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This is an old revision of this page, as edited by Fuzzypeg (talk | contribs) at 12:34, 25 June 2006 (→Proposal to split ''pentacle'' into a separate article). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

There is an error in the formula shown for "sin of 18 degrees". It currently shows "(sqrt(5)-1)/2" but the correct formula is "(sqrt(5)-1)/4". The formulas based on the golden ratio are correct. The correct formula can be found on Exact_trigonometric_constants. -- Phil Howard

I should also add that I don't know enough of the LaTex language to feel comfortable with editing formulas. I'm just barely a newbie at editing any wiki pages. -- Phil Howard

I've made this correction. I haven't myself checked the maths, so if this is in fact wrong could someone correct me please? Fuzzypeg☻ 05:52, 22 June 2006 (UTC)[reply]

Music Pentagram ?

Nice work on this article, folks. -- Zoe

what is the difference between a pentagram and a pentangle? -- Tarquin 09:27 Mar 20, 2003 (UTC)

As reply to question: no, the HTML entities does not include correctly accentuated Greek letters, and cannot be used for serious Greek wordings. The Greek HTML entities seem to be a (very) inferior subset aimed at inclusion in mathematic formulas. --Jörgen Nixdorf

Is it just me, or is the pentagram depicted in the article to illustrate the geometry and the ratio really not a perfect pentagram? -- till we *) 15:21 21 Jul 2003 (UTC)

You're right, it was just a quick illustration. Feel free to improve it. -- Nixdorf 08:24 22 Jul 2003 (UTC)


What follows is the "new" opening paragraph twice inserted by User:192.211.25.53. There's an obvious POV issue here, but good points and information, too; perhaps a part of it could be incorporated into the article.

  • A pentagram is a mathematical shape joining the points of a pentagon to form a five-pointed star.There is nothing good or evil about this mathematical symbol. It is ignorance and the desire to control of the Roman Church and others that have clouded this symbol with so much false evil. Pentagrams have been in art and sculpture throughout history to this day. The American Flag has fifty of them, each representing a State in the Union. Great Cathedrals have pentagrams designed in their walls, in spite of the false claims of the Church that they are evil. The Pentagram represents the feminine. The human woman having 5 extremities.

Sara 09:31, 10 Feb 2004 (UTC)


By the way, I believe there is a difference between pentagram, pentangle, and pentacle. Pentangle is another word for pentagon. I'm hazier about pentacle; I believe the word is used by Pagans as a synonym for pentagram, but I think it is also used to refer to one of the magickal tools, consisting of a disc with a pentagram and other symbols carved or painted on it.

Actually, in Pagan terms the Pentagram is the symbol, and the pentacle is usually the inscribed or physical form of the Pentagram. So you draw a pentagram, and a pentagram drawn on an altar tile or made into a necklace is a pentacle. -Persipone

Pentagram vs. Pentacle

24.63.34.198 seems to believe that the pentagram has a circle and a pentacle does not. Since they failed to cite any evidence of this and randomly edited the page, I decided to ask for debate since they did not.

Which is encompassed by a Circle? Pentagram or Pentacle?

According to Religious Tolerance it is the Pentacle. --Morningstar2651 03:59, Apr 4, 2005 (UTC)

According to this site, the circle is not what denotes the difference, but rather whether the object is 2D or 3D. --Taliesin84 08:41, 10 October 2005 (UTC)[reply]

More on pentacle vs pentagram

Here was something I had put in under an article about pentacle:

"Pantacle or Pentacle An amulet, talisman, a geometrical figure so used. There is much confusion as to the derivation of this word, but it seems most likely that it comes through Italian and French from the root pend- "to hang," and so is equivalent to a pendant or charm hung about the neck. From the fact that one form of pentacle was the pentagram or star-pentagon, the word itself has been connected with the Greek pente (five). The word is used specially in The Secret Doctrine to denote the pentagram or pentalpha. The Solomon's seal is another pentacle, and there are many others, including the sigils of the seven planets." [1]

I believe this should be put back in, but I won't do it myself unless there is consensus on it . . . It answers the question as to why certain groups have "pentacles" that do not have a five pointed star on them. Vidkun 19:20, 3 October 2005 (UTC)[reply]

Wholeheartedly agree here. It's become very common to refer to "pentagrams in circles" as pentacles for quite some time now, and if it's as untrue as it seems, best to make that clear.

