Re: value of pi and 22/7

[Lawrence D’Oliveiro]

On Tuesday, June 21, 2016 at 10:24:46 AM UTC+12, Wildman wrote:
> I am not convinced on any of the theories on how the pyramids
> were built, or any other of the monolithic sites.

“Reality is that which, when you stop believing in it, doesn’t go away.”
 -- Philip K Dick
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Re: value of pi and 22/7

[Gregory Ewing]

Marko Rauhamaa wrote:

   And he made a molten sea, ten cubits from the one brim to the other:
   it was round all about, and his height was five cubits: and a line of
   thirty cubits did compass it round about. [1 Kings 7:23]


I think I know how that came about. It was actually filled
with molten neutronium, and the gravitational field was
distorting space enough to give a local circumference/diameter
ratio of 3.

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Re: value of pi and 22/7

[Steven D'Aprano]

On Tuesday 21 June 2016 02:01, Ian Kelly wrote:

> On Mon, Jun 20, 2016 at 12:22 AM, Steven D'Aprano
>  wrote:
>> There's a difference though. Nobody has tried to legislate the value of pi
>> to match your casual reference to "about 1900 square feet", but there's been
>> at least one serious attempt to legislate the value of pi to match the
>> implied value given by the Bible.
> 
> If you're referring the Indiana Pi Bill of 1897, it was actually a
> poorly conceived attempt to publish an amateur mathematician's claim
> of a way to square the circle. It had nothing to do with biblical
> interpretation and would have implied a value for pi of 3.2, not 3.
> 
> https://en.wikipedia.org/wiki/Indiana_Pi_Bill

Thanks for the link, that's interesting.




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Re: value of pi and 22/7

[Marko Rauhamaa]

Wildman :

> As you can see, a stone had to be cut, transported and put in place
> every 6 minutes 24 hours a day for 23 years. And if the stone count
> was actually 2.4 million, the time would be reduced to 5 minutes per
> stone. All I can say is wow!

It probably means mostly that the Nile produced enough grain to feed a
lot more people than were needed to till the land. Feudal ownership
produced public works and a working economy. Nowadays, very few people
are needed to till the land, but so far the farmers have been content
with the amenities and gadgets provided by the industry.

It has somewhat similarly been shown how the slave trade of the 17th
century was generated by maize, which was introduced to West Africa. The
soil produced vastly more people, which the local warlords sold to
European slave traders.


Marko
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Re: value of pi and 22/7

[Wildman via Python-list]

On Mon, 20 Jun 2016 01:01:21 -0700, Lawrence D’Oliveiro wrote:

> On Monday, June 20, 2016 at 7:32:54 PM UTC+12, Marko Rauhamaa wrote:
> 
>> Width/height ratio of the pyramid of Cheops was so close to π/2 that UFO
>> enthusiasts were convinced alien technology was used in the construction
>> of the pyramids.
> 
> They were also able to get the bases of the pyramids horizontal
> to within about a centimetre. Amazing achievement, but entirely
> achievable with bronze-age technology.

I am not convinced on any of the theories on how the pyramids
were built, or any other of the monolithic sites.  But, I am
in awe as to the fact that it was actually done.  Just look
at the numbers for the Great Pyramid.  It is believed that it
took 23 years for construction.  It is estimated that there
are somewhere between 2.0 to 2.4 million stones.  I will use
2.0 million for the math...

23 * 365.25 * 24 * 60 / 200 = 6.04854

As you can see, a stone had to be cut, transported and put in
place every 6 minutes 24 hours a day for 23 years.  And if
the stone count was actually 2.4 million, the time would be
reduced to 5 minutes per stone.  All I can say is wow!

Another example is the fact that some ancient Central American
cultures were able to lift and transport stones weighing up
to 300 tons.  We would have a very hard time doing that today
with our modern machinery.

I'm not trying to say that ET or $DIETY did it.  I'm just
point out the fact that something amazing was done.  I
keep an open mind to any possibility.  Right now there
is no actual proof to support any theory.

-- 
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and let every new year find you a better man."
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Re: value of pi and 22/7

[Marko Rauhamaa]

Gregory Ewing :

> Lawrence D’Oliveiro wrote:
>
>> I feel a new phrase coming on: “good enough for Bible work”!
>
> I understand there's a passage in the Bible somewhere that
> uses a 1 significant digit approximation to pi...

Yes:

   And he made a molten sea, ten cubits from the one brim to the other:
   it was round all about, and his height was five cubits: and a line of
   thirty cubits did compass it round about. [1 Kings 7:23]

This and other entertaining stories in:

   https://www.amazon.com/History-PI-Beckmann/dp/B004XYXQ96>


Marko
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Re: value of pi and 22/7

[Grant Edwards]

On 2016-06-20, Steven D'Aprano  wrote:

> One of the most underrated yet critical functions of government is
> to standardise weights and measures, and that function evolved very
> slowly over time. I doubt that the Egyptian Pharoahs cared about it,

Oh, I bet they did.  How you measure things affects how much tax you
collect -- and the people at the top of every government pay a lot of
attention to that.  The state doesn't check all those gas pumps
against a volumetric flask every year to protect Joe Carowner.  I've
designed various sorts of measurement and instrumentation, and when a
device is used for doing a measurement that affects how much tax gets
paid, things get deadly serious.

> although their scribes probably did, a bit.

-- 
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  at   well-tapered, half-cocked,
  gmail.comill-conceived and
   TAX-DEFERRED!

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Re: value of pi and 22/7

[Grant Edwards]

On 2016-06-19, Gregory Ewing  wrote:
> Lawrence D’Oliveiro wrote:
>
>> I feel a new phrase coming on: “good enough for Bible work”!
>
> I understand there's a passage in the Bible somewhere that
> uses a 1 significant digit approximation to pi...

