the geometry of paper money

dollar-cube          All of us have looked at and held paper money such as our present Federal Reserve “notes”. But how many people have wondered about the measurements used to create those bills? Why did the money architects use those proportions and not some others? Is there something hidden in the dimensions of these paper substitutes for what was, at least in the beginning, intrinsic values of gold and silver?

         That the answer to this question is “yes” shouldn’t come as too much of a surprise to readers of the previous chapters. They have unveiled in some detail a system of geometry underlying the choices for the weights and measures of the U.S. gold and silver coinage. And again, like with the coinage, there is no mention of this geometry in any historic or contemporary sources regarding the paper “money”.

         When I began to look into the paper currency the first thing that caught my attention was the strange choice of measures for the length and width of our present bills:

6.14” X 2.61”

          I’m sure that most builders and designers would agree, that in a nation with the “inch measure” as its basic unit of measure from it’s beginning to this day, it is a bit odd. It would seem that, with all other agendas aside, 6.125” X 2.625” makes more sense since the “inch” is inherently divided into halves, quarters, and eighths:

6 1/8” X 2 5/8”

 A bill this size would be practically indistinguishable from the actual bills since both   pairs of measures correspond to each other to an accuracy of better than 99%. Moreover, the perimeter of this hypothetical bill is identical to the actual bill’s perimeter:

2(6.14” + 2.61”) = 17.5”


2(6 1/8” + 2 5/8”) = 17.5”

         Dividing 17.5” into 6.14” and 2.61” increments is certainly an obvious incongruity. But by now we know it had to have been done for a reason, and for this reason we have to look to the size of the notes prior to 1929. That’s when our current paper notes evolved to their present size.

         Beginning in 1864, with the first United States legal tender notes, through 1928 the size of the finished note was approximately 7.4218” X 3.125”; or 189mm X 79mm. Most sources agree on the 3.125” width dimension but the actual length is slightly ambiguous. A good example of this is the figures given above which came from the same source. When the 189mm is converted to inches the measure is 7.44094…” which is slightly longer than 7.4218”. The one thing we know for certain is that it can’t be both measures; and in actuality, it may be neither.

         Assuming the width dimension of 3.125” is accurate, and having learned that these bills were printed 32 per sheet (4 lengths X 8 widths) means that one side of the sheet measures exactly 25” (8 X 3.125”). But what does the other side measure if it is 4 X the length?

         Let’s think like the illuminati’s coinage architects. The true length is somewhere between 7.4218”, the measure most often cited, and 7.44094…”, which is the greatest deviation that I’ve found. The division from one-into-two plays prominent in the geometry of their coinage, so if we divide these lengths by two perhaps we can deduce the actual intended measure:

 7.4218” / 2 = 3.7109”

7.44094” / 2 = 3.72047”

Eureka! The measure for each half-length resides somewhere between 3.71 and 3.72 inches. And since 3.7125” literally enshrines in measure the 371.25 grains of pure silver defining the dollar coin, it is certainly a worthy candidate for further investigation.  

         If the length of one of these large bills really is (3.7125” X 2), it becomes 7.425”. Four of these lengths total 29.7 inches. This means that the sheet of paper on which 32 of these bills were printed measured 29.7” X 25”. This is quite astounding since simple calculation again reveals the powerful occult geometry at the heart of its proportions:

29.7” X 25” = 742.5 square inches


742.5 square inches / 2 = 371.25 square inches

         Additionally, in geometry’s third dimensional accounting system, a cube comprised of 2,970 grains pure silver contains eight sub-cubes of 371.25 grains each.

         This is pretty in credible. It appears that they purposely designed the proportions of this “large note” paper-money to be a facsimile of the actual coins, the true money. They made both the length of the bill (2 X 3.7125”), and the area of the bill (371.25 sq.” / 16) shout out the numeric equivalent of the pure silver content within, what was and still is, an honest “dollar” (coin). And the 742.5 square inches comprising the full print sheet is mirrored in the 7.425” individual bill length. Once again we have to ask why this is not taught in schools, at least as an interesting and colorful aspect of our nation’s history and monetary system. The answer is probably that they want it kept secret.

         From 1834 until 1933 one grain of gold was equal to 16 grains of silver. The 16:1 ratio was unwavering for over 99 years. This relationship between gold and silver is as boldly expressed in this large bill’s proportions, as is its concealment beneath occult vales and secrecy. As was just demonstrated, every 16 bills measures 371.25 sq. inches and represents the number of pure silver grains in the dollar coin. And each individual bill, with a measure of 23.203125 square inches, represents the number of pure gold grains in the dollar (gold) coin. In 1834 the ten dollar gold Eagle was reduced from 247.5 grains pure to 232.0 grains. Later in 1837 it was slightly raised to 232.2 grains at which it remained. 232.0 grains is slightly over 16:1 (16.002…) and 232.2 slightly under (15.988…). A perfect 16:1 ratio is 232.03125 grains. And this is the same number patterning the area of the bill in square inches.

