“If I’d only known I would have been a locksmith”
~ Albert Einstein

Triten Measure and lixcaliber,
the Golden Section scale of “Earth Measure”


The first of four illustrations in the series, TriTen Measure, is an exact scale drawing of
the Solar Systems planetary mean distances based on the Astronomical Unit and the Golden Section.

drawings, exterior dimensions: 2.207 x 3.571 lix,   (phi16x phi17divided by 1000)

The scale lixcaliber is an artifact discovered in TriTen as the final draft neared completion and is
here imbedded in the North face of the Great Pyramid, number 5E on the lix grid.
Its origin is elsewhere.

The Astronomical Unit and the Soul of the British Foot

“Never chase after buses, wo/men or cosmological theories.
There will always be another along in a few minutes” Isaac Asimov

The AU., the mean distance from the Sun to the Earth, is the basis for measuring long distances within
the Solar System. Joe Batter believed it was one source of a universal Unit of measure. At the time he was
plotting Planetary mean distance numbers from the 1979 Astronomical Ephemeris, with Feet, in tenths, (1/600).

Joe first converted the A.U. into Feet. The number is usually given now in Meters:
1.4959787 x 1011 meters

Converting to Feet by dividing Meters by 0.3048 = 4.9080666 x 1011 Feet. Because he was working to
a high degree of accuracy a remarkable order of coincidence occurred within the Planetary mean
distance numbers. When the pattern wouldn’t gel we began to suspect
the Unit might not be the British Foot after all.

One of the exercises Joe performed with the A.U. in Feet was to multiply it by 33:

A.U. = (4.9080666 x 1011) x 33 = 1.619661978 x 1013 Feet.

He noticed the result is a close approximation of the Golden Section
and divided it by 1.618033988 to produce the Conversion Ratio:
1.619661978 / 1.618033988 = 1.001006153

Conversely, dividing the Golden Section by 33 produces the Astronomical Unit but not in feet.
Joe applied the “ancient” conversion to other known measurements such as Planetary mean
distances, Light Speed and the Great Pyramid at Gizeh. The results confirm the existence
of a Planetary System of  Measure based on the Golden Section and pi.
Joe Batter named the System “TriTen” and the unit “lix”.

1.001006(153) feet = 1 lix

“l” is for light speed, “i” is the Planetary mean distance set and ‘”x” is for Time.
This introduction reveals some of the “phi nominal” rediscoveries we’ve made with them:

phi and the a.u.

(1.6180339887 / 33) x 1013 = 4.9031333 x 1011lix = 1 A.U.

(4.9080666 feet – 4.9031333 lix = .0049333)

Light Speed:

982,582,582.5825 lix per second

Joe felt this astonishing correction to a repeating number is, “not too surprising considering
Light Speed is measured in Earth seconds and the mean distance to the Sun is a function
of the Golden Section and the number 33″.

25 x 5 x 33 = 5280,   52 x 33 = 825

S.O.L. = 2.997924580 x 108 meters per sec / 0.3048 / 982582582.5825 = 1.001005996

lix conversion, 1.001006153 – 1.001005996 = .000000157

The length of one Earth second fluctuates through Time as Light “speed” does and by extension
“distances” through Space. For accurate measurements the unit must be adjustable. Joe was so intrigued
by the adjustment he later worked out the conversions to eleven decimals of accuracy, the “lix Ephemeris”.

982,582,582.58259 lix x 1.001006 ft  / 5280 miles = 186,282.3978 mps

A phibonacci formula for the lix conversion:
phibo #11 = 89,    phibo #5 = 5
(89 / 5phi) – 9.999999 = (89 / 8.09016995) – 9.999999 = 1.001005996

in 333 seconds Light travels 3272 x 108 lix:
982,582,582.5825 x 333 = 327,199,999,999,9725 lix

pi, phi and 33

+ 1618
= 33033

The first “0″ in pi occurs at the 33 digit.
There is also a 0 at digit 55 and 66.

There are 33 digits
between the first three 0′s of phi.