--Taliesin84 11:34, 19 October 2005 (UTC)[reply]

Ant made a few minor changes that cleared up a POV issue in what I added. I would like to note that when I first looked into this article, it was because of a redirect from pentacle, which originally had its own page. Given that numerous groups in the magical and NeoPagan/NeoWiccan/Wiccan communities use pentacles with various designs on them, and that historically (as in the case of John Dee and Edward Kelly) this is also seen as the case (that pentacle referred to a disc, not nec. with a pentagram on it), I would almost consider having a seperate page for pentacle again. For example, pentagrams in NeoPagan/NeoWiccan/Wiccan use refer to the five elements, but pentacles are seen as an earth aligned tool.--Vidkun 16:04, 19 October 2005 (UTC)[reply]
I'll also note that the Latin word used describing this tool, pentaculum, would not refer to five, as the Latin root for five is quinqu- see the article on Numerical_prefix and the article on Diminutive under Latin. -pend- is the Latin root for to hang as in suspend, pendulum, appendix. Popular usage does not make proper language; see, for example, 2000 vs 2001 as first year of 21st century. Pentacle and pentagram are not from the same language root.--Vidkun 16:09, 19 October 2005 (UTC)[reply]

And now I am REALLY on the tear about this one, because while Ant wants to cite sources showing the etymology to be a Latin-Greek hybrid, with an Italian descendant being pentacolo (five cornered), there is usage as early as 1600 showing a pentacle to be made WITHOUT a five pointed star. The Heptameron of Peter Abano. --Vidkun 17:18, 2 November 2005 (UTC)[reply]

According to "Tilings and Patterns" by Grumbaum and Shepard, a pentagon is the polugon produced by the path of lines commonly seen in a pentagram while a pentacle is a star, it is the pentagram with all the inner lines removed, it is the extremity of a pentagram. Neither are surrounded by a circle. --206.191.28.13 05:47, 9 February 2006 (UTC)[reply]

I'm not quite clear on what you mean. Are you saying -
  • = pentagon
  • = pentagram
  • = pentacle?
Could you quote the exact text from Greunbaum and Shephard? I certainly think that a mathematical definition should take precedence here. - AdelaMae (talk - contribs) 06:16, 9 February 2006 (UTC)[reply]
Basically yes but your vertices there are look a little messed up, just take your pentagram and erase the inner line segements and you'll have a pentacle according to Grumbaum and Shepard. I suspect that the pentacle is just a concave decagon which has angles of 36 degrees for the points and 108 for the inner vertices. I don't have the text with me right now but I'll add it later. It is the authoritative and seminal work on tilings and patterns so it does hold a good deal of legitimacy. --129.97.140.126 15:43, 6 March 2006 (UTC)[reply]
Except that those authors weren't the first to use the word pentacle. pentacle and pentagram are not linguistically related at all.--Vidkun 17:16, 6 March 2006 (UTC)[reply]

I've never heard any mathematical definition for pentacle. I agree on the first two pentagon/pentagram. I can only call the as a special case of a concave decagon. Tom Ruen 06:45, 9 February 2006 (UTC)[reply]

