended by whatever means, some of the best dialogue occurs between RD Jr and his binary entourage.
Jeff Bridges is barely recognisable. Cuba Gooding Jnr, on the other hand, is instantly recognisable - even though he's not in it.
I missed the post-credits scene - but it apparently sets up the sequel (or should I say - the next instalment in the franchise).
Suzy gave it four and a half stars, and you'll find her review on the "At The Movies" website.
FOB United have jolly-well done it again. 4 wins. No losses.
From one all at half time, we finished up winning by 8-1.
Egad!!!!
Also forgot to mention in my recent updates that we saw Iron Man on the weekend - and enjoyed it. It's the best of the Marvel franchise (you have to use the word franchise these days, it's some manner of by-law as I understand it.) Robert Downey Jr is excellent. The plot and structure are certainly predictable and formulaic -and it's always that bit harder to suspend disbelief when the premise tries to be believable. It's somehow easier to accept a Kryptonian with super powers, or human becoming spider-esque after being bitten by a radioactive spider, than to believe that artificially intelligent robots would resort to sarcasm. It's worth the effort though, because with disbelief suspended by whatever means, some of the best dialogue occurs between RD Jr and his binary entourage.
Jeff Bridges is barely recognisable. Cuba Gooding Jnr, on the other hand, is instantly recognisable - even though he's not in it.
I missed the post-credits scene - but it apparently sets up the sequel (or should I say - the next instalment in the franchise).
Suzy gave it four and a half stars, and you'll find her review on the "At The Movies" website.
Tuesday, May 6, 2008
NOTICE ANYTHING?
Connick drew this the other night, and it certainly amused me.
He then went on to tell us that his school books are full of pictures like this, and that the teacher always gets the other kids to look at them. Hmmm ... Weird ...
Then he clarified - they don't all have the front ripped out of their pants, they mostly have limbs cut off and stuff like that.
Well ... that set my mind at rest. He's not just a pervert ... he's also a budding psychopath. Whew!!!
At least he's not putting all his eggs in one basket.
He then went on to tell us that his school books are full of pictures like this, and that the teacher always gets the other kids to look at them. Hmmm ... Weird ...
Then he clarified - they don't all have the front ripped out of their pants, they mostly have limbs cut off and stuff like that.
Well ... that set my mind at rest. He's not just a pervert ... he's also a budding psychopath. Whew!!!
At least he's not putting all his eggs in one basket.
FOB - 3 WINS ON THE TROT
Did I forget to mention last Wednesday's soccer?
We are undefeated for the season - and the other teams turned up even!!!
We are undefeated for the season - and the other teams turned up even!!!
RETURN TO GOD'S OWN COUNTRY
ANZAC Day long weekend saw us back in Harrietville.
The Oven's Valley
God's Own Country as it were.
We danced, we sang, we made love. It was a whirlwind of romance and ... stuff.
As you'll undoubtedly recall from a previous thrilling blog entry, we left the van at mum and dad's after Easter. This meant a quick trip (relatively) over Dargo on the Thursday night after work.
I bought some books from the op shop - surprise surprise - including Billy Bathgate which you've no doubt seen on my current reading list (because I know you couldn't wait to look across there as soon as the page loaded).
We walked part-way up the Feathertop track, which looked a little something like this:
Suzy and Rachel (the 5th Eddy) turned back just before Picture Point - which is about 2kms up. Dad, Jo, Miles, Indi and Jesamine made it to Picture Point, while Danny and I continued passed Tobias Gap and Wombat Gap (but only because we missed it). So, we were probably about 6 kms up. Then we ran back down, which is not really standard bush-walking procedure, and Danny took a tumble which is also not standard bush-walking procedure, and I laughed at his mis-fortune, which after his constant stumbling had become standard bush-walking procedure (for me at least).
Much of the track we walked was covered in snow the following day!!! Get's me excited thinking about skiiing.
The kids played poker in the shed, which looked a little something like this:
We had Connick with us - and he looked like this:
We also had Jesamine with us - and she looked like this:
We towed the van back, which meant a looooong trip back down the Hume and through Melbourne.
That'll do for now. Thanks for your patience.
The Oven's Valley
God's Own Country as it were.
We danced, we sang, we made love. It was a whirlwind of romance and ... stuff.
As you'll undoubtedly recall from a previous thrilling blog entry, we left the van at mum and dad's after Easter. This meant a quick trip (relatively) over Dargo on the Thursday night after work.
I bought some books from the op shop - surprise surprise - including Billy Bathgate which you've no doubt seen on my current reading list (because I know you couldn't wait to look across there as soon as the page loaded).
We walked part-way up the Feathertop track, which looked a little something like this:
Suzy and Rachel (the 5th Eddy) turned back just before Picture Point - which is about 2kms up. Dad, Jo, Miles, Indi and Jesamine made it to Picture Point, while Danny and I continued passed Tobias Gap and Wombat Gap (but only because we missed it). So, we were probably about 6 kms up. Then we ran back down, which is not really standard bush-walking procedure, and Danny took a tumble which is also not standard bush-walking procedure, and I laughed at his mis-fortune, which after his constant stumbling had become standard bush-walking procedure (for me at least).
Much of the track we walked was covered in snow the following day!!! Get's me excited thinking about skiiing.
The kids played poker in the shed, which looked a little something like this:
We had Connick with us - and he looked like this:
We also had Jesamine with us - and she looked like this:
We towed the van back, which meant a looooong trip back down the Hume and through Melbourne.
That'll do for now. Thanks for your patience.
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