A lot of the time, 3 is a good-enough approximation of π (it's less
than 5% off). Yesterday I needed to know if the globe on a light
fixture was 5", 6", or 7" diameter.  Measure the circumference with a
tape, divide by 3, and Bob's your uncle.  Of course if you have to do
that very often, you just by a diameter tape. :)

-- 
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  at   overnight sensation right
  gmail.comnow!!

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Re: value of pi and 22/7

[Ian Kelly]

On Mon, Jun 20, 2016 at 10:01 AM, Ian Kelly  wrote:
> I'm not aware of any other such legislative attempts. Snopes records
> one that allegedly occurred in Indiana but dismisses the claim as
> false.

s/Indiana/Alabama
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Re: value of pi and 22/7

[Ian Kelly]

On Mon, Jun 20, 2016 at 12:22 AM, Steven D'Aprano
 wrote:
> There's a difference though. Nobody has tried to legislate the value of pi to
> match your casual reference to "about 1900 square feet", but there's been at
> least one serious attempt to legislate the value of pi to match the implied
> value given by the Bible.

If you're referring the Indiana Pi Bill of 1897, it was actually a
poorly conceived attempt to publish an amateur mathematician's claim
of a way to square the circle. It had nothing to do with biblical
interpretation and would have implied a value for pi of 3.2, not 3.

https://en.wikipedia.org/wiki/Indiana_Pi_Bill

I'm not aware of any other such legislative attempts. Snopes records
one that allegedly occurred in Indiana but dismisses the claim as
false.
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Re: value of pi and 22/7

[Lawrence D’Oliveiro]

On Monday, June 20, 2016 at 7:32:54 PM UTC+12, Marko Rauhamaa wrote:

> Width/height ratio of the pyramid of Cheops was so close to π/2 that UFO
> enthusiasts were convinced alien technology was used in the construction
> of the pyramids.

They were also able to get the bases of the pyramids horizontal to within about 
a centimetre. Amazing achievement, but entirely achievable with bronze-age 
technology.
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Re: value of pi and 22/7

[Marko Rauhamaa]

Lawrence D’Oliveiro :

> On Monday, June 20, 2016 at 10:26:03 AM UTC+12, Gregory Ewing wrote:
>
>> If you're building something the size of a pyramid, that could
>> add up to quite a lot of error.
>
> Particularly since so many of their neighbours had worked out how to
> do much better than that, thousands of years earlier...

Width/height ratio of the pyramid of Cheops was so close to π/2 that UFO
enthusiasts were convinced alien technology was used in the construction
of the pyramids.

The whole story involving cubits, drums and fingers is here: http://doernenburg.alien.de/alternativ/pyramide/pyr12_e.php>.

   This is the definite proof, that no god, astronaut or Atlantean
   wizard had any intention of coding Pi into one of the many pyramids
   erected in Egypt. Pi is simply a result of the measurement methods
   used in old Egypt!


Marko
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Re: value of pi and 22/7

[Steven D'Aprano]

On Monday 20 June 2016 15:19, Ian Kelly wrote:

> Sure, but I think you've missed my central point, which is not that
> they wouldn't have made reasonably precise measurements in
> construction, but only that the storytellers would have rounded things
> off for their audience.
> 
> We still do the same thing today. A house appraisal will report its
> footprint to the nearest square foot, but most people when talking
> about it casually aren't going to say "my house is 1936 square feet".
> More likely they'll just say "about 1900 square feet", since past the
> first couple of digits nobody really cares.

There's a difference though. Nobody has tried to legislate the value of pi to 
match your casual reference to "about 1900 square feet", but there's been at 
least one serious attempt to legislate the value of pi to match the implied 
value given by the Bible.

And some very large percentage of people in the world, especially in but not 
limited to the USA, will dispute your suggestion that "storytellers would have 
rounded things off for their audience" on the basis that every single word in 
the Bible is the inerrant, literal word of the god known as God. If the Bible 
implies that pi is 3, then by gum, that means it is 3.

Or at least, that's what they *say* they believe. In practice, the literalists 
accept that the Bible contains metaphors, stories, and other non-literal text 
the same as everyone else does, they just pick and choose[1] which bits they 
choose to accept as literal in ways that strike others as naive, stupid, out-
dated or outright wicked.




[1] To be fair, as we all do, as the ancient Hebrews unaccountably failed to 
mark up their texts using tags.

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Re: value of pi and 22/7

[Lawrence D’Oliveiro]

On Monday, June 20, 2016 at 10:26:03 AM UTC+12, Gregory Ewing wrote:

> If you're building something the size of a pyramid, that could
> add up to quite a lot of error.

Particularly since so many of their neighbours had worked out how to do much 
better than that, thousands of years earlier...
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Re: value of pi and 22/7

[Ian Kelly]

On Sun, Jun 19, 2016 at 4:25 PM, Gregory Ewing
 wrote:
> Ian Kelly wrote:
>>
>>  Remember, the cubit was based on the length of the
>> forearm, so it's not like it was a terribly precise measurement to
>> begin with;
>
>
> Let's not sell them short. Just because it was based on a forearm
> doesn't mean they didn't have a precise standard for it, any more
> than people who measure things in "feet" do it by plonking down
> their own foot.
>
> No doubt it wasn't as precise as what we have nowadays, but
> it was probably a lot better than human body part variations.

Sure, but I think you've missed my central point, which is not that
they wouldn't have made reasonably precise measurements in
construction, but only that the storytellers would have rounded things
off for their audience.

