Ancient PI (π)

archimedespi
Andrew Hoy
Project 314

While a number of slightly different approximations of π have been used for practical purposes since ancient times, French mathematician François Viète is typically credited with perfect mathematical approximation of the constant. Like the Greek mathematician Archimedes, Viète understood that a circle’s circumference could be approximated by an infinite number of polygons inscribed inside a circle(1), as illustrated below:  

Archimedes pi

Understanding that a circle’s circumference could be approximated by a polygon perimeter with an infinite number of sides, Viète consequentially deduced the following formula for calculating π in 1593:

Pi Formula

This formula allowed Viète to accurately approximate the constant π to nine digits, as 3.141592654.

Long before the Greek mathematician Archimedes used polygons to approximate π, it is apparent that Egyptian and Babylonian builders recorded more practical approximations of π.  For example, a Babylonian clay tablet (~1900-1600 BC) implies a value of 25 / 8, which is equal to 3.125. Also, the Rhind Papyrus of Egypt treats π as 19 / 6, which is equal to 3.1605. Nearly a thousand years later in India, Sanskrit texts recorded π as 9785 / 5568, which is equal to 3.088.  Indian mathematicians also approximated π as √10, or 3.1622.  After 100 AD, Ptolemy expressed π to four digits as 3.1416 - close enough to build almost anything in the ancient world.

Gizah Pyramids

The Pyramids of Giza in Cairo, Egypt

 

Perhaps of greater relevance to the history of π is Egypt’s Great Pyramid.  Giza's wonder of the ancient world was built with a perimeter of about 1760 cubits and a height of about 280 cubits.  Some have noted that the ratio was equal to 44 / 7, which is two times the familiar 22 / 7 ratio, which is still used today to conveniently calculate π to two decimal places, or 3.14.  This Giza Pyramid geometry is summarized in the illustration below:

PI Ratio of the Great Pyramid

The PI Constant as Conveyed in the Great Pyramid 

While some Egyptologists try to suggest this recorded “ratio in stone” is but a matter of mere coincidence, it would be absurd to propose that people building on a scale such as Giza would not be able to arrive at 3.14 by means of empirical measurement – provided that their engineers and mathematicians were remedial. After all, the Pyramid builders aligned sides of the square pyramid base to true north within 4 minutes of arc (equal to a total of 0.067 degree), which implies that the accuracy with which they measured or surveyed was twice that of their convenient π approximation! If they had the technology to place over 2 million blocks while controlling the base dimensions of the structure to greater than 0.1% accuracy, surely they could have measured the ratio between a circle and its diameter with equal or greater precision.

Ikonos satellite image of the Great Pyramid

Although several scholars have debated Israel's involvement in creating the Giza Pyramid, few would suggest that the Pyramids were not standing at the time of Israel's Exodus.  Moses was said to have been "Learned in the wisdom of the Egyptians".  While skeptics can easily dismiss the relationships between the structure's and the 22/7 ratio for π, it's hard to believe that Moses would have left Egypt at 40 years old not knowing how to calculate the circumference of a circle.  

 

References:

1.  http://commons.wikimedia.org/wiki/File:Archimedes_pi.png

2.  http://www.theglobaleducationproject.org/egypt/studyguide/gpmath.php

The Exodus Tabernacle: An Ancient Journey with the Ancient Hebrew Language

Could the ancient Exodus Tabernacle shed new light on the Ancient Paleo Hebrew Language?  See how the ancient pictographic Hebrew Letters, along with the spelling of ancient Hebrew words, further testify to the shape and configuration of the ancient Hebrew tent and dwelling place!

As I reflect back upon my Hebrew journey which began over a decade ago, I recall what a strange and unexpected joy it was to learn the alphabet—or more specifically, the Hebrew “aleph-bet”—from scratch as an adult. While the foreign letters were unfamiliar and thus a little intimidating at first, I found it was pretty easy to learn the names of the twenty-two Hebrew letters—especially if they were put to a simple and catchy “aleph-bet” tune. Likewise, learning the phonics associated with the each of the letters also came pretty easy, as most of the Hebrew letters bear obvious similarities to an English alphabet counterpart. Coupling the sights and sounds of the Hebrew characters together, I had mapped all of them into my mind in just a couple of weeks. In fact, it seemed as if the letters were somehow already familiar—perhaps embedded into the very core of my DNA since my conception.

How does the Tabernacle testify to that ancient paleo Hebrew script, and what does the ancient paleo script reveal about the Tabernacle?  Click the above PDF link to find out.

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Jeff Benner's Ancient Hebrew Alphabet Chart
Click to go to the chart

What is PI, a.k.a. "π" ?

pi
Andrew Hoy
Project 314

What is “PI”, and what is its significance?  PI, designated by the Greek letter π, is a mathematical constant defined as the ratio of a circle’s circumference to its diameter.  This Circumference/Diameter ratio used to calculate π is depicted below: 

 Pi formula

 

Often approximated fractionally as 22/7 or rounded to 3.14159, π is an irrational number that cannot be represented with terminating or repeating decimals.

 

In engineering and construction, understanding π is of critical importance, as it is impossible to build various  structures and building features without measuring or controlling critical diameter or circumference dimensions.

Ferris Wheel At Aussie World Leaning Tower of Pisa

St. Peters Dome Izumo Dome

Aussie World Ferris Wheel1 (upper left); Leaning Tower of Pisa2 (upper right); 
St. Peter's Basilica3 (lower left); Izumo Dome4 (lower right).  

In building the Exodus Tabernacle Courtyard curtain set, the same basic understanding of π or PI (approximately equal to 314/100) is also required, as illustrated in the sketch below:  

Tabernacle Curtains

 

References

1.  By Softeis (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons

2.  By Aussie world (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC BY-SA 4.0-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/4.0-3.0-2.5-2.0-1.0)], via Wikimedia Commons

3.  Giacomo della Porta [Public domain], via Wikimedia Commons

4.  https://www.flickr.com/photos/kentamabuchi/3511199478/in/photostream/