The Washington Monument: Icon by Design© 2006 Bernard I. Pietsch and S. Thompson

To the public eye, the towering blocks of masonry of the Washing-ton Monument commemorate our first president and the aspirationsof the republic. But to an inner eye, the architecture of the colossalobelisk conceals an invisible–and some might say sacred, realm ofvalue and meaning. Though not hidden from view, the higher as-pect of the monument’s design expresses itself indirectly and byimplication. It is not discerned by logic alone--one must be educat-ed to its perception.

To fully enter the mystery of the Washington Monument, it is neces-sary to go beyond that which we see and attempt to apprehend itssubtle and sublime intended form. By deconstructing the form, wewill better understand the monument itself, and also the ancientcanonical ideal which inspired the work.

Quomodo Legis? How do you read?In order to “read” the invisible aspects of the monument, we willapply the same analytical methods I have used to decipher ancientworks of art and architecture around the world. The first step in theprocess is to define the components of the visible form. This in-cludes all the lengths, angles, areas, surfaces, and volumes of theexisting structure. These attributes are the vocabulary of the lan-guage used to encode/decode its meaning.

For the Washington Monument there are three geometric compo-nents: a slightly tapering tower or shaft, a truncated four sided pyra-mid atop the shaft called the pyramidion, and a smaller pyramidsitting atop the pyramidion called the capstone. The physical de-tails of these features are listed in Appendix A. Both the dimen-sions from the U.S. Park Service and those I adopt as intended aregiven.

Actual and Intended: A note on accuracyIt is apparent from Appendix A, that some of the measures I usedepart slightly from the official dimensions suggested by the ParkService. Because no measuring of the physical world can ever becompletely accurate and because perfection in the physical worldcan only be approximated, the reader is asked to tolerate a marginof inexactitude. For the purposes of reading a monument, the vir-tue of any single measure is determined by the extent to which itaccords with the overriding harmonics of the work. By making mi-nor adjustments to the figures, the artful statement of a work be-comes visible, and its metaphors surface. Consequently, I haveadopted those values I conclude as intended by the architect. Forexample, my adopted measure of 555.555 feet for the monument’sintended height is more congruous with the overall scheme of thestructure than the published figure of 555.427 feet--a difference ofonly 1.54266 inches. Discrepancies in reporting the exact dimen-

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sions and weight of the capstone, lead us to comment on the vir-tue of the canon system of measure (which will be discussed furtheron.) We submit that if an iconic work appears to fall short of physi-cal perfection, it will nevertheless direct us to its ideal manifesta-tion. The intended communication will shine through in the purity ofits geometry. The profit gained by this approach surpasses any sup-posed error in metric accuracy.

The second part of the deciphering process involves identifying theunderlying harmonies of the structure. Some correspondences aredirect, others implied. But it is in the inferential realm where the char-acteristics that distinguish ordinary from iconic, and sacred frommundane, reveal themselves. How the Washington Monument ful-fills the following ten elements of iconic architecture proves this formto be among the world’s most extraordinary structures.

The reader is invited to participate in our process of investigation.Just as literature utilizes analogy to convey inferential meaning, wewill similarly use the languages of number, geometry and measureto articulate the deeper levels of the Washington Monument’s de-sign and give voice to its otherwise mute stones. Through discovery,that which was invisible will become, by demonstration, self-evident.

Ten Elements of Iconic ArchitectureI. The design is generated from a singular idea.Those architectural achievements most worthy of note are generat-ed from a singular principle that pervades and unifies the structure.This is especially true of the Egyptian obelisk, after which the Wash-ington Monument is modeled. In the case of the Washington Monu-ment, that singular notion is the number 10 – a number used inmany traditions to represent “unnamable perfection.” The followingis a partial listing of the ways in which the perfect 10 manifests itselfin the structure of the Washington Monument.

1. The entire monument is 10 times the height of its pyramidion.

2. The height is 10 times the length of one base side of the monu-ment.

3. The number 10 generates the volume of the perfect pyramidi-on.

▪ The volume of the pyramidion in cubic feet is the same num-ber as the anti-natural logarithm of 10.

▪ The volume of the pyramidion: 22026.46579 cubic feet. The anti-natural log of 10: 22026.46579

The entire obelisk is 10 times theheight of its pyramidion.

Old photo of the stone pyra-midion atop the shaft of theWashington Monument.

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4. The number designating the cubic volume of the capstone,94.25959089,a is very nearly 10 times the number designat-ing the length of the apothem (face plane) of the capstone,9.423579201 inches.

