Attn Harry Potter and Games of Thrones fans… this is going to be the next Harry Potter deathly series…

Legends of Amun Ra is a bold new science fiction/fantasy series of the year. A unique blend of history, mythology, fantasy, and science fiction wrapped in a heart-pounding adventure mystery, you will uncover the magic spells, mythology, and wonders of the ancient Egyptian gods and goddesses.

You will cross boundaries that will lead you into another dimension. A dimension of magic, rooted in genuine the mythology of ancient Egyptian religion. Legends of Amun Ra explores the transformative processes of the soul, and is truly unlike anything you have ever read.

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All Fantasy World’s said: “The battle scenes were perfect, just like in “The Emerald Tablet”. Vivid images, a lot of action, and a determined Thea who is not very sure of what she is doing, but she knows she wants to save Messenia.”

Tome Tender reviews said: “The attention to detail throughout the story creates a living and breathing world laced with the author’s knowledge of ancient Greek history and its gods.”Student Spyglass blog called The Emerald Tablet: “A middle ground between Harry Potter deathly and Game of Thrones

With the finale of one of my favorite shows Spartacus and the news of a sequel to the movie 300 coming out, I thought I would talk a bit about the history of slave wars. The wars did not start with Spartacus. Rather, Spartacus was one of many leaders of freedom fighters in the course of Egyptian, Greek, Roman, British, and American history. Before Rome had Spartacus, Sparta had Aristomenes. (Fun fact: Spartacus was not from Sparta but was from Thrace, though he is named after the famous city-state).

In 750 BCE, Spartan king Theopompus went to war over the northern city-state of Messenia, which was also spartan-armyGreek. He did so because his territory needed expanding and his men needed slaves so they could focus on warfare. The First Messenian War lasted twenty years and enslaved the population of Messenia. The ratio of Messenian Helots to Spartan citizens was 7:1. It is estimated that around 700 BCE, the Spartan population was between 10,000 and 20,000. The only thing I could compare this to would be if Arizona went to war with California and enslaved all the Californians. We are all Americans, but live in separate states. What the Spartans did to the Messenians was unprecedented. Typically, in ancient times, you made slaves of foreign people, not domestic.

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It is widely known that many Christian traditions and holidays were modified forms of pagan festivals. In 313 CE, Constantine the Great (you know, the Roman Emperor who converted and turned the Western world Christian overnight), declared the official religion of the Roman Empire as Christianity. To smooth this idea over with the public and assist with the conversion process, he tied many Christian holidays to pagan ones which the public already celebrated. He didn’t want a revolt on his hands. (Although it’s an oversimplification, just imagine if the President of the United States declared the official religion of the United States wasn’t Judaism or Christianity. That is essentially what Constantine did in 313 CE.).

But, if we know that most holidays have their roots in ancient cultures, where does Easter come from? By using symbology and finding the common threads throughout the ancient world’s religions, we can understand why we celebrate our holidays the way we do.

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Happy Pi Day

“Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number pi.” – William L. Schaaf

The ancient Egyptians started the hunt for the mysterious number 4,000 years ago. In his book The History of Pi (1971), Petr Beckman speculates that the ancient Egyptians drew a circle, and then measured the 1e06c2ec-48f2-4e90-a3bb-2c2c2f63c863circumference and diameter with rope. They determined that pi was a sliver greater than three, and came up with the value 3 1/8 or 3.125.

But the ancient Egyptians didn’t stop at rope measurements. According to the Rhind Papyrus, which was written by an Egyptian scribe named Ahmes around 1650 BCE, he claimed: “Cut off 1/9 of a diameter and construct a square upon the remainder; this has the same area as the circle.” For us non math geeks out there, Ahmes basically said pi = 4(8/9)2 = 3.16049, which was pretty accurate for a mathematician three thousand years ago.

The ancient Greeks, like most things, built upon what the ancient Egyptian mathematicians had done and made two revolutionary leaps forward. Antiphon and Bryson (who both hailed from the city-state Heraclea) thought of the clever idea to inscribe a polygon inside a circle, find its area, and then double the sides repetitively.

This leads us to the main who most people call the father of pi, Archimedes (from the city-state, Syracuse). archimedes-1-sizedWhere Antiphon and Bryson failed, Archimedes succeeded.  Archimedes focused on the polygons’ perimeters as opposed to their areas, so that he approximated the circle’s circumference instead of the area. He started with an inscribed and a circumscribed hexagon then doubled the sides four times to finish with two 96-sided polygons.

To quote Archimedes himself in his work entitled, Measurement of a Circle: Given a circle with radius, r = 1, circumscribe a regular polygon A with K = 3(2n-1 sides and semi perimeter and inscribe a regular polygon B with K = 3(2n-1 sides and semi perimeter bn. This result in a decreasing sequence a1, a2, a3… and an increasing sequence b1, b2, b3… with each sequence approaching pi. We can use trigonometric notation (which Archimedes did not have) to find the two semi perimeters, which are: an = K tan ((/K) and bn = K sin ((/K). Also: an+1 = 2K tan ((/2K) and bn+1 = 2K si n ((/2K). Archimedes began with a1 = 3 tan ((/3) = 3(3 and b1 = 3 sin ((/3) = 3(3/2 and used 265/153 < (3 < 1351/780. He calculated up to a6 and b6 and finally reached the conclusion that 3 10/71 < b6 < pi < a6 < 3 1/7.

Well, I didn’t get any of that. But, for the next few hundred years most people accepted Archimedes’ James_Gregorycalculations. That was until Archimedes’ calculations were refined by James Gregory in 1672 and Gottfried Leibniz in 1685. By 1750, mathematicians could express pi in an infinite series.

Now we have computers to do the work for us, but it all comes back to what the ancient Egyptians started with a piece of rope and drawing a circle in the sand.

Sources:

Archimedes. Measurement of a Circle. From Pi: A Source Book.

Beckman, Petr. The History of Pi. The Golem Press. Boulder, Colorado, 1971.

Wilson, David. History of Mathematics, Rutgers, Spring 2000