         As we will see next, this number also leads back to the 412.5 grains gross weight of the silver dollar coin, and the 6.14” length measure of the later (and still current) “small” notes. The sketch below shows how these coin-weight quantities and measures are built into geometry. They all come together in the same simple geometric transformations that we’ve seen throughout the evolution of the coinage system. The 412.5 grains, in the form of a regular tetrahedron, has the same edge-length-sum as a cube containing 437.5223… grains (which is one avoirdupois ounce). Divide this cube’s volume in half, and again repackage it the form of a regular tetrahedron. The cube, with an edge-length-sum equal to this tetrahedron’s edge-length-sum, has a volume of 232.03125 grains. And the edge of this cube measures 6.14490… which mirrors the length of the small notes in inches. (Again, readers of the previous essays will recognize this geometric transformation sequence as a familiar template governing the quantitative relationships among the various coinage quantities.)  

The Weight Of The Silver $ Leads Through The Avoirdupois Oz. And Half Oz. To The Weight Of The Gold Eagle In A Length Measure Mirroring That Of The Current U.S. Dollar Bill




Occult Measures in Paper Money

Found in the Paper Itself

          When the proportions of these first large size (legal tender) notes were designed it is obvious the intent was to convey to them the same magical properties and powers they believe their geometry had imbued to their coinage system. When the size of these notes was reduced in 1929 the intent was again to convey this perceived power into the new bills. Here are some of the mechanisms by which this was accomplished.

         Most research sources tell us that the paper composition used in today’s bills is essentially unchanged from its inception back in the 1860’s. This paper isn’t really “paper” since it is comprised of 72.3% cotton and 27.7% linen. Once again, this appears to be a strange choice of quantities . . . until we do a few simple calculations:

72.3% / 27.7% = 2.61010… / 1.00

          This shows that for every 2.61 parts cotton there is 1.00 part linen. We can also see that this 2.61 proportional quantity, chosen in 1862, became in 1929 the width measure in inches of the new small notes.

         A closer inspection of some relevant historic events reveals an even deeper mystery involving the paper’s composition. In 1853, the “money agents” persuaded Congress to reduce the pure silver content of the fractional silver coins (half-dollars, quarters, and dimes). In was lowered from 0.7734375 to 0.72 troy ounce. It remained this weight until 1873 when again it was argued for change. This time it was raised ever so slightly to 0.723391798… troy ounce (22.5 grams) and remained that weight until the last silver coin was struck in 1964. This was the money architects targeted weight in the first place, since this quantity of pure silver as a cube has the same “face value” (i.e. surface area) as a whole troy ounce of pure silver in the form of a sphere.


         Now the first legal tender “paper” note issued in 1864 came on the heels of the money architects failure in 1853 to steer Congress into approving their “proper” reduced weight quantity. Undaunted, they enshrined this quantity anyway in the composition of the paper for their new notes when they specified 72.3% of the fibers would be cotton. It took them nine more years to do it, but in 1873 they succeeded, and forever there after an American fractional dollar contained 72.3% of one troy ounce pure silver. Finally in 1929, as is mentioned above, this quantity appears again veiled in occulted equivalency as the 2.61 inch width measure of that bill presently in your purse or pocket.


More Evidence Confirming

Occult Measures in Paper Money

          Another artifact from that 1860’s designed bill was melded into the length measure of the new small bills. The large bills length is 7.000 inches, plus a quantity of 0.425 inch. This 0.425 quantity is carried forward into the new small bill and is clearly seen in its width to length ratio:

2.61” / 6.14” = 0.425081… / 1.000

          This is showing that if the length of the current small bills is considered as 1.000 unit, its width by comparison is 0.425 of that unit. All of this is present day evidence giving strength to the previously deduced assertion that the intended or designed length measure of the old bills is indeed 7.425”.

         And this evidence continues to build. Compare the length of four old large bills to that of 5 new small bills:

4 X 7.425” = 29.7”

5 X 6.14 ”   = 30.7”

 In the light of what has preceded, this can hardly be a coincidence: the 5 new small bills are exactly 1.0” longer than the 4 old large bills.

         There is something else noteworthy about this 29.7” quantity besides it being eight times 3.7125”. Since there is 371.25 grains of pure silver in every dollar coin there will be exactly 29.7 avoirdupois ounces of pure silver in every stack of 35 one-dollar coins. And remember, the sum of the perimeters of two small size bills is also 35 inches.