We still do the same thing today. A house appraisal will report its
footprint to the nearest square foot, but most people when talking
about it casually aren't going to say "my house is 1936 square feet".
More likely they'll just say "about 1900 square feet", since past the
first couple of digits nobody really cares.
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Re: value of pi and 22/7

[Steven D'Aprano]

On Mon, 20 Jun 2016 08:25 am, Gregory Ewing wrote:

> Ian Kelly wrote:
>>  Remember, the cubit was based on the length of the
>> forearm, so it's not like it was a terribly precise measurement to
>> begin with;
> 
> Let's not sell them short. Just because it was based on a forearm
> doesn't mean they didn't have a precise standard for it, any more
> than people who measure things in "feet" do it by plonking down
> their own foot.
> 
> No doubt it wasn't as precise as what we have nowadays, but
> it was probably a lot better than human body part variations.

And let's not make the mistake of presentism, judging the past by the
standards of the present.

The biggest problem with the cubit is not that it is *inaccurate*, as that
different places had their own idea of what a cubit was. I dare say that on
any specific building site, the foreman would ensure that everyone was
working with more or less the same idea of what a cubit was. But once you
moved from one village or town to another, chances are that they were using
a different idea of a cubit that was not quite the same as yours.

To be honest, I don't actually know much about the situation in Ancient
Egypt. For all I know, every tradesman did measure his bit of the pyramid
by laying his forearm down on the rock and adjusting by eye. (But I doubt
it.) And they did have two distinct measures, what we today call the "Royal
cubit" and the "short cubit". So I expect that there actually was quite a
bit of day to day confusion and frustration due to the lack of accurate and
consistent measurements.

One of the most underrated yet critical functions of government is to
standardise weights and measures, and that function evolved very slowly
over time. I doubt that the Egyptian Pharoahs cared about it, although
their scribes probably did, a bit.

If you look at, say, Medieval and even Renaissance Europe, one of the
biggest problems people faced was the lack of standard definitions of
units. Every village and town had their own idea of what a hogshead was, to
say nothing of unscrupulous merchants who would deliberately underweigh or
undermeasure. It was a big enough problem that governments eventually
evolved entire bureaucracies to ensure that when you ordered 1 yards of
cloth, you got 1 yards of cloth, and not an argument about what a yard
actually is.

But even today, we still have lack of agreement at the national level:
1,000,000 US gallons are about 832,674 UK gallons. Similarly for miles: US
statute miles are ever-so-slightly less than UK miles.

But at least the metric system is the same everywhere.


>> they might not have understood significant figures, but
>> they probably wouldn't have been overly concerned about the difference
>> between thirty and thirty-one.
> 
> If you're building something the size of a pyramid, that could
> add up to quite a lot of error.

Indeed.


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Steven

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Re: value of pi and 22/7

[Gregory Ewing]

Ian Kelly wrote:

 Remember, the cubit was based on the length of the
forearm, so it's not like it was a terribly precise measurement to
begin with;


Let's not sell them short. Just because it was based on a forearm
doesn't mean they didn't have a precise standard for it, any more
than people who measure things in "feet" do it by plonking down
their own foot.

No doubt it wasn't as precise as what we have nowadays, but
it was probably a lot better than human body part variations.


they might not have understood significant figures, but
they probably wouldn't have been overly concerned about the difference
between thirty and thirty-one.


If you're building something the size of a pyramid, that could
add up to quite a lot of error.

--
Greg
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Re: value of pi and 22/7

[Gregory Ewing]

Lawrence D’Oliveiro wrote:


I feel a new phrase coming on: “good enough for Bible work”!


I understand there's a passage in the Bible somewhere that
uses a 1 significant digit approximation to pi...

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Re: value of pi and 22/7

[Johannes Bauer]

On 18.06.2016 01:12, Lawrence D’Oliveiro wrote:

> I’m not sure how you can write “30” with one digit...

3e1 has one significant digit.

Cheers,
Johannes

-- 
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Re: value of pi and 22/7

[boB Stepp]

On Sat, Jun 18, 2016 at 12:47 AM, Tim Harig
 wrote:

>
> The main problem I have with significant figures is that measurement
> accuracy is often not constrained to a decimal system.  A scale that can
> measure in 1/5 units is more accurate than a scale that can measure only
> in whole units but it is not as accurate as a scale that can measure
> all 1/10 units.  Therefore it effectively has a fractional number of
> significant figures.

Probably in this type of discussion a more careful distinction between
"precision" and "accuracy" should be made.  A measuring instrument may
allow for many significant digits in its reported result, giving it a
high level of precision, but could, in fact, be giving an inaccurate
measurement (How close it is to the "true" value.), especially if it
is an instrument that has not been properly calibrated (Made to agree
as well as possible with known standards.).

boB
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Re: value of pi and 22/7

[Pete Forman]

Lawrence D’Oliveiro  writes:

> On Saturday, March 19, 2011 at 3:16:41 AM UTC+13, Grant Edwards wrote:
>>
>> On 2011-03-18, peter wrote:
>>
>>> The Old Testament (1 Kings 7,23) says ... "And he made a molten sea,
>>> ten cubits from the one brim to the other: it was round all about, and
>>> his height was five cubits: and a line of thirty cubits did compass it
>>> round about. ".  So pi=3.  End Of.
>>
>> There's nothing wrong with that value.  The measurements were given
>> with one significant digit, so the ratio of the two measurements
>> should only have one significant digit.
>
> I’m not sure how you can write “30” with one digit...

>>> int('U', 36)
30

-- 
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Re: value of pi and 22/7

[Christian Gollwitzer]

Am 18.06.16 um 03:19 schrieb Steven D'Aprano:

If I tell you that some physical phenomenon [let's call it the speed of
light] is 299,999,999 m/s, how many significant digits would I be using?