I'm surprised that no-one here seems to know 'pentacle' or ' pantacle' in the sense used in Solomonic magic. It is an amulet, generally made of parchment or paper (although it can be of other materials), on which the symbol of a spirit being evoked is drawn. It is often worn around the neck, or placed in the triangle of evocation. Protective symbols can also be included (sometimes on the reverse), a common one being the five-point seal of solomon (perhaps this is where the "penta-" comes from?). So, for example, a slip of paper with a Goetic demon's sigil on it is a pentacle. This usage of the term pentacle is expanded to include all papers, tablets or discs marked with sigils for the purpose of evoking certain energies or beings. I suspect that this was once a more commonly understood meaning amongst magicians than any of the meanings given in this article. I need to do a bit more research though... 60.234.107.84 11:26, 10 February 2006 (UTC) -- (Funny old Wikipedia, losing my session info. This is Fuzzypeg 11:29, 10 February 2006 (UTC))[reply]
Fuzzypeg, check this section out in the first section of the article: "Some sources assert that pentacle derives from the French root pend- to hang (compare pendant) and means some sort of physical object such as an amulet; this explains why some groups use pentacles that do not have pentagrams inscribed upon them, as attested in the Theosophical Society's Encyclopedic Theosophical Glossary[1] But some dictionaries give the etymology as from Italian pentacolo or Medieval Latin pentaculum, ultimately from Greek pente. However, there is Latin usage as early as 1600 showing that a pentacle or pentaculum need not have a five pointed star on it.[2] See also Man, Myth & Magic vol. 77. Richard Cavendish, ed. Purnell for BPC Publishing Ltd., London: 1971. p. 2159."--Vidkun 15:17, 10 February 2006 (UTC)[reply]

Proposal to split pentacle into a separate article

Following on from the discussion above, I would like to split pentacle back out into its own article, since its meaning and usage are, I believe, quite different from pentagram. I found the following in Francis Barrett's Magus (Book 2, part 2):

We now proceed to speak of the holy and sacred Pentacles and Seals. For these pentacles are certain holy signs and characters, preserving us from evil chances and events, helping and assisting us to bind, exterminate, and drive away evil spirits, alluring the good spirits, and reconciling them to us. These pentacles consist either of characters of good spirits of the superior order, or of sacred pictures of holy letters or revelations, with apt and proper versicles, which are composed either of geometrical figures and holy names of God, according to the course and manner of many of them, or they are compounded of all of them, or many of them mixed.

I also found some discussion of magic squares (such as the Sator-Arepo-Tenet square) being used as pentacles in Mathers' introduction to Abramelin. This all fits my understanding of pentacle, and the way I was taught. If needed, I should be able to find more supporting evidence by, say, googling pentacle site:athenaeum.asiya.org, however the two examples already given are from highly authoritative and influential sources in Western magic. It seems that the pentacle salomonis (i.e. the 5-point star of Solomon) is a common form for a pentacle, but of course not the only form. I suspect that discussions about the exact shape that a pentacle should be (as a 5-point star), or whether it should be flat or 3-dimensional etc. are beside the point. These are more recent innovations by various people, and it's not surprising there isn't widespread agreement on them. (The concept of coin/pentacle from various tarot decks is however a widespread usage.) Any comments? Fuzzypeg 22:43, 6 March 2006 (UTC)[reply]

I like the idea, but it just might get thrown back into this article, because I am not sure how much we can put about pentacle which would keep it from being only a stub.--Vidkun 23:15, 6 March 2006 (UTC)[reply]

I'll see if I can drag together a bit more material, examples of different types of pentacles, possibly even historical development of the idea... something to make a decent article out of. I don't see any problem with an article being brief though. I think the stub tag is only warranted when it's clear that useful information is missing. Fuzzypeg 00:46, 8 March 2006 (UTC)[reply]
Done. I've split the article. I actually split it a couple of weeks ago, and I should have left this note then. Better late than never. Fuzzypeg 11:44, 27 March 2006 (UTC)[reply]

Multiple sections for each may be in order. The confusion over this simple, yet immediately identifiable shape to so many people requires a lot of attention. The swastika would be easy compared to this.Φndex 02:55, 29 April 2006 (UTC)[reply]

I don't follow you. Multiple sections for each what? Fuzzypeg 02:38, 1 May 2006 (UTC)[reply]
My suggestion was to recommend a general definition that would branch to mathematical/religious/occult aspects of this symbol that is known by so many to mean so many things all while being called the same thing.Φndex 15:00, 23 June 2006 (UTC)[reply]
As far as I'm aware, the Pentagram article already follows your suggested format. The Pentacle article has a note at the bottom about mathematical use of the term, but there are not so many distinct major definitions for that term as there are for Pentagram, hence fewer sections to that article. Have a look. Are there still any specific improvements you would suggest? Fuzzypeg☻ 12:34, 25 June 2006 (UTC)[reply]

