Many people reading through the bible having some math
background will often stumble across the 1 Kings 7:23-26
verse set and then claim, "they thought 'pi' is 3.0 in
the bible, but we know that 'pi' is 3.14159265...".
Why would they say this?
To start with, the 1 Kings 7:23-26 verse is describing
a fairly large bowl about 8 feet 4 inches tall sitting
on top of some other fairly large items. The bowl is described
initially by 3 measurements, 2 of which at first glance
seem to be redundant. A 4th dimension is also given
a couple of verses later and this one people often ignore
while instead only focusing on 2 of the 4 given dimensions.
Since "pi" is defined as the "circumference/diameter"
for a circle, the value of "pi" becomes:
pi = circumference/diameter
= 3.14159265...
and when they see the bible give a "compassed it round
about" (circumference) value of 30 and "from the one
brim to the other" (diameter) value of 10, it keys them
to think, "the bible says 'pi' = 30/10 or 3.0, therefore
the bible is saying the Hebrews were very inaccurate as
they'd have to have missed another 1.4 cubits in the
circumference.".
But does the bible claim this?
No.
The bible claims that there is an ADDED brim that is a
"hand width" thick that was added onto the cast metal
bowl. That brim is WIDER than the original bowl.
So let's review the data the bible gives about that bowl:
1. Diameter of the brim to brim edges (10 cubits)
2. Height of the bowl (5 cubits)
3. Circumference of the body of the bowl (30 cubits).
4. Thickness of the brim (one hand width, about 4.5").
(Note: a cubit is 18" to 22" in length)
From these four dimensions the bowl can now be rendered:
As you can plainly see, all FOUR listed dimensions are
EASILY rendered and match the given description.
Now remember, they were writing this some 3000 years
ago and giving those FOUR dimensions to the people
constructing the bowl.
So where are the FOUR dimensions in the bible?
Watch where these show up in the verses.
1. Diameter of the brim to brim edges (10 cubits)
2. Height of the bowl (5 cubits)
3. Circumference of the body of the bowl (30 cubits).
4. Thickness of the brim (one hand width, about 4.5").
1Ki 7:23 And he made a molten sea,
(A "molten sea" is a cast metal bowl filled with water)
(1) >> ten cubits from the one brim to the other:
it was round all about, and his
(2) >> height was five cubits: and a line of
(3) >> thirty cubits did compass it round about.
24 And under the brim of it round about there were
knops compassing it, ten in a cubit, compassing
the sea round about: the knops were cast in two
rows, when it was cast.
25 It stood upon twelve oxen, three looking toward
the north, and three looking toward the west, and
three looking toward the south, and three looking
toward the east: and the sea was set above upon
them, and all their hinder parts were inward.
(4) >> 26 And it was an hand breadth thick, and the brim
thereof was wrought like the brim of a cup...
Notice that #2 and #3 are said right after the brim to
brim value (#1). If you assume that #3 is the circumference
value for the brim, then you also have to assume that
#2 says the brim is 5 cubits high. But as you see in #4,
it's saying the brim is shaped like the brim of a cup.
Hence, #2 and #3 can't be about the brim since it would
say that the brim is 5 cubits tall, hence shaped like
a cylinder... so the values for #2 and #3 have to be
a continuance of the discussion about the bowl body, not
about the brim.
The brim was only briefly mentioned in #1 as being an
attribute of the bowl, not that the brim would be
30 in circumference or 5 tall... the bowl body was.
Further confirmation is that the brim is said to have
knops placed UNDER it, the handwidth thick brim allowing
room for the knops.
The 30 cubit value for the inner bowl body circumference,
that would be measured while making the inner mold used
to cast the metal bowl.
Let's see how accurate they got "pi" using my "handwidth"
in the calculation and 20"/cubit.
Brim to brim diameter = 10 cubits
= 10 cubits * 20"/cubit
= 200"
Bowl body circ = 30 cubits
= 30 cubits * 20"/cubit
= 600"
Brim thickness as a = 4.5"
"handwidth"
To find the bowl body diameter, just subtract the two brim
thicknesses from the brim to brim diameter:
Bowl body diameter = 10 cubits - (2 * 4.5")
= (10 cubits * 20"/cubit) - 9"
= 200" - 9"
= 191"
Now let's see what the Hebrews had for a value for "pi"
using the bowl body circumference and bowl body diameter:
pi = circ / dia
= 600" / 191"
= 3.14136
The actual value of pi goes on for forever, but basically
you can use 3.14159 for most math problems. The error
in the Hebrew "value of pi" becomes:
3.14136 - 3.14159
pi error = ----------------- * 100%
3.14159
= - 0.0073 %
This result is based on an estimated average value for
the "cubit". And given the wide variation expected, I'll
now show what the typical error expected would be for
the bible "pi". To do so, I'll now also use my own "cubit"
in the calculations:
My "cubit" = 19.25"
My "handwidth" = 4.5"
pi = circ / dia
= 30*19.25"/(10*19.25"-2*4.5")
= 577.5"/183.5"
= 3.1471
3.1471 - 3.14159
pi error = ----------------- * 100%
3.14159
= + 0.175 %
That's reasonably close and it's using actual known
values for one person's "cubit" and "handwidth".
Something else to notice is that the error in pi tends
to remain at about that level or near it. You can quickly
see this by defining a constant "k" such that:
k = h/c
This given:
h = One person's handwidth: place the thumb against
the hand and measure along the thumb to the
opposite side of the hand where both are
parallel for about an inch, the hand placed
flat on a table top.
c = One person's cubit: measure from the tip of
the middle finger to the elbow, the arm laying
flat on a table top.
For my own cubit and handwidth, k = 0.234.
To then find the approximate value of 'pi':
"pi" = 30*c/(10*c - 2*h)
Substituting for h:
"pi" = 30*c/(10*c - 2*k*c)
= 30*c/[(10 - 2*k)*c]
"pi" = 30/(10 - 2*k)
As you can see, the approximate value of "pi" only depends
on the physical constant "k". "k" being pretty much the
same value between human beings, the value of "pi" calculated
then ends up at about 3.147, about 0.2% off from the true
value of "pi".
Given that "k" is roughly constant between human beings
and over time, this says the error in building the bowl
remains at about 0.2%, not bad for people building a
large bowl about 3000 years ago.
The bible is right and does NOT say pi=3.0, but instead
shows FOUR different dimensions used to build a commonly
shaped bowl.
God made it all, Jesus died for our sins.
Note: The above information was written by John P. Boatwright and is freely given. The information is simply my opinion based on how I perceive the content discussed. Anyone reading such should use their own judgement as to whether or not the information has any value to them. You may copy portions of the above opinions as long as a reference to this page is included and no text within said portion is altered. If copied to another medium other than the internet, include the entire text. The above content may change over time.
Best wishes.