What if I tell you that it's 300,000,001 m/s?

What if the figure to nine significant digits *actually is* three followed
by eight zeroes?


You can't read off the number of significant figures from a value 
itself, it must be given as a side information. It is a common way to 
indicate uncertainty estimes, however, by giving a number to as many 
decimal places as there are significant digits, i.e. to indicate the 
uncertainty as a power of ten. You need to use exponential notation to 
express that clearly, in that case:


3*10^8 -> (3 +/- 0.5) * 10^8
3.0 *10^8 -> (3.0 +/- 0.05)*10^8

For more accurate error estimates, the second notation is used. Another 
common way to express this is something like


3.42(3) which means 3.42 +/- 0.03

Note, however, that in current SI units the speed of light is known exactly:

c = 299,792,458 m/s

There is no error! This is possible because the unit metre is defined by 
this value from the unit second.


Christian
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Re: value of pi and 22/7

[John Ladasky]

On Friday, March 18, 2011 at 5:17:48 AM UTC-7, Neil Cerutti wrote:
> RIIght.  What's a cubit?
> 
> -- 
> Neil Cerutti

How long can you tread water?  (Showing my age...)
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Re: value of pi and 22/7

[Tim Harig]

On 2016-06-18, Steven D'Aprano  wrote:
> On Sat, 18 Jun 2016 09:49 am, Ian Kelly wrote:
>
>> If I tell you that the speed of light is 300,000,000 m/s, do you think
>> that measurement has 9 significant digits? If you do, then you would be
>> wrong.
> What if the figure to nine significant digits *actually is* three followed
> by eight zeroes?

The you can either write it as 3. (notice the trailing decimal
indicating that all of the zeros are indeed significant) or write it it
scientific notation.

> For all that it is in widespread use, I think the concept of "significant
> figures" is inherently ambiguous.

Only for those who do not understand it.

The main problem I have with significant figures is that measurement
accuracy is often not constrained to a decimal system.  A scale that can
measure in 1/5 units is more accurate than a scale that can measure only
in whole units but it is not as accurate as a scale that can measure
all 1/10 units.  Therefore it effectively has a fractional number of
significant figures.

I could just cut my loses and express the lower number of significant
figures but, I usually express the error explicitly instead:

 +- 0.2 units

where +- looks like the  html entity.
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Re: value of pi and 22/7

[Ian Kelly]

On Fri, Jun 17, 2016 at 10:30 PM, Lawrence D’Oliveiro
 wrote:
> On Saturday, June 18, 2016 at 3:48:43 PM UTC+12, Random832 wrote:
>>
>> On Fri, Jun 17, 2016, at 19:12, Lawrence D’Oliveiro wrote:
>>>
>>> I’m not sure how you can write “30” with one digit...
>>
>> One *significant* digit.
>
> Like some credulous past-Bronze-age tribespeople understood the concept of 
> “significant digits” ...

I don't see why they should need to in order to measure one thing as
"thirty cubits" and another thing as "ten cubits" and write those
numbers down. Remember, the cubit was based on the length of the
forearm, so it's not like it was a terribly precise measurement to
begin with; they might not have understood significant figures, but
they probably wouldn't have been overly concerned about the difference
between thirty and thirty-one.

Check out the rest of the chapter. Every single measurement in it
above seven is a multiple of ten.

> I wonder what the quality of their workmanship was like, if a measurement 
> accurate to one significant digit was considered sufficient ...

You realize there can be a difference between the quality to which
something is constructed and the precision of the measurements later
used to describe it? "Threescore cubits long"  is an impressive
figure. "61 and a half cubits" doesn't do the job of communicating the
scale any better, and ultimately amounts to wasted words in what was
originally an oral tradition.
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Re: value of pi and 22/7

[Lawrence D’Oliveiro]

On Saturday, June 18, 2016 at 3:48:43 PM UTC+12, Random832 wrote:
>
> On Fri, Jun 17, 2016, at 19:12, Lawrence D’Oliveiro wrote:
>>
>> I’m not sure how you can write “30” with one digit...
> 
> One *significant* digit.

Like some credulous past-Bronze-age tribespeople understood the concept of 
“significant digits” ...

I wonder what the quality of their workmanship was like, if a measurement 
accurate to one significant digit was considered sufficient ...

I feel a new phrase coming on: “good enough for Bible work”!
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Re: value of pi and 22/7

[Random832]

On Fri, Jun 17, 2016, at 19:12, Lawrence D’Oliveiro wrote:
> I’m not sure how you can write “30” with one digit...

One *significant* digit. Though, as it happens, some ancient number
systems, including Hebrew and Greek, have one set of digits for 1-9, one
for 10-90, and one for 100-900.
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Re: value of pi and 22/7

[Ethan Furman]

On 06/17/2016 06:19 PM, Steven D'Aprano wrote:

On Sat, 18 Jun 2016 09:49 am, Ian Kelly wrote:



If I tell you that the speed of light is 300,000,000 m/s, do you think
that measurement has 9 significant digits? If you do, then you would be
wrong.


Hmmm.

If I tell you that some physical phenomenon [let's call it the speed of
light] is 299,999,999 m/s, how many significant digits would I be using?


I know!  I know!  9!


What if I tell you that it's 300,000,001 m/s?


Oh!  9 again!


What if the figure to nine significant digits *actually is* three followed
by eight zeroes?


Hmmm... thinking thinking... oh yeah!  You put a bar over the last 
significant digit -- or you use scientific notation:


30e7 has two significant digits.


For all that it is in widespread use, I think the concept of "significant
figures" is inherently ambiguous.


