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in 1 Kings 7:23-26, God describes a cauldron as being "round all about", however this cannot be the case, as in the extract:

"And he made a molten sea [cauldron], 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"

the cauldron is described to have a diameter of 5 cubits and a circumference of 30 cubits. 30/10=3, and pi=/=3 thus the cauldron cannot have been "round all about" as God described in the verse. My question is, why would God describe the cauldron as "round all about" if it is not, and why did God not take this verse of a cauldron as an opportunity to miraculously give the value of Pi?

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  • The diameter of 10 cubits is given from one edge of the brim to the other. The question assumes that the circumference is also measured at the brim, or that the side is perfectly vertical, when it could be easily bowl shaped (ie convex), and the circumference measured at the widest part. The alternate word given in your quote, ie "cauldron" would also imply that shape to me.
    – Bork Blatt
    Commented Jul 3, 2019 at 16:20
  • The C of the cauldron(widest part) must be>the C of the brim. Because the circle of the brim is inside the circle of the cauldron. Where the cauldron C has to > 31.4.... But since 30 cubits is given as the cauldron’s C, this suggests that biblical pi<3. I also do not see how a bowl shape makes a difference.
    – Ubaid Hassan
    Commented Jul 3, 2019 at 17:50
  • Everybody keeps saying "God's description," but I Kings is a history kept by people, not written by God, Himself. It's a nice idea that God's word would never be inaccurately scribed, but were that true, the Synoptic Gospels would record all of Christ's statements in the same way (they don't). I suspect this is nothing more than a case of round numbers written down by the scribe rather than God not knowing the geometry of a sphere, and that assumes the phrase "round all about" is even applicable in three dimensions. AKA, a tempest in a caul... I mean, tea pot.
    – JBH
    Commented Jul 4, 2019 at 0:43
  • I’d like to see a picture of what you imagine it’s saying it looked like.
    – Nihil Sine Deo
    Commented Jul 4, 2019 at 4:55
  • @autodidact static.thenounproject.com/png/405108-200.png
    – Hisham
    Commented Jul 4, 2019 at 13:35

4 Answers 4

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The Scripture writer was following common practice rules of significant digits. 30 and 5 have one significant digit, so that solution must be given in one significant digit: 3.

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  • Well put. And that is all that needs to be said, in my own view.
    – Nigel J
    Commented Jul 4, 2019 at 2:51
  • And while the idea of significant digits was a bit tongue in cheek, the point stands that precision wasn't exactly a concern of the author, and likely not a concern of the measurer either.
    – Thomas Markov
    Commented Jul 4, 2019 at 13:03
  • The rim would have been measured by a line put around it and the line estimated against a measuring stick. The rim may well have not been exactly circular. The exact value of pi is irrelevant.
    – Nigel J
    Commented Jul 4, 2019 at 14:09
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There are about three things that this very famous passage, 1 Kings 7 implies about the temple's large laver.

1. Shape.

First note that the vessel was 10 cubits across and 5 cubits deep - this it was (in modern terms) hemispherical. This may explain the comment, "round all round" not simply circular, but this is not essential. In any case, the top rim was circular. More likely, the shape was approximately cylindrical, and 5 cubits deep.

2. Precision

Ancient measurements of length were nowhere near as accurate as modern ones. Errors of a few percent were common. If our modern ratio of "pi" (= 3.1415926535 …) were approximated by just 3, then this represents an error of less than 5% - a lot even for the ancients. However, as shown below, such an error is not even necessary to assume.

3. Which Circumference?

The large bronze basin would have had a finite thickness of many inches. Just how thick is suggested in the same text as about one hand breadth (1 Kings 7:26), that is about 3 to 4 inches thick.

Now, let us suppose (for the present discussion) that a cubit is approximately 18 inches in length (whether a little more or less does not alter the argument below). If we assume that 10 cubits (180 inches) was the outside diameter and 30 cubits (15 feet = 540 inches) was the inside circumference (as would be expected from using a straight edge), then this would represent a thickness of just 4 inches!!

Thus, I see no problem here at all.

APPENDIX - Volume

If we assume, as is more likely, that the ancient cubit was closer to 19.5 inches (= 0.5 meters), then we get some very interesting results for the volume of the water contained by the large laver. For a cylindrical laver, the internal volume works out to be about 44,000 liters or about 2000 Hebrew baths as per v26. This confirms the other measurement in v26 and also confirms that the 30 cubits is the inside measurement of the circumference and thus, 10 cubits was the outer diameter.

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God's description would seem to suggest that it was in the shape of a sphere and not a flat circular object, or a bowl shaped object. The fact that it is a cauldron itself dictates a spherical object capable of holding molten material. A sphere is also more able to distribute heat to its contents.

Any cauldron of those dimensions would almost certainly require the maximum in heat transference.

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The Cubit

The Cubit - From Encyclopedia Britannica
The cubit was based on the length of the arm from the elbow to the tip of the middle finger and was considered the equivalent of 6 palms or 2 spans.

Ancient Egyptian units of measurement - From wikipedia.org
The ancient Egyptian units of measurement are those used by the dynasties of ancient Egypt prior to its incorporation in the Roman Empire and general adoption of Roman, Greek, and Byzantine units of measurement. The units of length seem to have originally been anthropic, based on various parts of the human body, although these were standardized using cubit rods, strands of rope, and official measures maintained at some temples.

... and a line of thirty cubits did compass it round about

30 Sides Makes a Triacontagon

Using the Polygon Calculator entering 30 for (n) number of sides and circumradius of 5 results:

  • n = 30 number of sides
  • a = 1.0452846326765 side length
  • r = 4.9726094768414 inradius (apothem)
  • R = 5 circumradius
  • A = 77.96688405666 area
  • P = 31.358538980296 perimeter
  • x = 168 ° interior angle
  • y = 12 ° exterior angle

Ancient Egyptian royal cubit - From wikipedia.org
These cubit rods range from 523.5 to 529.2 mm (20.61 to 20.83 in)

Measuring the Difference
Using the larger measurement of 529.2 mm with the calculated side length of 1.0452846326765

529.2 (Royal Cubit) X 1.0452846326765 (Calculated Side Length) = 533.1646276124038 mm

533.1646276124038 (Side Length Measure in mm) - 529.2 (Royal Cubit) = 23.9646276124038 mm

Converting mm to inches
Makes 0.9434892760788897714 of an inch.

Conclusion

The measurement occurred by placing each of the 30 measuring rods on top of the bronze. Making thirty cubits when measuring its circumference.

If anyone feel the need to figure out the width of the measuring rod, go for it because my math time is over.

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