Goat's head/Baphomet

I don't know how credible a source this site is, but in the section on satanic pentagrams it mentions that the goat's head is often mistaken for that of Baphomet. The section that follows gives, at least a possible, meaning behind the goat's head. That said, it seems to me that "with the head of Baphomet inside the pentagram" should, perhaps, be changed. Though I'm not sure exactly how it should be changed, as in what to add and where. MeLoco 05:09, 12 October 2005 (UTC)[reply]


Pythagoreans

There is some serious mathematics here. The pentagram actually depicts the golden ratio as well as one possible proof of its irrationality (applying the Euclidean algorithm twice replaces the circumscribed pentagon by the inscribed pentagon, proving nontermination of the continued fraction). Possibly the first irrational identified as such (before the famous square root of two) and this picture may have been intended to indicate that. See David Fowler and, I think, Knorr. [Possible connection between the devilish properties of irrationals in mathematics and later use by witches. Cf. "diabolus in musica" which however refers to the square root of 2.] I'm not going to try to insert any of this, and it might well belong on a separate page anyway. Everything here involves speculation based on the mathematics itself; textual evidence bearing on Pythagorean doctrine is skimpy, late, and in most cases self-contradictory. Abu Amaal 20:06, 11 February 2006 (UTC)[reply]

Merge with pentangle?

I don't care about a merge, but all geometry should stay under this article name! Tom Ruen 06:50, 23 February 2006 (UTC)[reply]

i read somewhere that a pentacle was a 3 dimensional pentagram. like for jewelry. and the pentagram is 2 dimensional.

Read above. The historical definition of pentacle is given time and again--Vidkun 13:15, 15 March 2006 (UTC)[reply]

I read the discussion and the two articles and Pentagram and Pentangle. I believe they should be merged. However, about the Pentacle, I believe it to be crucial for the matter to be in separate articles, especially considering the state of a curious researcher who just emerges out of the "Da Vinci Code" world. Fleet Command 20:28, 25 March 2006 (UTC)FleetCommand[reply]

Merge. Pentagram, pentalpha and pentangle are synonyms. The only difference is the context in which they are commonly used. The Pythagoreans used the term pentalpha; the term pentagram is the most common term today, with pentangle being a slightly more archaic version, now uncommon (it is found in Sir Gawain and the Green Knight, among other places, and I suspect it was the standard heraldic term). Fuzzypeg 06:22, 2 May 2006 (UTC)[reply]

I had a closer look and realised that there was very little extra information in pentangle; I merged it in and it makes a short paragraph in this article. I see no reason now not to finish the merge (this discussion has been untouched for a very long time). So I will. Fuzzypeg 07:05, 2 May 2006 (UTC)[reply]

Inverted pentagram and Wiccan 2°

The information that was recently added regarding the use of the inverted pentagram within the 2° initiation was correct, however quite incomplete. I'm not aware of this information being published before, however it may have been. I would feel quite uneasy about giving a full exegesis on the symbolism of the inverted pentagram and the 2° initiation on Wikipedia - I consider this oathbound. Because I consider the added explanation incomplete, and thus a slight misrepresentation, I would be much happier if it had a cited source, so perhaps it wouldn't seem like it originates in the combined wisdom of the Wiccan editors to the article. I hope this makes sense... Fuzzypeg 01:50, 20 March 2006 (UTC)[reply]

I'm intending to remove the explanation in question if no-one can come up with a reference for it. I will keep the statement that it is related to Wiccan 2nd degree, but remove the explanation regarding confronting the shadow self etc. Comments? Fuzzypeg 06:26, 2 May 2006 (UTC)[reply]
Removed. Fuzzypeg 06:16, 23 May 2006 (UTC)[reply]

