I thought pi was arrived at fron cutting a circle into triangles and simplifying the result with and equation...in any event using straight lines (triangles) when there is a curved line in the mix must leave the exact result always an approximation given that curved lines are converted to straight for the sake of approximation.
And so I ask why all the fuss pi must always contain a small flaw I would expect..no matter how many triangles you use to describe the circumfrence there will be an small sector ?segment? left out of pi.....
alex
"....supercomputers cruncin' past 200billion decimal places of pi and it continues" ... sounds to me like the eventual answer will be "42"
(Ave Douglas Adams)
What about some thought for the man who is said to have first worked out the relationship...who knows who it was?...
Interestingly he did not rate pi as his greatest achievement but favoured the relationship of a sphere within a cylinder... volume and surface area being 1.5 times for the cylinder to the sphere.. he was so happy with that one that he wanted a diagram on his tomb stone showing a sphere within a cylinder...and he got his wish...
He also worked out the laws relating to levers... and at the insistence of his King (Hiero) set up a lever system to pull a laden boat upon the shore...
He was able to tell his king that the maker of his crown had added something other than gold to the crown the king had called to be made... having supplied the gold the king asked the Pieman to make sure all the gold was used.... so who was he... think early Australia history and an effort to stand against authority by early gold prospectors..a small tie in there...
alex
He was also credited with a "death ray" ... a lens that set Roman ships on fire... a house hold name... finally killed by a Roman soldier whilst he drew diagrams in the sand.(probably of his ball in a cylinder maybe)
alex
Archimedes was a noted mathematician, scientist, astronomer and inventor but the death ray was a experimental/theoretical weapon, not a real one tested in battle.
Too many factors needed to be at their optimum for it to work.
Wull I think It has become smaller with the years. I remember it to eight places as 3.14159267 circa 1971. The latest value rounded to eight places is less....3.14159265.
I had a draughting apprentice prepare a production drawing for a hobbing cutter once and he used 22/7 for Pi!! sSo much for year 11 maths, maybe he should have stayed at school and finished year 12?
It was only recently that I realized that the area of a circle is the same as a right angled triangle with one side equal to the radius and the other the circumference....
one good representation of the number i've seen is (if i remember it correctly) is..
1-1/3+1/5-1/7+1/9-1/11+1/13-1/15.....
and so on & so on.
Personally I much prefer blueberry pi, with some apple mixed in
...had a lil think on this... it's the law of diminishing returns really...
Pi = 1/∞ or expressed another way, ∞=1/Pi .... it's what "relatively" speaking, contains all the universe within the expanding singularity..
...like two 3-inchers add up to a 4 1/2 not a six.. 2 x D squared = Pi .... kinda puts the dampners in my bino plans.. 'cept for the fact that humans have a dualistic central nervous-system... two hemispheres to complement the two eyes..
quoted from memory, but beyond that memory fades a bit now)