The first seven phibonacci numbers:
1 + 1 + 2 + 3 + 5 + 8 + 13 =

more connections between phi and pi

Sun: (Cypher, “0″ on the lix grid)


Solar Diameter = 4.56234 x 109 lix

4,562,340,000 (lix) x 1.001006 (ft) x 0.3048 (meters) / 1000 (km) = 1,392,000.177 km

(10 / 1.618034) – 1.618 = 4.56234

SOHO screensaver

Golden Section

For newcomers and aficionados, a brief refresher on phi, the Golden Section Ratio:

1 : 6180339887+

Nature is replete with the golden ratio in the proportions of area, volume, the pallisading growth
of crystals such as quartz and spirals, like the seed rows on a Sunflower.


number phive

5.5 x .5 + .5 = 1.6180339887 = phi

Phive to the power of point phive times point phive plus point phive equals phi.

1.61803398872 = 2.6180339887 = phi + 1
(5.5 + 3) x .5 = 2.6180339887

1 / 1.6180339887, the reciprocal, = .6180339887 = phi – 1

.6180339887 x .6180339887 + .6180339887 = 1

The Power of point phive

N phibonacci x 5.5 = phiN = NLucas

e.g.) phibo #19 = 4181, 4181 x 5.5 = 9349.0002 = phi19 = 9349 = #19 Lucas

(The Lucas addition series produces the powers of phi: 1, 3, 4, 7, 11, 18, 29, 47, 76, 123 etc.)

Long viewed as an aesthetic standard in Architecture and Art, the “Golden” section occurs
when the ratio between the shorter section of a line to its longer section is exactly equal
to the ratio of the longer section and the whole line.

numerically: .38196601 is to .61803398 as .61803398 is to 1

All addition series produce approximations of phi.
One that does so in a unique way is the “One Phive” series: 1 + 5 = 6 + 5 = 11 + 6 = 17 etc.

1, 5, 6, 11, 17, 28, 45, 73, 118, 191, 309, 500, 809, 1309, 2118, etc.
between 118 and 2118, phive numbers are centred on 500:

191 /  500 .382
309 / 500 .618
500 / 500 1
809 / 500 1.618
1309 / 500 2.618
sum = 3118

The lix unit and the Great Pyramid at Gizeh

After examining in great detail the slope angles, hypotenuse, of quartz crystal, the Great Pyramid and two
right angles derived from pi and phi, Joe Batter resolved the “pyrameter” triangle, relative to the four faces
of the Great Pyramid and the slope angle of the six triangular faces of quartz crystal:
51 degrees, 47.2 minutes, + or – 3 minutes
(the three minute variation is due to the electrical sensitivity of quartz)


Balanced on a Point

“I have evidence to show that the core masonry and the paving stones of the Great Pyramid were
positioned according to this triangle. It is not a right angle but approximately 89 degrees, 56 minutes.
This accounts for its longevity as the Great Pyramid was among the first built along the Nile Valley.
Subsequent Pyramids, built with the plumb bob method deteriorated over time as earthquakes loosened
the stonework. The masonry stones of the Great Pyramid slope four minutes, down towards the centre.
Built this way, earthquakes tend to tighten the joints.”
“quotes”, j.e.b.

Using the Pyrameter triangle as a module Joe plotted the mean distances of the Planets
and cross section of the Great Pyramid, revealing the lix grid and the scale, “lixcaliber”.

Further applications of lix:

After his death in 1994 i continued the exploration, opening web pages in 1996 and discovering, in 2008:

The Numerical Source of Great Pyramid Chamber dimensions.

lix start

John N. Harris writes: “I am happy to report I have been able to independantly confirm the
fundamental form of the Great Pyramid, (pyrameter triangle), developed by Joseph Batter
and yourself as described on your “lix unit” page.”

John Harris’ beautiful and thought provoking site: Spira Solaris

useful and/or interesting links:


Saturns North Pole with long term hexagonal feature.
A huge and stunning example of the “cone cube”, which Joe referred to as “the basic shape of energy”.


Nexus: Under Seige: The Golden Mean in Architecture

Golden Knott                 Beauty of the Golden Section

Tim Hunklers’ massive collection of Great Pyramid data

Geometry Net     Pyramids of Egypt

phibo           Astronomy Canada         Kepple Henge


a joey bee philix production
joseph edward batter and stephen langton goulet
site opened dec 22 1996
updated October, 2011

copyright 2012 stephen langton goulet. all rights reserved.