The shape of the Washington Monument bids the observer to lookbeyond its exterior, where the truly sublime elements of theobelisk’s geometry lay. It is the area surrounding the monumentthat defines it. The identification of this geometry, which is externalto the structure, requires the active participation of the observer--the monument’s visible form must be projected to its geometric con-clusion. In this example, we consider how the apothem or faceangle of the pyramidion (Fig.1) relates to the whole obelisk, andhow again the number 10 by extension is an integral part of its de-sign.

5. If the axis of the face plane of the pyramidion , 17.24 degrees,is projected to the ground (Fig. 2), it strikes the earth 172.4feet from the center of the obelisk at its base level.

Observation: 172.4 is 10 times the number of the decimal angle ofthe pyramidion’s face, 17.2 4 degrees. b

Observation: At a height of 555.555 feet, only a face angle of17.24 degrees could generate this convergence.

6. When the corner edge or arris angle of the pyramidion (Fig. 3)is likewise projected to the base plane of the monument, itconverges with the ground at a point 243.8 feet from the cen-ter of the obelisk (Fig. 4). See that the length of the hypote-nuse projected along the arris angle from the top of thepyramidion to the ground is 606.72 feet. c

Observation: 606.72 feet is 10 times the length of the arris cor-ner of the pyramidion, 60.67 feet.

a 94.25959091 (the reciprocal of .010609) X 3 = 282.7787727282.7787727¸9 = 31.41986363, which ¸ by 10 = canon p . The Ö of 31.419 is 5.605342419, read asinches is the length of one base side of the capstone. To find the angle, divide the length of the baseby 2 = 2.80267121. Then divide half the base by the height, 9” to get .311407912, the tangent of17.29700181 degrees. The cosine of 17.297 degrees is .994776359. Divide the height, 9” by the co-sine of 17.297° = 9.426291206, the length of apothem in inches.(Slight departures in the decimalplaces occur due to the indeterminate height of the capstone and the use of canon p.)

b 17.2439725 degrees by calculation.

c 606.7235226 feet by calculation.

Fig. 1Face angle ofthe pyramidion.

Fig. 2Face angle of the pyra-midion projected tobase level.

Fig. 4 Arris angle ofpyramidion extendedto base level.

Fig. 3 Arrisedge of pyra-midion 60.67’.

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II. The smallest component informs the whole.The Capstone Initiates the Obelisk.Herodotus, an early Greek historian, was told by temple priests inEgypt that the Great Pyramid was “built from the top down.” This isveiled language for the notion that the design of the Great Pyramidis driven by the geometry of its top portion. The uppermost orculminating detail restates the first. Likewise, in the WashingtonMonument, it is the smallest and top most component, the 9”capstone, which similarly illuminates the whole monument. Thecapstone is both the geometric conclusion of the monument’s formand also the “seed” from which the rest of the monument is generated.

The capstone has a square base, a height, an apex angle and aweight. With even the slightest adjustment of any one of theseattributes, the obelisk projected from the capstone would be altered.By selecting a perfect height of 9” and a base area of 31.41 squareinches, an angle of 17.24° is assured.

7. The ratio between volume of capstone and the volume of thepyramidion can be closely derived from the capstone:

▪ The capstone, a 9 inch pyramidal form with a base sidelength of 5.605342419 inches has a volume of94.25959091 cubic inches.

▪ The pyramidion (including capstone) is 666.6666 inches highwith a base side length of 413.8572194 inches and volumeof 38,061,732.89 cubic inches.

▪ The ratio between volume of pyramidion and capstone is:

38,061,732.89 cubic inches in pyramidion 94.25959091 cubic inches in capstone

Observation: If the number of inches in the base side length of thecapstone (5.605342419), is used as a common logarithm--we de-rive, within a small departure, the same number as the ratio be-tween the two volumes:

5.605342419

The common log of the actual ratio number of the two volumes,403,796.9242, would render a side length of the capstone at5.606163007”, a difference of only .00999853627 from the mathe-matically determined figure above.

= 403,796.9242

= 403,034.6813

Laying of the Capstone CeremonyDecember 6, 1884.

Stone Pyramidion

Aluminum capstone atop stonepyramidion--in situ.