Not at all -- just have to keep your notations correct*.

--
~Ethan~

* Mine might be 30 years out of date, but maybe not.
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Re: value of pi and 22/7

[Steven D'Aprano]

On Sat, 18 Jun 2016 09:49 am, Ian Kelly wrote:

> If I tell you that the speed of light is 300,000,000 m/s, do you think
> that measurement has 9 significant digits? If you do, then you would be
> wrong.

Hmmm.

If I tell you that some physical phenomenon [let's call it the speed of
light] is 299,999,999 m/s, how many significant digits would I be using?

What if I tell you that it's 300,000,001 m/s?

What if the figure to nine significant digits *actually is* three followed
by eight zeroes?

For all that it is in widespread use, I think the concept of "significant
figures" is inherently ambiguous.



-- 
Steven

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Re: value of pi and 22/7

[Ian Kelly]

On Jun 17, 2016 5:44 PM, "Lawrence D’Oliveiro" 
wrote:
>
> On Saturday, March 19, 2011 at 3:16:41 AM UTC+13, Grant Edwards wrote:
> >
> > On 2011-03-18, peter wrote:
> >
> >> The Old Testament (1 Kings 7,23) says ... "And he made a molten sea,
> >> ten cubits from the one brim to the other: it was round all about, and
> >> his height was five cubits: and a line of thirty cubits did compass it
> >> round about. ".  So pi=3.  End Of.
> >
> > There's nothing wrong with that value.  The measurements were given
> > with one significant digit, so the ratio of the two measurements
> > should only have one significant digit.
>
> I’m not sure how you can write “30” with one digit...

If I tell you that the speed of light is 300,000,000 m/s, do you think that
measurement has 9 significant digits? If you do, then you would be wrong.

By the way, you're also replying to posts that are more than 5 years old.
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Re: value of pi and 22/7

[Lawrence D’Oliveiro]

On Saturday, March 19, 2011 at 3:16:41 AM UTC+13, Grant Edwards wrote:
>
> On 2011-03-18, peter wrote:
> 
>> The Old Testament (1 Kings 7,23) says ... "And he made a molten sea,
>> ten cubits from the one brim to the other: it was round all about, and
>> his height was five cubits: and a line of thirty cubits did compass it
>> round about. ".  So pi=3.  End Of.
> 
> There's nothing wrong with that value.  The measurements were given
> with one significant digit, so the ratio of the two measurements
> should only have one significant digit.

I’m not sure how you can write “30” with one digit...
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Re: value of pi and 22/7

[Lawrence D’Oliveiro]

On Friday, March 18, 2011 at 8:21:36 AM UTC+13, Rotwang wrote:

> sum_{j = 1}^\infty 10^{-j!} 

You forgot a “\” in front of “sum”.

(Of course I had to try it in IPython...)
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Re: value of pi and 22/7

[MRAB]

On 2016-06-17 17:51, hed...@hedgui.com wrote:

Pi simply is not 3.14159

Time to go to remedial school everyone.

If I do something on one side of the equation, I have to do the same on the 
other side of the equation.

With Pi, we are TAKING the diameter, so subtract the width of diameter from the 
circumference of the circle and you have an ellipse, now there is thousands of 
diameters. ⭕o

I suggest that Pi is = D*-7

Don't forget to put the diameter back.


You're replying to a post from March 2011.

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Re: value of pi and 22/7

[hedgui]

Pi simply is not 3.14159

Time to go to remedial school everyone.

If I do something on one side of the equation, I have to do the same on the 
other side of the equation.

With Pi, we are TAKING the diameter, so subtract the width of diameter from the 
circumference of the circle and you have an ellipse, now there is thousands of 
diameters. ⭕o 

I suggest that Pi is = D*-7

Don't forget to put the diameter back.
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value of pi and 22/7

[Gerald Britton]

Surely on track for the *slowest* way to compute pi in Python (or any
language for that matter):

math.sqrt( sum( pow(k,-2) for k in xrange(sys.maxint,0,-1)  ) * 6.  )

Based on the Riemann zeta function:

   The sum of

1/k^2 for k = 1:infinity

   converges to pi^2 / 6

Depending on your horsepower and the size of sys.maxint on your
machine, this may take a few *days* to run.

Note: The sum in the Python expression above runs in reverse to
minimize rounding errors.

-- 
Gerald Britton
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Re: value of pi and 22/7

[Steven D'Aprano]

On Fri, 18 Mar 2011 07:22:43 -0700, Kee Nethery wrote:

 On Mar 18, 2011, at 5:17 AM, Neil Cerutti wrote:
 
 On 2011-03-18, peter peter.mos...@talk21.com wrote:
 The Old Testament (1 Kings 7,23) says ... And he made a molten sea,
 ten cubits from the one brim to the other: it was round all about, and
 his height was five cubits: and a line of thirty cubits did compass it
 round about. .  So pi=3.  End Of.
 
 RIIght.  What's a cubit?
 
 I use cubits all the time. The distance from my elbow to my finger tips
 equals one cubit. When you don't have a proper measuring tape, it can be
 pretty accurate for comparing two measurements.

Measure with micrometer, mark with chalk, cut with axe.

Just wait until you tell your apprentice to go fetch a piece of wood 
three cubits long... damn kids with their short/long arms...

