[This was not the best lesson we’ve done. The kids got bored – and let me know, lol. They did, however, get the point and ended up understanding sufficiently enough about the golden ratio. So, it that way it was a win.
We ended with the “Donald in Mathmagic Land” video but, you might want to start with it. When I went to measure the kids to show them the golden ratio in their bodies, I realized that when kids grow, various parts of their bodies grow at different rates. So, we ended up letting the kids measure the adults.]
Gather ‘round kids; it’s times for Moon School!
The first thing you should know is that symbols mean different things to different people, and that’s OK. Many symbols, like the pentagram and pentacle, have been around for a very long time. They’ve even found pentagrams all the way back in 3000 BCE (Alchemistra, 2009), that’s over 5 thousand years ago!
Pentagrams have been found in just about every ancient civilization from the Mayans in Mexica and Central America to China. Now, why is it that so many people who had little to no contact with each other, would create a pentagram? [Stand up with arms outstretched and legs wide enough that you look like a star] Can you see the star shape I’m making with my body? I believe, as do many others that it’s because the pentagram can easily represent the human body. We’ll talk more about that later when we talk about the Golden Ratio – the Divine Number.
Many religions use this symbol. Christians use the pentagram to show the “5 wounds of Christ”. It’s used as a symbol for the goddesses Ishatar and Venus. If you stand on the Earth looking us at Venus, the path that Venus takes in the sky forms a petal pentagram.
You may notice that I’m using pentacle and pentagram as if they were the same word. That’s because they are and they aren’t. Confused? You’re not the only ones! You see, they come to us from different languages, so two different paths. Pentagram comes from ancient Greek and means five lines (Wikipedia). Pentacle comes from Latin but, came through to us from old French. It probably came from “Pendaculum, Latin for ‘little hanging thing’” (Valerie Voigt, 2017), which became the old French word “Pentacol,” or “amulet worn around the neck” (Online Etymology Dictionary, n.d.). The Oxford Dictionary defined pentacle as “A talisman or magical object, typically disc-shaped and inscribed with a pentagram, used as a symbol of the element of earth.” (Oxford English Dictionary, n.d.)
In modern day Paganism, especially in Wicca, the general agreement in that a pentagram is the 5-pointed star while a pentacle is the pentagram with a circle around it. But, this is just a common opinion, not a real definition. As English is a living language, one day that may become the definition. Often, though, many people just interchange the words pentagram and pentacle.
Many years ago, in ancient Greece, there was a man named Pythagoras. When you get older, you’ll hear more about him in your math classes. For him and his fellow philosophers, the pentagram was the perfect symbol to show the golden ratio. What is the golden ratio? A ratio is how one number compares to another. Like, let’s look at the ratio of boys to girls in today’s class. How about the ratio of adults to kids here? [The kids then did couches to pillows and many other comparisons]
The Greek name for the Golden ratio is called phi and looks like this:
The ratio is 1.61803399… but, I’ll save all of that for your math teacher. Basically, the golden ratio in the pentagram looks like this:
So, line d and line c are as long as line b. Line b plus line c are as long as line a. Here, let me show you: [I took a picture of a pentagram and pinned it to a cardboard box. Then we wrapped twine around the pins. We then selected lines, and I let the older kids cut it.]
While that was fun, you’re probably wondering what the heck has this to do with anything – right? Well, this golden ratio is found all over nature, in trees and how their branches grow, in artichoke heads and snail shells,
in flowers, everywhere – even in humans. That’s right, are bodies are examples if the golden ratio, too!
[Use these pictures from Sacred Geometry as a guide in measuring our own bodies.]
The pentacle is also a wonderful tool that can be used in many ways and symbolize various things in Paganism. For example, with one point up, it symbolizes the Goddess or feminine energy. With one point down, it symbolizes the God or male energy. There are those who say that the pentacle in this direction is evil and is the sign of the devil or Satan but, that’s because a man named LaVey said it did in the 1960’s. Then Hollywood and the rest of show business ran with that idea. People freaked out so much about it that it became stuck in their minds. As we Pagans don’t tend to believe in Satan or a devil, that definition doesn’t mean anything to us. But, you should be prepared for people not understanding if you should wear your pentacle “upside down,” or even wearing it at all. [We talked a bit about how people are afraid of what they don’t know.]
Pythagoras and his friends also used the pentagram to show the five elementals – Earth, Water, Air, Fire, and Spirit. The Pagans, specifically the Wiccans, use the Pentagram/Pentacle the same way. Our next lesson will be about the Elements, so we’ll talk more about this then.
What else could it represent? The pentagram can be used for directions – front, back, right, left, up. It can represent the five senses, five appendages, five fingers or toes. We talked about with one point up it represents the Goddess and two points up it represents the God, so you could use the pentacle to call on either one of them. You could use it to call the Goddess Aphrodite/Venus, or even Astarte, Isis, Ishatar, or Inanna.
Further reading and bibliography:
Alchemistra. (2009, June 30). Sacred Geometry-The Pentagram. Retrieved from Esoteric Online
Online Etymology Dictionary. (n.d.). Pentacle. Retrieved from Online Etymology Dictionary
Oxford English Dictionary. (n.d.). Retrieved from Pentacle
Valerie Voigt, H. (2017, March 9). (T. Dugan, Interviewer)
Wikipedia. (n.d.). Wikipedia. Retrieved from Pentagram
There was no music nor crafts this time as we were busy putting on the Ostara ritual for the public.