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The Alchemy of the CapstoneWe know that the capstone was fashioned of aluminum – an unusu-al choice of material, as in its time aluminum was considered a raremetal and difficult to manufacture. Beyond its value and utility inprotecting the tip of the pyramidion from lightning, there are non-linear correspondences which intimate the integral relationship be-tween the geometry of the capstone and its aluminum complement.For example:

8. The number of pounds in one cubic foot of aluminum can beextracted from the dimensions of the capstone:

§ Divide the length of the side of the capstone’s base by 2:

§ Multiply the anti-natural log of 2.802671209 by 10:

2.802671209e = 16.48863259

16.48863259 x 10 = 164.8863259

§ 164.8863259 is the number of pounds in one cubic foot ofaluminum.

§ To find the number of pounds per cubic inch of aluminum,divide the number of pounds per cubic foot of aluminum bythe number of cubic inches in one cubic foot (1728):

164.8863259 1728 = .095420362 lbs/cubic" aluminum.

The aluminum capstone is reported to have been 9” high andweighed 100 ounces. But given that the weight of aluminum is164.8863259 lbs. per cubic foot, or 1.5267253 ounces per cubic inch-- the weight of a 94.25959091 cubic inch aluminum pyramidal formought rightly to weigh 144 ounces. Based upon its reported weight of100 ounces, we must assume that the capstone is hollow or perhapsdesigned with an aperture for affixing it to the top of the pyramidion.This unaccounted 44 ounces however, is not inconsequential. Asshown below, the missing aluminum portends alchemy invoking thehighest levels of intuition.

9. How many cubic inches in 44 ounces of aluminum? To findthe number of missing cubic inches see that:§ 1 cubic inch = 1.5267253 ounces of aluminum.§ 1 ounce aluminum = .654996704 cubic inches§ In one cubic foot there are 1728 cubic inches.§ In one cubic foot there are 2,638.181241 ounces of alumi-

num.

Aluminum1 Cubic Inch = .095420362 lbs.1 Cubic Inch = 1.5267253 oz.1 Cubic Foot = 164.8863259 lbs.1 Cubic Foot = 2,638.181241 oz.1 Oz Alumin. = .654996704 cu “.

5.605342 2

= 2.802671209

Capstone replica.

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Therefore,▪ 44 ounces of aluminum would fill 28.81985498 cubic inch-

es, (roughly the space in a large coffee cup.)

Hold that figure in mind as the significance of the differences in acapstone weighing 144 ounces and one weighing 100 ouncescomes to the surface, through the medium of gold.

Aluminum to GoldGold as a standard of value, is referenced in many ancient works.In several monuments and artifacts we have observed categoricalcrossovers between the volume of an object itself and the weightof that volume if it were transformed to gold. Although aluminumand not gold was used in the Washington Monument’s capstone,the capstone nonetheless obliquely references gold in the follow-ing remarkably synchronistic way. See that:

▪ The capstone is reported to have weighed 100 ounces.100 ounces of aluminum would have a volume of65.45804925 cubic inches.

▪ However, by our reckoning, the geometric volume of asolid aluminum capstone, 9 inches in height should weigh-in at 144 ounces, not 100 ounces, and should contain94.25959091 cubic inches.

▪ Strangely, if the capstone could be magically transformedinto gold, it would weigh 65.45804925 pounds troy --thesame number as the number of cubic inches of aluminumin a 100 ounce capstone. The number 65.45804925 in twocases, refers to both weight as pounds gold, and to vol-ume, as cubic inches of aluminum.

10. Another referent to gold is indicated by the length of the meanwidth of the shaft of the monument. Here the number of gramsin one cubic foot of gold is suggested. Although the correspon-dence is not exact, we are reminded that the object itself is anartful statement—its ability to indicate many different levels atonce is to be appreciated.

▪ The mean width of the shaft (multiplied by 10,000) rendersvery nearlyd the number of grams in one cubic foot of gold:

44.77648678‘ x 10,000 = 447,764.8678 (447,771.3305 grams gold/cu ft.)

Note: The actual exact number of grams in one cubic foot of gold is447,833.4407--approximately 62.11 grams per cubic foot departurefrom that derived by using the mean width of the shaft.

d Within (.998613)

To Find the MeanWidth of Tapered Shaft:

The base side length of theshaft + the base side lengthof the pyramidion, divided by 2= the mean width of the shaft.

Photo showing engravings and apparentlypointed tip. Compare tip with SmithsonianPhoto on previous page.

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55.06616449’ base side length+ 34.48680907’ pyramidion side

89.55297356’

89.55297356’ 2

= 44.77648678’ mean shaft width

Fig. 8 Arris angle projected toa point on the ground and usedas The radius of outer circle B.Area of B is 2 times that of areaA and 2 times the obelisk’s sur-face area.