:)


-- 
Steven


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Re: value of pi and 22/7

[D'Arcy J.M. Cain]

On Fri, 18 Mar 2011 13:45:47 +0100
Stefan Behnel stefan...@behnel.de wrote:
 Neil Cerutti, 18.03.2011 13:17:
  RIIght.  What's a cubit?
 
 http://en.wikipedia.org/wiki/Cubit

I don't believe that Neil was asking a serious question.

http://www.youtube.com/watch?v=so9o3_daDZw

-- 
D'Arcy J.M. Cain da...@druid.net |  Democracy is three wolves
http://www.druid.net/darcy/|  and a sheep voting on
+1 416 425 1212 (DoD#0082)(eNTP)   |  what's for dinner.
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Re: value of pi and 22/7

[peter]

On Mar 17, 5:22 pm, Kee Nethery k...@kagi.com wrote:
 My favorite approximation is: 355/113  (visualize 113355 split into two 113 
 355 and then do the division). The first 6 decimal places are the same.

 3.141592920353982 = 355/113
 vs
 3.1415926535897931

 Kee Nethery

Or (more for fun than any practical application) try (2143/22)^(1/4) =
3.14159265268.

Other approximations I have seen are root(10) and 3.142.  This last
was especially popular at school, which for me was sufficiently long
ago to have used four figure log tables.

The Old Testament (1 Kings 7,23) says ... And he made a molten sea,
ten cubits from the one brim to the other: it was round all about, and
his height was five cubits: and a line of thirty cubits did compass it
round about. .  So pi=3.  End Of.








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Re: value of pi and 22/7

[Neil Cerutti]

On 2011-03-18, peter peter.mos...@talk21.com wrote:
 The Old Testament (1 Kings 7,23) says ... And he made a molten
 sea, ten cubits from the one brim to the other: it was round
 all about, and his height was five cubits: and a line of thirty
 cubits did compass it round about. .  So pi=3.  End Of.

RIIght.  What's a cubit?

-- 
Neil Cerutti
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Re: value of pi and 22/7

[Stefan Behnel]

Neil Cerutti, 18.03.2011 13:17:

On 2011-03-18, peterpeter.mos...@talk21.com  wrote:

The Old Testament (1 Kings 7,23) says ... And he made a molten
sea, ten cubits from the one brim to the other: it was round
all about, and his height was five cubits: and a line of thirty
cubits did compass it round about. .  So pi=3.  End Of.


RIIght.  What's a cubit?


http://en.wikipedia.org/wiki/Cubit

I think that particular author of that particular part of the bible just 
used it to make the text appear older than it was at the time.


Stefan

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Re: value of pi and 22/7

[Neil Cerutti]

On 2011-03-18, Stefan Behnel stefan...@behnel.de wrote:
 Neil Cerutti, 18.03.2011 13:17:
 On 2011-03-18, peterpeter.mos...@talk21.com  wrote:
 The Old Testament (1 Kings 7,23) says ... And he made a molten
 sea, ten cubits from the one brim to the other: it was round
 all about, and his height was five cubits: and a line of thirty
 cubits did compass it round about. .  So pi=3.  End Of.

 RIIght.  What's a cubit?

 http://en.wikipedia.org/wiki/Cubit

 I think that particular author of that particular part of the
 bible just used it to make the text appear older than it was at
 the time.

http://www.youtube.com/watch?v=n0KHt8xrQkk

-- 
Neil Cerutti
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Re: value of pi and 22/7

[Aage Andersen]

peter
Kee Nethery  My favorite approximation is: 355/113 (visualize 113355 split 
into two 113 355 and then do the division). The first 6 decimal places are 
the same.

 3.141592920353982 = 355/113
 vs
 3.1415926535897931

 Kee Nethery

Or (more for fun than any practical application) try (2143/22)^(1/4) =
3.14159265268.

Other approximations I have seen are root(10) and 3.142.  This last
was especially popular at school, which for me was sufficiently long
ago to have used four figure log tables.

The Old Testament (1 Kings 7,23) says ... And he made a molten sea,
ten cubits from the one brim to the other: it was round all about, and
his height was five cubits: and a line of thirty cubits did compass it
round about. .  So pi=3.  End Of.
---

3 is the best integer approximation to pi. So the bibel is right.

Aage












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Re: value of pi and 22/7

[Sherm Pendley]

Stefan Behnel stefan...@behnel.de writes:

 Neil Cerutti, 18.03.2011 13:17:
 On 2011-03-18, peterpeter.mos...@talk21.com  wrote:
 The Old Testament (1 Kings 7,23) says ... And he made a molten
 sea, ten cubits from the one brim to the other: it was round
 all about, and his height was five cubits: and a line of thirty
 cubits did compass it round about. .  So pi=3.  End Of.

 RIIght.  What's a cubit?

 http://en.wikipedia.org/wiki/Cubit

 I think that particular author of that particular part of the bible
 just used it to make the text appear older than it was at the time.

Sigh. Doesn't *anyone* know Cosby any more? Kids today, no appreciation
for the classics. :-(

sherm--

-- 
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   http://camelbones.sourceforge.net
Cocoa Developer
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Re: value of pi and 22/7

[Westley Martínez]

On Fri, 2011-03-18 at 02:10 -0700, peter wrote:
 On Mar 17, 5:22 pm, Kee Nethery k...@kagi.com wrote:
  My favorite approximation is: 355/113  (visualize 113355 split into two 113 
  355 and then do the division). The first 6 decimal places are the same.
 
  3.141592920353982 = 355/113
  vs
  3.1415926535897931
 
  Kee Nethery
 
 Or (more for fun than any practical application) try (2143/22)^(1/4) =
 3.14159265268.
 
 Other approximations I have seen are root(10) and 3.142.  This last
 was especially popular at school, which for me was sufficiently long
 ago to have used four figure log tables.
 
 The Old Testament (1 Kings 7,23) says ... And he made a molten sea,
 ten cubits from the one brim to the other: it was round all about, and
 his height was five cubits: and a line of thirty cubits did compass it
 round about. .  So pi=3.  End Of.
 