Seal of Solomon

From the article, "A pentacle may be marked with any sigil of evocation, including the common pentagram-shaped Seal of Solomon." The Seal of Solomon is a hexagram not a pentagram. --Evmore 18:06, 20 March 2006 (UTC)[reply]

Not according to some versions of the story - Seal of Solomon.--Vidkun 22:05, 20 March 2006 (UTC)[reply]
I know some Qabalists claim the pentagram was the true original form (can't recall who though), and this claim seems intended to support a particular story regarding Solomon and David. It's something along the lines of comparing Solomon and David by these signs and explaining through them why Solomon fell from grace. The pentagram indicated dominion and wisdom in the lower realms, the hexagram wisdom in the higher spiritual realms.
I just automatically tend to use "Seal of Solomon", but perhaps this confuses the issue. Fuzzypeg 00:24, 21 March 2006 (UTC)[reply]

"Prehistoric" astronomers and "around the sun"?

I take exception to a passage early in this entry:

"The pentagram has long been associated with the planet Venus and the worship of the goddess Venus, or her equivalent. It is most likely to have originated from the observations of prehistoric astronomers. When viewed from Earth, successive inferior conjunctions of Venus plot a nearly perfect pentagram shape around the Sun every eight years."

Where do I begin?

  • Prehistoric astronomers would not have been thinking in terms of Earth and Venus going around the sun; the heliocentric model was a much later development.
  • The association of the planet with the goddess is specific to only a couple of cultures, and therefore is not universal and would not have been prehistoric. The Greeks got the association of that planet with a goddess from the Babylonians, and the Romans got it from the Greeks. Other cultures have called the planet other things not assoicated with a goddess; see the Wiki entry on the planet Venus.

Pciszek 16:41, 23 May 2006 (UTC)[reply]

Your first objection I don't get. I see no heliocentricity in the quoted phrase: On the contrary, it only deals with what can be seen on the sky from Earth. Your second objection seems highly relevant, and I hope someone will edit the text accordingly, but am not knowledgeable enough about the subject matters to do it myself.--Niels Ø 10:32, 24 May 2006 (UTC)[reply]

It's surprising what the ancients figured out before the dark ages and heresy were invented... Eratosthenes measured the diameter of the earth with reasonable accuracy in the 2nd century BC; Aristarchus of Samos came up with the method of figuring out the moon's distance from the Earth. When they attempted to determine the distance to the sun they discovered that it was too far away to get an accurate triangulation. The vast distance involved indicated that the sun must be hugely larger than the Earth, which led Aristarchus to suggest that the sun, rather than the earth, was at the center of the universe. [2]
I don't know what the ancient Egyptians thought about heliocentricity, but they had certainly figured out about the interesting patterns in the synods of Venus. They calculated the 1460 solar years that it would take for the pentagram to gradually rotate until the points again returned to their original positions, and called this a Sothis Year after the Goddess Sothis. [3]
If you want to improve the wording, I'd suggest talking about a pentagram shape around the zodiac rather than around the sun, which is actually more correct, and doesn't assume a heliocentric view. If I had more time I'd be putting all this kind of information into the articles here. Anyone want to help? Fuzzypeg 06:57, 25 May 2006 (UTC)[reply]

Some of these removed references may still be useful

The following references and external links may be useful to the article, and I can't tell whether care has been taken in evaluating them before deleting. So I'm putting them here unitl I have a chance to check through them and possibly re-introduce some.

References:
External links:

Care should be taken when removing references and links - just because they don't conform to WP recommended reference style doesn't mean they aren't useful. Fuzzypeg 21:45, 25 May 2006 (UTC)[reply]

Geometry

The geometry section makes reference to the larger pentagon side being the same size as a blue line, and to the diagonal of the pentagon being teh same size as a green line. I wonder if this [:Image:Pentagram2.png]] diagram should be enhanced to show the larger pentagon and the diagonal as well. It's a bit beyond my drawing skills or I'd do it myself ++Lar: t/c 12:08, 26 May 2006 (UTC)[reply]

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