III. Design elements are self-reinforcing and redundant.In the best-crafted monuments, every detail holographically or ho-listically supports and enlightens the whole: design, measure, andmaterial are congruous with the concept. Such mutual relatednessresults in redundancies in the underlying relationships, which mani-fest as repeating geometric patterning or reiterated numeric values.These redundancies reinforce and recapitulate the intention of theoverarching design. Some of these redundancies have been notedabove, particularly in the section on the singular idea of the monu-ment. But I suspected the existence of other redundant indicatorsin the Washington Monument, and in fact discovered several mean-ingful instances in the course of my work.

11. Observation: The perimeter of the shaft’s base restates thevolume of the pyramidion.

▪ There are 220.26 feet in the perimeter of the base of theobelisk’s shaft. This number, times one hundred approxi-mates the number of cubic feet in the pyramidion:22,026.46579 cubic feet

12. Return to demonstration Number 5, where the line along theapothem or face angle of the pyramidion is projected to theground. (Fig. 6) This line would strike the base plane172.4405081 feet from the center of the monument. Let thispoint of intersection create the radius of a circle. The area ofthis circle A, 93,429.25446 square feet, is nearly equal to thesurface area of the entire obelisk. (Fig. 7)

13. The Area of B (Fig. 8) created by extending the line of thearris angle of the pyramidion to the base plane of the obeliskis 186,858 square feet – approximately double Area A anddouble the number of square feet in the surface area of theentire obelisk. (Fig. 7)

14. Observation: The ratio of the circumference of circle A(1083.61145’) to the circumference of Circle B(1532.458008’) is also the same number as the cosine of 45degrees: .7071067816.

Fig. 6 Point of intersectionof face angle extended tobase plane, as radius ofcircle A.

Fig. 7 Area ofall surfaces ofobelisk =area of circleA above and½ of areasA+B below.

1083.611450 ‘ A1532.458008 ‘ B

= .7071067816

Cosine 45°.7071067816

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IV. Iconic architecture references its location.Many ancient monumental works we have investigated, especiallyobelisks, show themselves to be geodetically site specific, operat-ing as markers on the earth. The Washington Monument announc-es its own latitude in at least two different ways; and as we will seebelow the evidence suggests that its longitudinal positioning mayhave been consciously selected as well.

From my own measurements I determined that the sides of themonument are actually slightly skewed--the base is not exactlysquare. Though slight, the difference in the two major diagonalangles is an important geometric signifier.

15. Observation: The length of the Southeast/Northwest diagonalof the monument’s base indicates the geographic latitude ofthe site. The diagonal of the base of the Washington Monu-ment in feet, divided by 100 and taken as the cosine of anangle, derives almost exactly the latitude of the site.

▪ The South East to North West diagonal measure of the baseof the obelisk is approximately 77.836 feet.

77.836 feet 100 = .77836

.77836 is the cosine of the angle 38° 53' 21" ... the latitude of the site of the Monument.

This observation is confirmed and reinforced by another method ofidentifying latitude from the form of the obelisk in the following:

16. The latitude of the site of the Washington Monument can bederived from the capstone’s apothem length.

▪ The number of the capstone’s apothem face length, 9.426inches, approximates the number of degrees of precessionof a Foucault pendulum on the latitude of the monument. e

Absent an apex, the precise height of the capstone is properly inde-terminate. If the capstone were taken to be exactly 8.99465 inch-es in height, (a difference of .00535 inches,) the degreesprecession derived from the apothem’s length, 9.417 inches acti-vated as a pendulum, would indicate the monument’s actual lati-tude of 38° 53’ 21”.

e The formula for deriving the precession of a Foucault pendulum is: 15º x sine ofthe latitude = degrees precession per hour. The actual latitude of the WM is38.88948º (TerraServe Web Map Service), the sine of the latitude would be.6278190681 x 15º = 9.417286022º precession per hour. See that 9.417 is not9.426, the inches of the capstone’s apothem length derived trigonometricallyfrom a 9” capstone height. Working backward from the apothem’s length numberderived from the 9” capstone, would render a latitude of 38.93360578 or 38° 56’00”.98, a location slightly to the north.

Diagonal of base.

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V. Iconic architecture references universal constants.In many instances, monumental architecture commemorates andencodes the great constants of the universe, both mathematicaland physical. The Washington Monument participates in this re-spect through its referent to pi.

