Why Pi = 3.141 .. instead of 3.144?

Pi is vaguely described as "(perfect) circle's circumference to its diameter".

sqrt(16/(lim_(n->infinity) F_(n+1)/F_n)) = sqrt(16/((sqrt(5)+1)/2)) = 4/sqrt(phi) = approx
3.1446055110296931442782343433718357180924882313508929506596 ..
It is based on the fundamental Fibonacci sequence (the F there is Fibonacci number).

Why do we nowdays still use the Pi's arithmetic value 3.141... instead of the "more natural" Pi value 3.144... even the ancient egyptians used and which does fulfill the description of (perfect) circles circumference to its diameter?

Proof:



"From here things begin to get really interesting . As can be seen, BC above is equal to one half the length of the pyramid's side. Therefore, the perimeter of the base equals BC x 8, and in relative terms this equals 0.618034 x 8 = 4.9443. The relative height of the pyramid is 0.78615, and, if one uses this length as the radius of a circle, then the circumference (perimeter) of that circle will also be 4.9443. Also, perhaps more important factor, is that the length of side OD (0.78615), when multiplied by 4 yields an amount (3.1446) that is almost exactly equal to Pi (3.1416). This finding means that the 38010' right triangle offers a unique and most interesting point of intersection between the Pi ratio and the golden ratio phenomenon. How this unexpected agreement comes to be is that :
As we saw in the 38010' right triangle, 0.618034 ÷ 0.78615 = 0.78615. This means, that 0.618034 = 0.78615 x 0.78615. Therefore, 8 x 0.618034 is the same as 8 x 0.78615 x 0.78615;
As we also saw, 4 x 0.78615 is a very close approximation for Pi . Therefore,2*Pi can be said to equal 8 x .78615. For the circumference of the circle using 0.78615 as its radius, we then have C =2*Pi*R = (8 x 0.78615) x 0.78615 .As a result, the Great Pyramid turns out to have the same perimeter length when measured in a horizontal plane, as a square, and in a vertical plane, as a circle. " [1]

There are several rumours that even nasa didn't use the ordinary Pi value in some of their lunar missions. Why?

You can solve the maths yourself: 4- 4sin²x = cos x , 0

This is quite interesting. I followed your logic, but perhaps more background information is necessary. Is the formula derived from the pyramid or applied to it?

OMG, your bringing back so many frustrating nightmarish periods in my maths class! I'm really struggling to follow this, which I personally find amusing. I actually passed 1st year engineering maths in uni (13 years ago) which to this day, I have no idea how I did it. It goes to show that if you don't exercise your brain everyday, it turns all flabby and squishy. Brains need abs too!

I hope some youngun's read this, please, don't give up when things get hard. Don't 'coast' and take the easy way. You will live to regret it one day. I wish I gave my brain the respect it deserved, that I now cant even follow a discussion about 3.14 without going insane.

Wow,something I didn't know.
I only remember using 3.14 in all our equations in math.
Of course,we where solving mathematical equations based in electronic theory,so I guess it didn't matter.
That was good enough for me!

I wasn't able to upload this here... Maybe someone else could?

What ever happened to the fractional 22/7 equivalent of PI?
(FYI 22/7 = 3.142857142857143)

reply to post by JackTheTripper



picpaste.com...

reply to post by abecedarian
22 over 7 or 22 divided by 7 is the way to go enter that in to your cal, pda, or i phone, don't for get the "app for that" then do the other math

Originally posted by JackTheTripper
Pi is vaguely described as "(perfect) circle's circumference to its diameter".
....

You mean, Pi is described as the ratio between a circle's circumference and its diameter, correct?
A circle is a "perfect" ellipse (a.k.a. oval), where both foci are the same point in space.

