Pi and the diameter and circumference of the molten sea in front of Solomon's temple

1 Kings 7:23 He made the molten sea of ten cubits from brim to brim, round in shape. Its height was five cubits; and a line of thirty cubits encircled it. (World English Bible, public domain)

The ratio of the circumference to the diameter of a circle is pi, an irrational number. The first few digits of pi are 3.14159. Taking 1 Kings 7:23 as a math text means that it is wrong about the dimensions of the molten sea, apparently reporting the ratio of the circumference to the diameter as three, or that the sea wasn't exactly round.

Answers in Genesis defends the accuracy of the bible on this point. Their defense, however, involves significant figures. But significant figures, according to this source, weren't considered until long after the temple was built. Or, the article from Answers in Genesis says, perhaps the circumference was thirty cubits, measuring the circle formed by the water in the molten sea, but not the container itself, inside the metal container, whereas the diameter was measured across the outside of the construction, including the container. 

It seems, however, that the description of the building of the temple wasn't meant to give directions, or exact sizes. There are no detailed directions for other parts of the temple, just brief general descriptions. (Lest there be any doubt, the illustration at the top of this post is an artist's conception, and may differ significantly from the original Temple's design.)

Consider these verses:

1 Kings 7:15 For he fashioned the two pillars of bronze, eighteen cubits high apiece; and a line of twelve cubits encircled either of them. 16 He made two capitals of molten bronze, to set on the tops of the pillars. The height of the one capital was five cubits, and the height of the other capital was five cubits. 17 There were nets of checker work, and wreaths of chain work, for the capitals which were on the top of the pillars; seven for the one capital, and seven for the other capital. 18 So he made the pillars; and there were two rows around on the one network, to cover the capitals that were on the top of the pillars: and he did so for the other capital. 19 The capitals that were on the top of the pillars in the porch were of lily work, four cubits. 20 There were capitals above also on the two pillars, close by the belly which was beside the network. There were two hundred pomegranates in rows around the other capital.

The Bible doesn't tell us what a net of checker work, or wreaths of chain work, were like, or what lily work might mean. What kind of lilies? Lily buds, flowers, leaves, or the entire above-ground shoot? What was a "capital" like? It seems likely that the ten cubits and thirty cubits in verse 23 were the same sort of description -- "you see, it was about thirty cubits around, and about ten cubits across." There's no valid reason to accuse the Bible of error on this point, or to defend descriptions from pre-Christian Jewish culture by using recent measuring practices.

The Bible is not a math text, or a detailed blueprint for temple construction. It does tell us that God expected and valued good workmanship, and provided a beautiful, well-constructed place for worship for the Israelites.

Thanks for reading.

Sunspots 514

Things I have recently spotted that may be of interest to

someone else:

Christianity (and Mathematics): He Lives has addressed the question, posed by some, about 1 Kings 7:23, which implies that the Israelites thought that the circumference of a circle was 3 times its diameter, not pi (3.14159...) times its diameter.
Computing: Gizmo's Freeware gives an annotated list of 18 free Android games that have been downloaded more than 100 million times each.
Education: Relevant reports on a study that says that US Millennials "aren't very skilled."
First Things has a short essay on why studying the humanities in college is important, and how university officials, who say that, aren't really being specific enough.
 
History: King Richard III of England is to be re-buried. He died in 1485. Read more at the History Blog.
Humor: "The 50 Funniest Puns in the History of Funny Puns." Sample: A plateau is the highest form of flattery. Thanks to a niece for drawing my attention to this web site.


Image source (public domain)

Pi day - on the ratios of similar shapes

Today, March 14, or 3/14, is celebrated by some, especially by schoolteachers, as pi day. The reason is that 3.14 is an approximation for pi. Why isn't 3.14 pi?

Pi is the ratio between the circumference, the distance around, and the diameter, the distance across, of a circle.

Let's consider a seemingly unrelated topic. Suppose you think about someone you are very familiar with, someone you have seen many times in current photos. Perhaps yourself, perhaps someone else. Can you recognize that person in a small photo, as well as a large one? Of course, unless the photo is so small that you can't make out details at all. Why is that so? The photos are different, yet they are all of the same person, and they are similar. Similar in what way? Several ways, such as eye color, perhaps, but they are similar in many ratios. The distance between that person's eyes, in the photos, has the same ratio to the distance from one corner of the mouth to the other, in every photo. The distance from one corner of the left eye to the tip of the nose has the same ratio to the distance from one corner of the right eye to the tip of the nose, in every photograph. You haven't measured these distances, or calculated the ratios, but if these, and many other ratios, weren't the same in each photograph, you would start to think that some of the photographs weren't of the same person. (For a person's face, we need to allow some leeway for whether they are smiling, the angle that the photo was taken from, and the like, but the ratios need to be close to the same, or the same, for the photo to look natural.)

One more example. Consider squares. Are all squares the same size? No, of course not. But all squares have some ratios that are identical, or they wouldn't be squares. Most obviously, the ratio between any one side of a square, and any other side, is 1. The sides are all identical. Another ratio of all squares is the ratio between any side and the distance from one corner to the opposite corner. That ratio can be determined by the Pythagorean Theorem, which tells us that the sum of the squares of the shorter sides of a right triangle is equal to the square of the hypotenuse, the longest side. From that, the ratio of the distance across a square, from one corner to an opposite corner, to a side of that square, is equal to the square root of 2. Always, for all squares.

So a person's picture always has the same ratios, or nearly so, between dimensions. A square always has exactly the same ratios between various dimensions. Circles, too, are all similar, regardless of size, meaning that the ratios of their dimensions are the same. What ratio? What dimension? The ratio between the distance around any circle, the circumference, to the distance across the circle, through the center, which is the diameter, is always the same. And that ratio is pi.

It so happens that pi (and also the square root of 2) are irrational numbers. That is, even though they are ratios, they cannot be exactly expressed as ratios between whole numbers. Pi is nearly 22/7, but not exactly. Pi is nearly 3 and 14/100, but not exactly.

For much more on pi, see the Wikipedia article.