17. Observation: The area of the base of the capstone is

10 x or 31.41 square inches.f

18. The shaft of the Washington Monument is actually a truncat-ed pyramidal form. The sides of the shaft, were they not inter-rupted by the pyramidion, would come to their geometricconclusion 777.777 feet above the top of the monument.(Fig.11)

The Egyptian Great Pyramid is also truncated--its top does notform an apex or point, g but rather a rectangular platform. (Fig. 12)The top of the shaft of the Washington Monument, (coincident withthe base of its pyramidion) is 1,189.429 square feet in area. Thetop of the Great Pyramid is 1,892.798083 square feet in area. Therelationship between the two areas can be represented by the fol-lowing simple ratio with an interesting correspondence with pi .Again the elegance of communication exercised by consummatearchitectural design is affirmed.

19. Another way to find the area of the top of the shaft (or thearea of the base of the pyramidion) is derived by the follow-ing formula which again summons e, the base of natural loga-rithms and the height of the pyramidion:

20. Observation: A second novel derivation of a number close tothe base of natural logarithms can be conjured from the num-ber for the feet in the base side length of the obelisk.

f 3.141986363 is the figure we use for p in our computations in ancient metrolo-gy.g We hold the 206th to have been the topmost and last stone course intended onthe physical pyramid. More information about the significance of the 206 stonecourses or levels can be found in the article, "New Perspectives on the GreatPyramid," on our website: www.sonic.net/bernard.

Geometric model of theGreat Pyramid.

Model from above show-ing truncated apex.

Fig. 12 Photo top of GreatPyramid.

Fig. 11Sides ofshaft extend-ed to apex.

11892.798083 sq’1189.439153 sq’

= 1.59135 X 10 = 1.59135x 2

10e x 3 ¸ 55.5555 = 1,189.429153 square feet.

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▪ The mean base side of the obelisk is 55.06616 feet. Squarethe side, divide by 2 and then divide by 100. Now find thenatural log to get a number which approximates e, the baseof natural logarithms: h

The precise number of the base of natural logarithms:2.718281828.

21. The line projected from the apex along the face of the pyra-midion to the ground would be 581.7 feet in length. Multiplythis number by 10 and read it as inches: 5,817 inches. 5,817inches is also 484.75 feet – an approximate indicator for thetangent of one second of arc: .000004848136. i

22. Observation: In a perfect world, one could expect that thelongitude of the Washington Monument would exactly indi-cate the reciprocal of the number of seconds of arc in a 360°circle, divided by one billion:

1 1,296,000 seconds ¸ 1,000,000,000 = 77.16049383

§ Read sexigesimally, 77.16049383° is 77° 09′ 37″ W.

(The actual longitude of the Monument is: 77.03503° or 77° 02′ 06.108 ″ West)

The constraints of the swampy and uneven terrain surrounding themonument may have precluded it from perfect placement.

VI. Iconic architecture actualizes the co-in-cidence of thelength of a line with a period of time.Architecture can only indicate a length—perhaps in the height of astructure, a doorway or the perimeter of a building. It is contingentupon the observer to take what is given one step further and ask,

“What does this length signify? Is there another level to the informa-tion presented here? The answer to the question and the model forthe architectural metaphor lies with a simple instrument: the pre-cessing pendulum. This most elementary apparatus enables com-munication from one dimension to another—from length of line to

h e (2.718281828) A mathematical constant used in describing rates of changein natural growth and decay behaviors. The function of e might be used for ex-ample to calculate the rate of decay of a radio active isotope, or the rate ofgrowth of bacteria, or the spread of a disease in an epidemic, or the pattern of abouncing ball as it diminishes to a halt.i .000004848136 is the trigonometric tangent of one second of arc: 00º 00' 01"

Face angle extended toground level: 581.7 feet.

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)1515.141236 100

= 2.718753539(-e

3032.282471 = 1515.141236 2

55.06616449 = 3032.2824712

length of time. Through the pendulum, architecture can invoketime and all the dynamics associated with notions of frequency andduration from a simple length.j

23. Observation: Let the perfect indicated height of the obelisk,555.555’ represent the length of a Foucault pendulum.

§ A pendulum 555.555’ would swing back and forth one timein a period of 26.12011309 seconds.§ Find that the square root of the height 555.555’ is:

23.57022604.§ The ratio of the square root of the height to the period of its

time as a pendulum generates another “perfect” number:1.228068554.