(35 X 371.25 grains) / 437.5 grains (or 1 Av. Oz.) = 29.7


Comparing the Areas of the

Large and Small Bills

          The surface area of the large bill is 23.203125 square inches; the small bill’s surface measures 16.0254 square inches. They compare as:

 23.203125 / 16.0254 = 1.4478967… / 1.000 = 2(0.723948…) / 1.000

 This is saying that if the area of the small bill were regarded as 1.000 unit of surface, then the area of the large bill will equal twice the quantity 0.723948…

         These quantities can be modeled in the following way: let the small bill’s area of 1.000 unit represent one troy ounce of pure silver; the two (0.723948…) units of the large bill’s area each represent the pure silver content contained in one fractional dollar in silver coin. This is to a better than 99.9% accuracy:

 fractional $ silver   / one troy oz. = 0.723391…


0.723391… /   0.723948… = .999231…

 And here again, in this 0.723948… quantity is the specter of the 72.3% cotton content within the currency’s paper.

         There is a very significant “artifact” in the small note’s area quantity that deserves highlighting. The bills in current circulation measure 16.0254 square inches. This can equally be expressed as “16 inches” plusone 39.37007874th” of 1.0 square inch. This number 39.37007874 exact, is the number of inches in one international meter!

           Now this isn’t the first time that the technocrats (working among the monetary architects) slipped metric measures into the foundations of American life. This was unbeknownst, for the most part, to the American people themselves. These new small bills in 1929, with their explicit and exact increment of metric measure, were preceded by the 1873 Coinage Act which raised the fractional dollar’s silver content from 345.6 grains (22.3945… grams) to an exact 22.5 grams (347.2280… grains). Remember, the United States was NOT on the metric system! And since the pure silver content is 90% the coins weight, the gross weight of the American fractional dollar became exactly 25 grams. The practical (and symbolic) implications of this are immense.

         This is because after 1873 the American silver dimes, quarters, and half-dollars became perfect standards for measuring weight. The only problem was that it was in metric accounting, and the American people were accounting in grains, not grams! If the United States had been using grams, then it would all make sense. Why? Because any combination of fractional silver coins totaling one dollar weighs 25 grams; four dollars weighs 100 grams; and, forty dollars in silver “change” weighs 1.0 kilogram, exact! I don’t think this feature was widely touted at the time; nor any time thereafter, that I am aware. Why not?


How Thick is a Paper Note?

          The government’s Bureau of Engraving and Printing lists the thickness of a paper note at 0.0043”. Again, one must ask why? In light of everything we’ve thus far discovered about the geometry of paper money, I am suggesting that the exact number, or designed number, is really:


        Of course, .00425” rounds off to .0043”. This is the figure they would have to use if their working tolerance was as fine as a 10,000th inch. And like the other dimensions of 6.14” and 2.61”, it is now consistent by being expressed in two numbers after the decimal point rather than three.

         This .00425” thickness is obviously a power of the same quantity embodied within the two different sized bills as well: the ratio of the small bill’s width to length (2.61” / 6.14” = 0.425…); and the quantity over 7 inches (0.425”), which as 7.425” is the length of a large bill. It is this quantity that allows the edge of this bill to measure 2 X 3.7125”, enshrining the silver content of the dollar coin.


Modeling the Length Change

From Large to Small Notes

          In 1929 the familiar “large note” paper currency, which had been first introduced in 1864, was replaced with our current size “small note” paper currency.

The length of the note was reduced from 7.425 inches to 6.14 inches.

 6.14 / 7.425 = 0.82693602… / 1.0

          When the number 0.8269360… is re-written as {(2) X (0.4134680…)} a fundamental structural quantity appears which is at the very heart of the Geometry of Form. This quantity (0.4134680…) represents the surface area of a transit-tetrahedron, the form that accounts for surface and volume “differences” whenever a unit of volume divides its surface or volume into two new units identical in form to the original “unit”.

         The transit-tetrahedrons usually appear in pairs. Here is a simple example of their function in transformational geometry. Imagine starting with 1.0 unit of surface in the form of a cube. When this surface unit transforms by dividing into two new cubes (surfaces) the volume contained in the original cube will be greater than the sum of the volumes contained in the two new cubes. When geometry packages this “excess volume” in the form of two tetrahedrons, the surface area of each will measure 0.4139742… units. Since the surface area of each of the two new cubes is 0.5 unit, the total surface area of


the now four forms at the end of this transformation is {(0.5) + (0.5) + (0.413…) + (0.413…)}. This principle applies universally to any 3-D surface unit dividing one-into-two regardless of shape, and is illustrated in the simple graphic above.

         Now if we regard the original large bill as having a length equal to {(2) X (0.50 unit)}, then the length of the new smaller bill is {(2) X (0.413…)} units.


