ArticleslgStudy

mathematics

Pentacle

Pentacle is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Pentacle rather than just read about it. In short: A pentacle (also spelled and pronounced as pantacle in Thelema, following Aleister Crowley, though that spelling ultimately derived from Éliphas Lévi) is a talisman that is used in magical evocation, and is usually made of parchment, paper, cloth, or metal (although it can be of other materials), upon which a magical design is drawn. Symbols may also be included (sometimes on the reverse), a common one being the six…

Pentacle — main illustration
Pentacle — illustration

Key takeaways

  • Pentacle belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Pentacle to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Pentacle from memory before moving on to harder problems.

Reference excerpt

A pentacle (also spelled and pronounced as pantacle in Thelema, following Aleister Crowley, though that spelling ultimately derived from Éliphas Lévi) is a talisman that is used in magical evocation, and is usually made of parchment, paper, cloth, or metal (although it can be of other materials), upon which a magical design is drawn. Symbols may also be included (sometimes on the reverse), a common one being the six-point form of the Seal of Solomon. Pentacles may be sewn to the chest of one's garment, or may be flat objects that hang from one's neck or are placed flat upon the ground or altar. Pentacles are almost always shaped as disks or flat circles. In the Hermetic Order of the Golden Dawn, though, a pentacle is placed within the triangle of evocation. Many varieties of pentacle can be found in the grimoire called the Key of Solomon. Pentacles are also used in Wicca, alongside other magical tools. In the Hermetic Order of the Golden Dawn and Wicca, pentacles symbolize the classical element earth. In the 1909 Rider–Waite–Smith tarot deck (the pentacles of which were designed by Arthur Edward Waite), and subsequent tarot decks that are based upon it, and in Wicca, pentacles prominently incorporate a pentagram in their design. This form of pentacle is formed upon a disk which may be used either upon an altar or as a sacred space of its own.

Definitions The first documents to depict pentacles were the 16th-century grimoires called the Heptameron by pseudo-Pietro d'Abano, and the Key of Solomon. In the Heptaméron, there is only one pentacle, whereas in the Key of Solomon, there are dozens of different pentacles. The Heptameron's pentacle is a hexagram that is embellished by patee crosses and letters, whereas the Key of Solomon's pentacles have a very broad variety of designs, only two of which are pentagrammic. That contrasts with the later popular definitions of pentacles from the 1900s, which state that pentacles are inherently pentagrammic. Gerald Gardner, known by some as the 'Father of Wicca', got his concept of pentacles in large part from the 1909 Rider–Waite–Smith tarot deck, in which the pentacles are disks that are covered with a pentagram. In Gardner's 1949 book High Magic's Aid and 1954 book Witchcraft Today, Gardner defined a pentacle as a "five-pointed star", intending to mean a pentagram. In his 1959 book The Meaning of Witchcraft, Gardner defined a pentacle as a synonym of 'pentagram'. There is a particular definition of 'pentacle' among many latter-day Wiccans: Namely, a 'pentacle' refers to a 'pentagram' circumscribed by a circle.

Etymology The word is first recorded in English usage in 1561, from earlier French use. The French word had the meaning of "talisman". The French word is in turn from the Latinized word 'pentaculum' (using the Latin diminutive suffix -culum), which is in turn from the Italian word 'pentacolo'. The Oxford English Dictionary in earlier editions (2nd edition 1989) went on to say that "some would connect it" with the Middle French word 'pentacol' (1328) or 'pendacol' (1418), a jewel or ornament worn around the neck (from pend- hang, à to, col or cou neck). This is the derivation the Theosophical Society employ in their glossary:

...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).

As magical objects Pentacles, despite the sound of the word, often had no connotation of "five" in the old magical texts, but were, rather, magical talismans inscribed with any symbol or character. When they incorporated star-shaped figures, these were more often hexagrams than pentagrams. Pentacles showing a great variety of shapes and images appear in the old magical grimoires, such as the Key of Solomon; as Heinrich Cornelius Agrippa summarises it, their use was to "fore-know all future things, & command whole nature, have power over devils, and Angels, and do miracles." Agrippa attributes Moses' feats of magic in part to his knowledge of various pentacles. A Fourth Book of Occult Philosophy (c. 1565), which was falsely attributed to Agrippa, gives detailed instructions as to how pentacles should be formulated:

But we now come to speak of the holy and sacred Pentacles and Sigils. Now these pentacles, are as it were certain holy signes preserving us from evil chances and events, and helping and assisting us to binde, exterminate, and drive away evil spirits, and alluring the good spirits, and reconciling them unto us. And these pentacles do consist either of Characters of the good spirits of the superiour order, or of sacred pictures of holy letters or revelations, with apt and fit versicles, which are composed either of Geometrical figures and holy names of God, according to the course and maner of many of them; or they are compounded of all of them, or very many of them mixt. Francis Barrett, in his influential work The Magus of 1801 (Book 2, part 2), repeats these instructions almost verbatim. Another common design employed in pentacles is a magic square, such as the Sator-Arepo-Tenet square. In the Golden Dawn magical system, the Earth Pentacle is one of four elemental "weapons" or tools of an Adept. These weapons are "symbolical representations of the forces employed for the manifestation of the inner self, the elements required for the incarnation of the divine." Other pentacles for the evocation of spirits are also employed in the Golden Dawn system; these are engraved with the name and sigil of the spirit to be invoked, inside three concentric circles, having painted on their reverse a circle and cross like a celtic cross. According to Aleister Crowley's instructions for the A∴A∴, the pentacle is a disc of wax, gold, silver-gilt or Electrum Magicum, eight inches diameter and half an inch thick; the Neophyte should "by his understanding and ingenium devise a symbol to represent the Universe", and engrave this on the disc.

… excerpt ends here. Continue reading the full article.

Illustrations

Pentacle: Pentagram, a common symbol on a pentacle
Pentagram, a common symbol on a pentacle
Pentacle: Hexagram, a common symbol on the six-point version of a pentacle
Hexagram, a common symbol on the six-point version of a pentacle
Pentacle illustration
Pentacle illustration
Pentacle illustration

Worked examples

Example 1 — a first encounter with Pentacle

Start with the simplest possible case. Write down what Pentacle claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Pentacle before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Pentacle ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Pentacle

In research
Pentacle appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Pentacle in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Pentacle is common in secondary-school and first-year university syllabi. It links to neighbouring topics 5 (number), Ceremonial magic, Ceremonial weapons, so understanding it makes those chapters shorter.
In everyday life
Look for Pentacle outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Pentacle in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Pentacle means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Pentacle out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Pentacle in simple terms?

A pentacle (also spelled and pronounced as pantacle in Thelema, following Aleister Crowley, though that spelling ultimately derived from Éliphas Lévi) is a talisman that is used in magical evocation, and is usually made of parchment, paper, cloth, or metal (although it can be of other materials), u…

Why does Pentacle matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Pentacle?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Pentacle.

Tags

  • 5 (number)
  • Ceremonial magic
  • Ceremonial weapons
  • Magic items
  • Magic symbols
  • Modern pagan beliefs and practices
  • Religious symbols
  • Ritual weapons
  • Star symbols
  • Talismans

Keep exploring