26.12011309 = 1.108182545 23.57022604

1.1081825452 = 1.228068554

1.22806554 is a primary number in the most synchronistic sense. Itrepresents the node of unification between a measure of time anda measure of length. Using this perfect unit, a builder can indicatea period of time using a linear measure of length: a pendulumlength of 1.22806554 feet beats a period of time lasting1.22806554 seconds. At this node, time and length are commensu-rate –length in time and length in feet are the same number.

VII. Iconic architecture is astronomically oriented.ILinks to Saturn or Kronos as the source of measure are never farfrom the roots of iconic architecture. Saturn’s timing or position rela-tive to other planets is often referenced. k

24. Observation: A pendulum the height of the pyramidion, 55.5feet high, would beat 10609 times in one canon day. l 10609references the number of canon days in the orbit of the plan-et Saturn.

25. A strange and wonderful relationship exists between the num-ber representing the cubic volume of the capstone,94.25959091 cu” and the reciprocal of the number represent-ing Canon days m in the orbit of the planet Saturn. (Note

j Formula for determining the time a certain length would beat as a pendulum: 2p L = T L= Length in feet, G = gravity, 32.15481179' , T = Time in seconds. G

k For more background on this most significant correlation, see our article“Saturn, Source of Measure” online @ The Philosopher’s Stone:www.sonic.net/bernard/l 10609.80724 times in 87636 seconds or one sacred day of 1460.6 minutes(360 sacred days to one year).m A canon (sacred) year is adjusted to 360 Earth days, as opposed to 365.25astronomical days.

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that this figure diverges only in last two decimal places fromthat of the volume derived mathematically.)

1 .010609

26. Observation: If the angles at the base of the shaft were to beextended upward beyond the pyramidion to their geometricapex, (Fig.13) they would converge at a point 1,333.333 feetabove the base. In another synchronistic correspondence,that height in a process coupled with 10609 (mentioned earli-er as a number referencing Kronos or Saturn) indicates thediameter of the Earth, a necessary referent from which toreckon all other measures. n

10609 1,333.333

27. Observation: An indicator of the rate of the precession of theequinoxes can be extracted from the pyramidion’s arrislength, 60.672 feet:

60.672 feet = .60672 100 .60672 = 1.8344047

1.8344047 = .0050956 360

.0050956 x 10 = 50.9 seconds of arc precession/year.

VIII. The form is contained by a geometric receptacle: Thebox it came in.

The physical Washington Monument has an "essential" conceptualcounterpart disclosed through geometry. This invisible or comple-mentary form reveals information about the existential form not oth-erwise apparent or available. Just as a block of stone contains thesculpture before it is released by the sculptor, so too can the geom-etry of the shaft and pyramidion of the Washington Monument(exclusive of the capstone) o be conceived as contained in an imagi-nary rectangular box. (Fig.13a) We call this imaginary solid "thebox it came in." The square base of the monument (55.06' perside)p is the bottom of the box, and the distance to the top of the

n In the canon system, the circumference of the Earth is 25,000 canon miles.There are 5,258.16 feet in one canon mile, commensurate with the number ofminutes in one Sacred Year of 360 days: 525,816 minutes.o The aluminum capstone is categorically different than the rest of the monument.Conceptually, it is in the world as part of the monument, but it is not “of” theworld nor of the same substance. The capstone informs from without. Note thatthe height of the shaft, 500 feet divided by 9 = the height of the pyramidion:55.55 feet.p 55.06616449'

= 94.25959091 as cubic inches in capstone.

= 7.9567502 x 1000 = 7,956.75 miles Earth’s diameter.

Fig. 13 Sidesconverging to apex.Fig. 13 Sidesconverging to apex.

Fig. 13a Fig. 13b

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e

3

pyramidion, minus the capstone,q its height. The volume of this rect-angular container would be:

base2 x height = volume or

3,032.28 sq feet r x 554.81 feet s = 1,682,363.274 cubic feet

The process of containment in a rectangular form can be carriedfurther by reducing the rectangular volume to a perfect cube thatwould exactly encase the form’s volume. (Fig. 14) This process of

“homogenizing” or “coercing” a form into a perfect cubic counterpartallows it to be compared to other cubes of different media – so that,for example, the densities of different materials can be correlated,as between gold, aluminum, water, jade, granite etc.