         As we’ve just seen, all four of these units, both of these pairs, occur together in geometric transformations whenever a (3-dimentional) surface unit divides into two new units identical in form to the original’s.


 A Possible Source for the

Length Measure Ambiguity

          Another way of comparing the areas of these bills is to see how much bigger in square inches the large bill is over the small bill:

 23.203125 ― 16.0254 = 7.177725


8 X 7.177725 = 57.4218

          A large bill has 7.177725 square inches more than a small bill. And every 8 large bills have 50 square inches plus 7.4218 square inches more area than 8 small bills.

         This 7.4218 is the number of inches most often cited for the length of a large note. As just demonstrated, it certainly is a quantity inherent to the geometric relations between the large and small notes but it arises as a consequence of the large note’s edge being 7.425”, which we know is a reflection of the dollar’s silver content (2 X 3.7125”).

         In an earlier chapter exploring a “gram-based” measure system, it was shown that 50 square units, configured as the surface of a single cube, is directly related to the dollar coin’s pure silver content of 371.25 grains. This is because this cube’s volume is 24.05626… and as “grams” contains 371.2448… “grains”.


 The Silver Dollar’s Diameter;

The Length of the Old Notes; and

Prime Coinage Weights

          About 25 years before the appearance of the old notes measuring 7.425 inches in length, the silver dollar coin’s diameter had been standardized at 1.5 inches. When these measures are compared to one another we can easily distill the higher levels of occult measures.

7.425” / 1.5” = 4.95

 The above equation can be re-written as:

 (3.7125” + 3.7125”) / 1.5” = 2.475” X 2; or, 4.125’ / 10

 371.25 grains pure silver in dollar coin

412.5 grains gross weight dollar coin

247.5 grains pure gold in 10 dollar “eagle”

          In this way the prime coinage quantities are revealed, just as the designers of this system had intended. But this view was only for those amongst their confidants, and it was never their intent that it be exposed to you (the reader of this essay).


 The Dollar and the Gallon


A “Gallon” Unit In The Form Of A Cube Has An Edge-length Of 6.14 Inches. The Length Of U.S. Currency Is 6.14 Inches

         The “gallon” is a unit of volume. It was formally defined as 231 cubic inches ever since 1706 when it was codified into English law. It was described as a volume measuring 3” X 7” X 11”.

         As a geometric unit of volume, it is easily modeled as a cube having an edge length equal to 6.135792439 . . . inches. This measure corresponds to the same 6.14” measure purposely chosen for the length of U.S. paper notes (dollars) ever since 1929. These measures are identical to better than 99.9%:

 6.135792439 . . . / 6.14 = .999 3 . . .

          So again, it is just like the silver dollar’s gross weight of 412.5 grains being a geometric equivalent to another fundamental base unit of common weight measurement. In a previous section, it was demonstrated that 412.5 grains in the form of a regular tetrahedron would have the sum of its six edges equal in length to the sum of the twelve edges of a cube containing one avoirdupois ounce of 437.5 grains. Both forms can be made from the exact same line. The correspondence between these two forms in this case is to better than 99.99%. Thus we can clearly see that the paper dollar is designed to the “gallon” unit just as the silver dollar is designed to the “ounce” unit.

         And remember, since the silver dollar coin is exactly 1.5” in diameter, and the 1-cent coin exactly .75”, they can be used to layout measures of length based on the inch. And if you need a perfect one troy ounce weight of 480 grains, you can use 10 pre-1982 copper pennies. 10 pennies after 1982 weigh exactly 25 grams. This makes $4.00 of these new cents weigh exactly 1.0 kilogram. $40.00 in our old fractional silver coinage also weighs exactly 1.0 kilogram; and $20.00 dollars in fractional imitationsilver coins (nickel clad copper, post 1964) weighs exactly 1.0 avoirdupois pound. This makes every $1.25 in dimes, quarters and halves equal to 1.0 avoirdupois ounce. This all should be common knowledge taught in our schools.


 The Gallon Unit and a Sheet of Common Paper

          Aside from toilet paper, the “paper” dollar bill is probably the most frequent standardized size piece of paper that the average American encounters on a daily basis. In all probability, its closest rival is the A size 8½” X 11” letter or copy paper. It too is a natural delineation of the gallon unit. Simply fold it into a ninety-degree angle, length-wise, at a point 7” from the edge. That’s it! Now the folded sheet of typing paper is a template for a perfect gallon unit. In the photo below two of these sheets are joined together. The space within the confines of the two sheets of paper measures 231 cubic inches. i.e. one “gallon”.

Two Sheets of Standard Letter Size Paper, Joined at Dotted Line and Folded as Specified Above, Perfectly Delineates The Modern Gallon Unit of 231 cu. in.