The idea that “necessity is the mother of invention” is said to date back to Plato’s Republic (~380 BC).  While it is a historical fact that inventions are sometimes conceived under circumstances of true need and desperation, it’s also worth considering that necessity isn't the only parent in the room. For example, the airplane, the automobile, and the telephone were never life-or-death necessities before they were invented.  These few examples clearly demonstrate that premeditated want or desire can equally inspire innovation, especially given the fact that most inventions must be nurtured with time and resources, which is contrary to the conditions of duress and scarcity of resources which usually define a condition of absolute need.  

Given my admitted levels of indifference, it would be a gross exaggeration to say that my discovery of the ancient Pi constant was as a result of intensive study or subject matter interest. Truth be known, my study of the Tabernacle really began with an unrelated independent Hebrew etymology study—which was marginally related to the Tabernacle in the first place.

Nevertheless, as I began to peripherally survey the traditional models of the Exodus tabernacle, some things just didn’t add up. For example, I wondered why the Tabernacle models (like the full size model built in Timna, Israel, as shown in pictures) would feature a flexible leather rooftop with almost no pitch for watershed.

Driven by a combination of frustration and curiosity, I sat down with the Hebrew Exodus account, put my "engineering hat" on, and followed the advice of my father—who was an engineer and professor.  Diligently following Dad’s advice, I made an "FBD with TLC"; which, in his vocabulary, meant that I drew a “Free Body Diagram with Tender Loving Care”. Just like I had done so many times in school and as an engineer, I drew a simplified sketch of what the text described—and only what the text described—without adding assumptions of my own, taking creative latitude with the descriptions, or deferring to traditions.  Knowing that I might be in for a long night, I sharpened my pencil, started drawing curtains, and with a watchful eye, kept a careful inventory of every single letter—and number—in the Exodus Hebrew texts. 

According to the Exodus account, the Israelites were to weave 11 fabric sheets (depicted in the image below), each measuring 4 by 30 cubits (which is around 6-8 feet wide and 45-60 feet in length, depending upon assumed cubit conversion standards), complete with loops on opposite edges.  Using the fabric loops in the edges, the craftsmen were instructed to unite all sheets together into a single assembly, at which point they were also told to fold the 11th sheet back over upon itself. It is traditionally assumed that these curtains are joined together in a top-to-bottom arrangement (i.e., long edge-to-long edge), in order to make a single flat plane sheet measuring 42 x 30 cubits.

However popular this traditional long-edge-to=long edge rectangular fabric swatch assembly approach may be within religious commentaries and artwork, the assumed fabrication method nevertheless fails to comply with the exact Exodus specifications.  In particular, it fails to account for two unjoined edges on opposite ends of the assembly, whereas the Exodus text describes all sheets as having loop joints on both edges. Regardless, by means of assumption, a rectangular assembly is created while end sheet edges are left unconnected (depicted in the image above via curtain 1 and the half-sized 11th black-and-yellow curtain above).  Nevertheless, given this universal assumption, at this point it becomes very difficult—if not impossible—for students and scholars to perceive anything but a rectangular building, such as the physical models depicted in photos above.

Although scholars have come to universally assume and fully accept the same top-to-bottom (i.e., long edge-to-long edge) curtain joining approach as depicted above, there is another simple—and more practical—approach to joining eleven sheets together.   In following the Exodus texts literally, the Tabernacle builders were to join the eleven like-for-like sheets via the "end edges" lengthwise (i.e., short edge-to-short edge), thus creating an extremely narrow strip. Of course, at only 4 cubits wide but 330 cubits in length, the narrow strip would hardly function as a practical roof for “covering” a tent.  However, joining all sheets at both edges (see the image below) would ultimately yield a cylindrical assembly, appropriate for "covering" over a building's sides (just as described in Exodus 27:13), where the "covering" functions not as a roof, but as a barrier wall instead! 

Of perhaps equal or greater significance, the combined sheet dimensions and quantities point to a cylindrical sheet assembly. If joined together in a cylindrical arrangement, the sum of the eleven sheets measuring 30 cubits length, minus the end sheet overlap (folded over per Exodus 26:12), and minus the nominal one cubit overlap adjustment (as each curtain end must slightly overlap with the adjacent one per Exodus 26:13), would be expressed as ([30 x 11] - [30 / 2] - 1), or (330-15-1), as is graphically depicted below.