28. The rectangular box (Fig. 13b) which would contain the shaftand pyramidion of the Washington Monument (minus cap-stone), would have a volume of 1,682,363.274 cubic feet. Ifthe rectangular volume of 1,682,363.274 cubic feet (Fig. 13b)were reshaped into a perfect cube, that cube would have amajor diagonal of 206 feet t-- the same number as the 20.6inches of the common cubit multiplied by 10. (Fig.15)

29. The 118.934-foot vertice edge of such a cube (Fig. 15) multi-plied by 10 would be nearly the same number as the numberof square feet in the area of the base of the WashingtonMonument’s pyramidion: 1189.34. The square root of thatnumber being an indicator for the side of the pyramidion’sbase:

Ö1189.34 = 34.48680907

IX. Iconic architecture references other iconic works.Because the Washington Monument is modeled after the Egyptianobelisk, it is circumstantially linked to the tradition of ancient archi-tects, and thus certain correspondences with the Egyptian systemare insured. In the following analysis we find yet more homage tothe Great Pyramid of Cheops.

30. Observation: A referent to the Great Pyramid is derived fromthe length of the apothem (face) of the pyramidion (Fig. 16)of the Washington Monument which is 58.17 feet.58.17 x 100 = 5,817. Read as inches, 5,817 is coincidentallythe geometric height of the completed Great Pyramid.

q See that by "tempering" the height of the capstone to 8.85708726", the perfect box "coerced" to acube with 206' diagonal can be constructed as shown in the next exercise.

r 3,032.282471 sq. feet

s 554.8174649 feet

t 206 is a germinal number generating other canon numbers: as 20.6 inches in the common cubit,as 206 courses in the Great Pyramid, 20.6 minutes difference per day between the solar year andsacred year of 360 days.

Fig 15. Cube with206’ major diagonal.

Fig. 14. Volume of13b as a cube.

Fig. 16. Length of Apo-them 58.17’

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31. Observation: Another similar reference arises when the apo-them angle of 17.24º, is extended from apex (peak) to thelevel of the base of the obelisk. ( Fig. 17) As an hypotenusestriking the ground, it will be 581.7 feet in length, again onetenth the number of the number of inches in the height of theGreat Pyramid.

581.7 x 10 = 5817

32. Observation: The height of the entire Washington Monumentis 555.555 feet, or 6,666.666 inches. If the height in inches isdivided by the number of inches in the canon remenu of 17.4inches, we arrive at a height of 381.4814813 remen. Seethat this figure divided by 10 and read as an angle becomes38.1481 degrees. 38.1481 degrees is the complement of51.8518587 º, the angle of the side of the Great Pyramid: 51º51’ 06" .69 (Fig. 18)

X. Iconic art transcends time and culture.Monumental and iconic works of art awaken the recognition of thesacred within and are accessible to the perceiving individual regard-less of his or her culture or epoch. The deepest expression of icon-ic form is perennial. Its intention can be read and understoodthrough its essential geometry. More than an image, an icon sug-gests potentiality beyond the image it represents. As an icon of thenation, the Washington Monument points to a higher state of evolu-tion, and ultimately to a “more perfect” union.

We know from history that the founding fathers were committed tothe establishment of a national system of weights and measures.Their dream was to bring into the world a system wherein all unitsassigned as standards would have relevant relationships to all oth-er standards in the system--weight, temperature, distance,volume—all unified by congruent principles. It was a vision not real-ized but the intent was clear. The ideals of truth, justice, liberty andindividuality were to be epitomized by the notion of commensurabili-ty which, in its highest form, is the understanding of harmony.

As a public structure, the Washington Monument may ultimatelyprove of greatest benefit and utility as an instrument of learning. Inthe future, school children might come not only to experience theWashington Monument’s grandeur, but to be energized by the ad-venture of discovering its integrity – the service of each attribute tothe whole. Working collaboratively with protractor, ruler, and calcu-lator, the intellect and intuition of each student would investigateour national icon as form, metaphor and consummate demonstra-tion of e pluribus unum.

u Our survey defines the Canon Remen perfectly at 17.47572816 inches. We have found numerousapplication and reference to this measure in Egyptian/Hebrew works.

Fig 17. Apothem angle extend-ed 581.7 feet to ground level.

Fig. 18 . Angle of the Great Pyra-mid: 51° 51’.

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The preceding observations are a beginning. A great work of art,be it music or literature or architecture, continues to enlighten theinner landscape of those whom it engages, even as she or heevolves to deeper levels of awareness. The Washington Monu-ment is just such a work–a singularity among the world’s most no-ble structures.