It's 3.141... because that's the length of a circle with radius 0.5 in base10. There's not much more to explain than that. If it was 3.144 the radius would be slighter larger than 0.5 and wouldn't be as easy to work with.

reply to post by abecedarian


Right. Cannot edit the original post anymore. Anyway, even the arithmetic value 3.144... fulfills the description. Why do we use the 3.141 instead? Fractional 22/7 is good for fractions and other stuff depending of the accurancy required. But am I completely wrong with this thread? Has anyone tried to circle the square?

It seems that Pi is 3.141592... because we care more about accuracy now than they did way back when.
3.144 was good enough then, and in general is now, but times have changed.
When one is laying bricks around a fountain, there's room for "fudge".

22/7

355/113

52518/16717


But the actual exact formula for pi is

Pi = 4 -4/3 +4/5 -4/7 +4/9 -4/11 ...

infinite number of odd fractions

Originally posted by this_is_who_we_are

But I see the old Pi in the pyramid
is still around turning early French Archaeologists
into obsesed recreationists who are "certain" that
the Ancient Egyptians must have had differential equations.













Trundle



The Ancient Egyptians may have had a trundle.
If the pyramid is 100 cubits tall, then yes pi will
appear in the ratio of height to base because the trundle
was used to measure out the lengths of the sides.

This presuposes that the Egyptian trundle was one cubit in diameter.


David Grouchy

Originally posted by circlemaker
It's 3.141... because that's the length of a circle with radius 0.5 in base10. There's not much more to explain than that. If it was 3.144 the radius would be slighter larger than 0.5 and wouldn't be as easy to work with.

How it would not be as easy to work with?

Originally posted by davidgrouchy
...

This presuposes that the Egyptian trundle was one cubit in diameter.

David Grouchy

edit on 29-10-2011 by davidgrouchy because: (no reason given)

Presuppose being the origination of "presumption", which is an assumption, and we all know what "assume" means.

Originally posted by JackTheTripper

Originally posted by circlemaker
It's 3.141... because that's the length of a circle with radius 0.5 in base10. There's not much more to explain than that. If it was 3.144 the radius would be slighter larger than 0.5 and wouldn't be as easy to work with.

How it would not be as easy to work with?

edit on 29-10-2011 by JackTheTripper because: (no reason given)

Sure you could have a circle with a circumference of 3.144, but that's relative to it's diameter, radius, area, and other things.

With pi the diameter is 1, with 3.144 it would be 1.000766282161838...

Originally posted by davidgrouchy

But the actual exact formula for pi is

Pi = 4 -4/3 +4/5 -4/7 +4/9 -4/11 ...

infinite number of odd fractions

W H Y ?
Why and who have made this pact the pi must be calculated like that - which is not any way related to nature (as fibonacci sequence and golden ratio and hence the pi value of 3.1446... are)?

Originally posted by circlemaker

Sure you could have a circle with a circumference of 3.144, but that's relative to it's diameter, radius, area, and other things.

With pi the diameter is 1, with 3.144 it would be 1.000766282161838...

Can you then tell me what's wrong in this image:


.78615 * 4 = 3.1446

c=πd
or
c/d=π

If the result for π is not correct, then the measurement of c (circumference) and/or d (diameter) is not accurate.

Originally posted by JackTheTripper

Originally posted by davidgrouchy

But the actual exact formula for pi is

Pi = 4 -4/3 +4/5 -4/7 +4/9 -4/11 ...

infinite number of odd fractions

W H Y ?
Why and who have made this pact the pi must be calculated like that - which is not any way related to nature (as fibonacci sequence and golden ratio and hence the pi value of 3.1446... are)?

Why and who?

Nature and she insists.
If an axel is even the faintest bit oval instead of perfectly circular,
it has friction and may even get stuck in the first quarter turn if too oval.

In other words, circles are not natural.

And a perfect circle as defined by the
rigorous methods of geometry allows for
a very precise measurement of the
exact diameter or circumference
and the immutable ratio between them.

Pi defines circle, not something from nature.


David Grouchy