Triangulars, Rectangulars, and Bible Prophecy

Some years ago (10-15 years back), on a sheer whim, I added up all the numbers 1 to 36, and found the total is 666 — perhaps the only number in Bible prophecy to gain pop culture status.

Why did I think there might be something to that? The backstory is that the ancient Sumerians and Babylonians used a number system based on 360, in turn based on the approximate number of days in a year. 360 happens to be very easy to work with mathematically, much more than 365/366. It is evenly divisible by 2, 3, 4, 5, 6, 8, and 9 — every single digit but the number 7 — as well as many common multi-digit numbers (10, 12, 15, …). A number system built on 360 has many practical uses in construction, science, astronomy, and probably astrology. It is because of the ancients’ use of 360 that today we have 360 degrees in a circle, 60 minutes in an hour, etc.

Trivia note #1: The number 360 happens to be the sum of 60 x 6. Those dimensions, 60 x 6, are the dimensions of the giant idol that Nebuchadnezzar created (Daniel 3:1). So in the book of Daniel we find one possible intersection with the Babylonian number 360 and its relation to the number 6.

Trivia note #2: The numbers 6 and 36 have intriguing relationships, which may very well have been known to the Babylonians. The number 36 is 6 × 6; add up 1 to 36, you get 666. Of course, we find 666 in the book of Revelation, which is the New Testament companion to the Old Testament book of Daniel. That was interesting, but I didn’t know what to make of it.

Seventh-day Adventists, and others, have traditionally looked to numbering systems (gematria) to find a value of a name that would equal 666. Notably, Uriah Smith used this method in the book Daniel and the Revelation, based on numbering a Latin title of the pope, “Vicarius Filii Dei.” This has become the traditional Adventist view. However, I was surprised when I learned that Ellen White, one of the founders of the Seventh-day Adventist Church, never wrote about the meaning of 666, even though she was a contemporary of Uriah Smith.

Because of the absence of information in Ellen White’s writings, which I believe to be inspired, I have tried to keep an open mind on this subject. Others have noted that the papal title in question seems to lack much support, while proponents of this theory have offered counter-evidence (see Wikipedia; a long article on Aloha.net; an article by Robert Correia; and examples of various other numbering systems that yield 666).

I recently purchased a book, Sacred Number, by Miranda Lundy. It’s part of a series produced by Wooden Books, which typically I’ve found inspiring because of my interest in art and mathematics. This particular volume contains lots of useful and interesting observations, if you don’t mind the discussion of pagan, occult, and new age beliefs. Although I didn’t find it as useful as the other books in the series, on the very last page there was a table of various number series. Along with Fibonacci, there were lists of triangulars, rectangulars, and many more. What caught my eye were the final numbers, the 36th numbers, in the triangular and rectangular number series: 666 (triangular of 36) and 1260 (rectangular of 36).

Obviously 666 and 1260 would stand out to anyone familiar with Bible prophecy, and the book of Revelation in particular.

Perhaps I’m going to disappoint you by telling you I still don’t know what significance, if any, this has. But if you are curious, there is a chart of how triangulars and rectangulars are calculated here. Basically with a triangular series, you are building a pyramid, and the triangular value of n is the number of building blocks in the pyramid when the base is n blocks wide. With a rectangular you are building a block where the height is always one block more than the width; the rectangular value of n is the number of blocks in the building, based on the base which is n blocks wide. I worked out the formulas myself (you ought to be proud, it took me a while), and here they are:

The triangular of n = n × (n + 1) ÷ 2

So in this case, the triangular of 36 is calculated as 36 × 37 (= 1332) ÷ 2 = 666. Oddly enough, 1332 is close to another prophetic number, 1335 (Daniel 12).

The rectangular of n = n × (n − 1)

Thus the rectangular of 36 is calculated as 36 × 35 = 1260. Note: Other sources define this series essentially as n = n × (n + 1). In that case, 1260 is the rectangular of 35, not 36.

So there you have it — no conclusions, but something to ponder on!

PS: One last trivia item: Computer systems using Base 36 (36 numerals, instead of 10) use the numbers 0 through 9, and then the letters A through Z. It just so happens that our standard numbers and alphabet have a total of 36 characters!

3 thoughts on “Triangulars, Rectangulars, and Bible Prophecy

  1. Interesting thoughts– something to ponder.

    By the way, your stylesheet is making the EM and STRONG or LABEL (not sure which) tags not show up in my browser (Firefox 3). The resulting text is the same color as the background.

    This not only affects text in the body of your post, but the “Name”, “Email” and “Website” in the “Leave a Reply” section at the bottom.

  2. A couple observations to add to the article: For every number in the rectangular series, there is a triangular that is exactly half the value of that number. So there is a direct correlation between the values, even though the physical diagrams of the structures look different.

    Also, on further investigation, another significant prophetic number is also related: 2300 (Daniel 8:14) is the tetrahedral of 23. A tetrahedral is basically a 3D pyramid. The formula for calculating a tetrahedral is: (n × (n + 1) × (n + 2)) ÷ 6. As with triangulars and rectangulars, you are calculating the total number of blocks — in this case, the number of blocks in the pyramid, based on “n” which is the number of levels in the pyramid (how many stories high it is). You can read more about it here: http://en.wikipedia.org/wiki/Tetrahedral_number. Each additional floor level of a tetrahedral is made of a number of blocks that equal the triangular of that floor level. (In other words, the base of a 3D pyramid *4* levels high contains *10* blocks; the triangular of *4* is *10*.) So there is a relationship between tetrahedrals and triangulars. The tetrahedral of “n” is the sum of all triangulars up through and including “n”.

    Also, 1335 (Daniel 12:12) is part of a series known as pentagonals; it is the pentagonal of 30. You can see a graph of pentagonal numbers here: http://library.thinkquest.org/.....ef1201.jpg. Pentagonals are much more complicated than all the other series I’ve discussed, so their significance is more of a stretch.

    If anyone else experiencing the problem with the text? I have not been able to duplicate it on my end, but I am looking into it.

  3. Since I haven’t followed the above post to any conclusion, some readers might be confused about my views. First, I fully believe that the time prophecies represent literal years, and I stand by the historical Adventist views of their start and end dates.

    Second, although there are apparent relationships between these numbers and various number series, it is also true that there are simpler (and biblical) ways to derive the same numbers. For example, the 1260 day prophecy (Revelation 11:3; 12:6) is the same as the “time, and times, and half a time” (Daniel 7:25; Revelation 12:14), and the “forty and two months” (Revelation 11:2; 13:5). This is easily shown once a person accepts that in ancient time a year was 360 days (not 365/366), and months were 30 days (not 28-31). From this, it is easily seen that 1260 days = 42 months (42 × 30 = 1260) = a year, two years, and half a year (360 + (360 × 2) + (360 ÷ 2) = 1260).

    Likewise, the 1335 day prophecy can be seen as the 1260 day prophecy plus exactly two and half months (30 + 30 + 15 = 75; 1260 + 75 = 1335). The 1290 (Daniel 12:11) is 1260 + one month (1260 + 30 = 1290). The seventy weeks of Daniel 9:24 can be computed the same way.

    What I am posing, very meekly, is that perhaps these numbers, rather than being arbitrary, reflect some kind of deeper math or symbolism. And apparently 666 fits into the same kind of patterns as the numbers well known to us as prophetic time periods.

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