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The authors welcome comments, suggestions and corrections. Youmay contact Bernard by email at

bernard@sonic.net

To view a 3-part video presentationof some of the ideas expressed here visit our

YouTube Channel, “Written In Stone” at

www.youtube.com/bernardpietsch

�

Additional work by Bernard Pietsch can also be found online at“The Philosopher’s Stone”

www.sonic.net/bernard

Appendices follow.Appendix A: Dimensions of Washington Monument

Appendix B:Characteristics that distinguish iconic/sacred architec-ture from the mundane.

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The following chart lists the published dimensions of the site and the reconciled measures utilized forthis treatment. Note: the decimal numbers are derived trigonometrically. 2/17/2006

Appendix A: Dimensions of Washington Monument Adopted figures Published figures

Height of shaft 500’ 500'Height of pyramidion 55.555’ 55’ 5 1/8”Height of capstone 9” 8.75”-8.875”-8.9”Total Height of the Monument 555.555’ 555' 5 1/8"

Av. width of base side of shaft 55.06616449’ 55' 1½"Perimeter of base of shaft (4 sides) 222’Diagonal length of base of shaft 77.87531665’Surface area of one side of shaft 22,357.10195 sq ‘ 22,354.22301 sq’Total surface area of shaft (4 sides) 89,428.4078 sq ‘ 89,416.89203 sq’Total Surface area of the Monument 93,566.26612 sq’

Face angle of pyramidion (apothem) 17.2439725° 17°Length of pyramidion apothem 58.17024188’Arris angle of pyramidion 23.69964257°Arris length of pyramidion 60.7065337’ 60.67235226’Width of one base side of pyramidion 34.4881’ 34' 5½" – 34’6”Perimeter of base of pyramidion (4 sides)137.9524065 ‘ 138’Surface area of one side of pyramidion 1,003.090607 sq’Surface area of pyramidion (4 sides+capstone) 4,012.362428 sq ‘Surface area of pyramidion w/o capstone 4,011.631171 sq’

Width of one base side of capstone 5.605342418” 5.6"Perimeter of base of capstone (4 sides) 22.42136967”Surface area of one side of capstone 26.32524814 sq “Surface area of capstone (4 sides) 105.3009926 sq “Arris length of capstone 9.828913856 “from 10Apothem length of capstone 9.423583184” from 10

Volume of shaft 1,055,427.906 cu ‘ 1,002,495.822 cu’Volume of pyramidion (includes capstone) 22,026.46581 cu’ 22,026.465 cu’Volume of capstone 94.25959091 cu”Weight of capstone 100 oz. or 144 oz. ? 100 oz.Total Volume of the Monument 1,024,522.288 cu’

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Appendix B:Characteristics that distinguish iconic/sacred architecture from the mundane.

§ The truly sacred in art and architecture is intangible. It is neither physical nor apprehended bythe senses. As the sacred resides only within, it can only be indicated or implied from without.

§ The iconic emerges into the world from a singular idea, encapsulating a grand view, incorpo-rating a whole concept.

§ Its meaning is conveyed through geometry and measure, material, location and time.

§ In order to access the deeper levels of a sacred work, participation from the observer is re-quired.§ When understood correctly iconic art can be entered at any single point.§ It often references astronomical, metrological, and physical constants.§ It is accessible to future generations, regardless of culture or epoch.§ The intention of an iconic work can be reconstructed from a fragment of the original.§ The integrity of an iconic work is characterized by redundant facets which fortify its intended

meaning.§ It shares aspects with other monumental work in the world and has relationship to other monu-

mental markers.§ Iconic forms may be contained or embedded in a larger geometric receptacle.§ Monumental architecture is often site specific and self-referencing via its geographic, magnet-

ic or astronomical framework.§ As with the Great Pyramid, iconic work can identify itself in the context of historical time in

some manner: aligning with or matching astronomical asterisks and events or biologicalgrowth patterns established over time e.g. tree rings, coral reefs, glacial deposits.§ The conclusion/origin of an iconic design may be exterior to its physical architecture.§ Nothing is hidden or secret in iconic art—that which is revealed is always apparent when seen

properly.§ The unified iconic field is guaranteed by the perennial emergence of a canon of measure

wherein all units of time, distance, weight etc. are commensurate with one another. The funda-mental unit is the canon inch. It is derived from and defined by its relationship to the secondof time. Through the mechanism of the swinging pendulum, that unit of length which beats amatching unit of time demonstrates the convergence of categories in the domain of intuition

"wherein all things may be considered."§ The iconic expresses itself elegantly—the intended referent is never far from its geometric

indicator. Iconic principles are expressed as geometric and numerical meta-phors; form is antecedent to physical expression.

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