 
 
 
 
 
 
 
The Bible uses integers due to memory constraints.

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Re: value of pi and 22/7

[Stefan Behnel]

Sherm Pendley, 18.03.2011 14:46:

Stefan Behnel writes:


Neil Cerutti, 18.03.2011 13:17:

On 2011-03-18, peterpeter.mos...@talk21.com   wrote:

The Old Testament (1 Kings 7,23) says ... And he made a molten
sea, ten cubits from the one brim to the other: it was round
all about, and his height was five cubits: and a line of thirty
cubits did compass it round about. .  So pi=3.  End Of.


RIIght.  What's a cubit?


http://en.wikipedia.org/wiki/Cubit

I think that particular author of that particular part of the bible
just used it to make the text appear older than it was at the time.


Sigh. Doesn't *anyone* know Cosby any more? Kids today, no appreciation
for the classics. :-(


And what about Heinz Erhardt? *That's* a classic.

Stefan

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Re: value of pi and 22/7

[Grant Edwards]

On 2011-03-18, peter peter.mos...@talk21.com wrote:

 The Old Testament (1 Kings 7,23) says ... And he made a molten sea,
 ten cubits from the one brim to the other: it was round all about, and
 his height was five cubits: and a line of thirty cubits did compass it
 round about. .  So pi=3.  End Of.

There's nothing wrong with that value.  The measurements were given
with one significant digit, so the ratio of the two measurements
should only have one significant digit.

-- 
Grant Edwards   grant.b.edwardsYow! It's some people
  at   inside the wall!  This is
  gmail.combetter than mopping!
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Re: value of pi and 22/7

[Kee Nethery]

On Mar 18, 2011, at 5:17 AM, Neil Cerutti wrote:

 On 2011-03-18, peter peter.mos...@talk21.com wrote:
 The Old Testament (1 Kings 7,23) says ... And he made a molten
 sea, ten cubits from the one brim to the other: it was round
 all about, and his height was five cubits: and a line of thirty
 cubits did compass it round about. .  So pi=3.  End Of.
 
 RIIght.  What's a cubit?

I use cubits all the time. The distance from my elbow to my finger tips equals 
one cubit. When you don't have a proper measuring tape, it can be pretty 
accurate for comparing two measurements.

Kee Nethery


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Re: value of pi and 22/7

[John Gordon]

In 8uh0rcfe1...@mid.individual.net Neil Cerutti ne...@norwich.edu writes:

 RIIght.  What's a cubit?

How long can you tread water?

-- 
John Gordon   A is for Amy, who fell down the stairs
gor...@panix.com  B is for Basil, assaulted by bears
-- Edward Gorey, The Gashlycrumb Tinies

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Re: value of pi and 22/7

[Adam Tauno Williams]

On Fri, 2011-03-18 at 14:16 +, Grant Edwards wrote:
 On 2011-03-18, peter peter.mos...@talk21.com wrote:
  The Old Testament (1 Kings 7,23) says ... And he made a molten sea,
  ten cubits from the one brim to the other: it was round all about, and
  his height was five cubits: and a line of thirty cubits did compass it
  round about. .  So pi=3.  End Of.
 There's nothing wrong with that value.  The measurements were given
 with one significant digit, so the ratio of the two measurements
 should only have one significant digit.

I've worked in landscaping and [low-scale] agriculture - pi as 3 is used
all the time.  It is easy to compute in your head and close enough.  


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value of pi and 22/7

[kracekumar ramaraju]

I tried the following
 22/7.0
3.1428571428571428
 import math
 math.pi
3.1415926535897931



Why is the difference is so much ?is pi =22/7 or something ?
-- 
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Re: value of pi and 22/7

[Wolfgang Rohdewald]

On Donnerstag 17 März 2011, kracekumar ramaraju wrote:

  22/7.0
 
 3.1428571428571428
 
  import math
  math.pi
 
 3.1415926535897931
 
 Why is the difference is so much ?is pi =22/7 or something ?

https://secure.wikimedia.org/wikipedia/en/wiki/Pi

-- 
Wolfgang
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Re: value of pi and 22/7

[Ian Kelly]

On Thu, Mar 17, 2011 at 10:46 AM, kracekumar ramaraju
kracethekingma...@gmail.com wrote:
 I tried the following
 22/7.0
 3.1428571428571428
 import math
 math.pi
 3.1415926535897931



 Why is the difference is so much ?is pi =22/7 or something ?

Pi is not 22/7.  That is just a commonly-used approximation.
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Re: value of pi and 22/7

[Ian Kelly]

On Thu, Mar 17, 2011 at 10:57 AM, Ian Kelly ian.g.ke...@gmail.com wrote:
 On Thu, Mar 17, 2011 at 10:46 AM, kracekumar ramaraju
 kracethekingma...@gmail.com wrote:
 I tried the following
 22/7.0
 3.1428571428571428
 import math
 math.pi
 3.1415926535897931



 Why is the difference is so much ?is pi =22/7 or something ?

 Pi is not 22/7.  That is just a commonly-used approximation.

I should add that math.pi is also not pi, because pi cannot be exactly
represented as a floating-point number.  It is another approximation
that has several more digits of precision than 22/7.
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Re: value of pi and 22/7

[Kee Nethery]

My favorite approximation is: 355/113  (visualize 113355 split into two 113 355 
and then do the division). The first 6 decimal places are the same.

3.141592920353982 = 355/113
vs
3.1415926535897931 

Kee Nethery



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Re: value of pi and 22/7

[Jeffrey Gaynor]

(pulls out doctorate in Math.) Take a circle and measure its diameter, then 
circumference (coffee cans and string are helpful). Then

pi = Circumference/diameter

approximating that is hard. It turns out that even though it *looks* like a 
nice fraction, the value that results is not (fractions of integers have the 
charming property that they always repeat, for instance 22/7 = 3.142857 142857 
142857 142857 142857... Pi does not. Again this was a very hard question only 
answered in the 18th century by Lambert, I do believe.)

It is the simple fractional look about pi vs. how hard it is to compute that 
drives most of the confusion about pi. The digits of pi are in effectively 
random order (each digit occur roughly 10% of the time), and to compute the nth 
one you need all the digits before it. Once upon a time (and maybe still) 
sending back and forth long strings of the digits of pi was a great way to test 
communications, since each side could look up the result in a table and tell if 
there were systematic errors. There are fun math questions, for instance, is 
there a run of a million 1's someplace in the decimal expansion of pi? Maybe 
so, but we just don't know, since we've only computed the first trillion or so 
digits. Computing pi also requires a lot of logistical organization too and 
cranking out the first several hundred million digits is still often used to 
test systems. 

FWIW my favorite approximation is 355/113. I can always seem to remember that 
one the best...

Jeff

- Original Message -
From: kracekumar ramaraju kracethekingma...@gmail.com
To: python-list@python.org
Sent: Thursday, March 17, 2011 11:46:25 AM
Subject: value of pi and 22/7


I tried the following 
 22/7.0 
3.1428571428571428 
 import math 
 math.pi 
3.1415926535897931 
 


Why is the difference is so much ?is pi =22/7 or something ? 
-- 
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kracekumar 

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Re: value of pi and 22/7

[Ian Kelly]

On Thu, Mar 17, 2011 at 11:36 AM, Jeffrey Gaynor jgay...@ncsa.uiuc.edu wrote:
 There are fun math questions, for instance, is there a run of a million 1's 
 someplace in the decimal expansion of pi? Maybe so, but we just don't know, 
 since we've only computed the first trillion or so digits.

Since pi is irrational I would be surprised if there isn't one
eventually.  Out of my own curiosity, do you know what the longest
known string of repeating digits in pi is?
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Re: value of pi and 22/7

[Jeffrey Gaynor]

There are a few long strings, but have fun yourself with the pi digit searcher:

http://www.angio.net/pi/bigpi.cgi

Longest string I heard of was nine 6's in a row, so search for 6 and 
see what you get.

- Original Message -
From: Ian Kelly ian.g.ke...@gmail.com
To: Jeffrey Gaynor jgay...@ncsa.uiuc.edu
Cc: python-list@python.org
Sent: Thursday, March 17, 2011 1:49:56 PM
Subject: Re: value of pi and 22/7

On Thu, Mar 17, 2011 at 11:36 AM, Jeffrey Gaynor jgay...@ncsa.uiuc.edu wrote:
 There are fun math questions, for instance, is there a run of a million 1's 
 someplace in the decimal expansion of pi? Maybe so, but we just don't know, 
 since we've only computed the first trillion or so digits.

Since pi is irrational I would be surprised if there isn't one
eventually.  Out of my own curiosity, do you know what the longest
known string of repeating digits in pi is?

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Re: value of pi and 22/7

[Rotwang]

On 17/03/2011 18:49, Ian Kelly wrote:

On Thu, Mar 17, 2011 at 11:36 AM, Jeffrey Gaynorjgay...@ncsa.uiuc.edu  wrote:

There are fun math questions, for instance, is there a run of a million 1's 
someplace in the decimal expansion of pi? Maybe so, but we just don't know, 
since we've only computed the first trillion or so digits.


Since pi is irrational I would be surprised if there isn't one
eventually.  Out of my own curiosity, do you know what the longest
known string of repeating digits in pi is?


Note that Liouville's constant, the number sum_{j = 1}^\infty 10^{-j!} 
is easily seen to be irrational (and is also transcendental), but no 
string of a million 1's, or any digit other than 0 and 1, appears in its 
decimal expansion. The relevant concept is that of a normal number, 
which is one whose digits look random:


http://en.wikipedia.org/wiki/Normal_number

Pi has not been proved to be normal but it is suspected on purely 
statistical grounds that it is, since almost all real numbers are normal 
(in the sense that the set of non-normal real numbers has Lebesgue 
measure 0).

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Re: value of pi and 22/7

[Erik Max Francis]

Jeffrey Gaynor wrote:
It is the simple fractional look about pi vs. how hard it is to compute that drives most 
of the confusion about pi. The digits of pi are in effectively random order (each digit occur 
roughly 10% of the time), ...


This is equivalent to stating that pi is normal, something which is 
widely suspected but has not yet been proven.


There are fun math questions, for instance, is there a run of a million 1's someplace in the 
decimal expansion of pi?


The answer is yes, if pi is normal.  Every finite sequence of digits 
will appear with the expected frequency.  In all bases.


--
Erik Max Francis  m...@alcyone.com  http://www.alcyone.com/max/
 San Jose, CA, USA  37 18 N 121 57 W  AIM/Y!M/Skype erikmaxfrancis
  They love too much that die for love.
   -- (an English proverb)
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Re: value of pi and 22/7

[Jabba Laci]

 My favorite approximation is: 355/113  (visualize 113355 split into two 113 
 355 and then do the division). The first 6 decimal places are the same.

 3.141592920353982 = 355/113
 vs
 3.1415926535897931

Another, rather funny, approximation of the first 15 digits of pi is
to take the length of the words in the following verse:

s = 
How I want a drink
alcoholic of course
After the heavy lectures
involving complex functions


print [len(w) for w in s.split()]

will produce:

[3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9]

Laszlo
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