*If I had only known, I would have been a locksmith." Albert Einstein*

From the late 1960's, until his death in July 1994, Joseph Edward Batter was fascinated with

the Geometry of Nature. In particular, Pi, Phi, and their application to "Earth Measure".

His extensive investigation yielded an array of profound real world discoveries

regarding Measure and Number.

Joe Batter was an accomplished "design draftsman".

Throughout the 1960's he produced the working technical drawings for office towers,

physical plants, hardrock mines and such. The profession demands more than steady hands,

sharp eyes and a disciplined mind. Drafting engineered designs of complex structures

requires fixed attention to detail as well as the capacity to view

and comprehend whole systems.

Joe and I met in the Fall of 1979, in Vancouver, Canada, over a coffee shop discussion

around phi, the Golden Section. At the time my interest was primarily in the artistic applications.

By then he was adept with numbers, solving eight decimal divisions longhand. After several

engaging discussions, and the introduction of a scientific calculator, a collaboration began.

My main role was to illustrate graphically, with pen and ink pointillism, Joe's numbers

and lines; to ground his "Earth measure", in a natural setting:

From the late 1960's, until his death in July 1994, Joseph Edward Batter was fascinated with

the Geometry of Nature. In particular, Pi, Phi, and their application to "Earth Measure".

His extensive investigation yielded an array of profound real world discoveries

regarding Measure and Number.

Joe Batter was an accomplished "design draftsman".

Throughout the 1960's he produced the working technical drawings for office towers,

physical plants, hardrock mines and such. The profession demands more than steady hands,

sharp eyes and a disciplined mind. Drafting engineered designs of complex structures

requires fixed attention to detail as well as the capacity to view

and comprehend whole systems.

Joe and I met in the Fall of 1979, in Vancouver, Canada, over a coffee shop discussion

around phi, the Golden Section. At the time my interest was primarily in the artistic applications.

By then he was adept with numbers, solving eight decimal divisions longhand. After several

engaging discussions, and the introduction of a scientific calculator, a collaboration began.

My main role was to illustrate graphically, with pen and ink pointillism, Joe's numbers

and lines; to ground his "Earth measure", in a natural setting:

TriTen: Venus One......(detail)

Suspended above the hand, the diameter of the sphere: .4181 lix

is one billionth Earths' diameter.

is one billionth Earths' diameter.

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

Nature is replete with this ratio in the proportions of area, volume

and the palisading growth of crystals and spirals.

( see: Ian Stewart. Mathematical Recreations, Scientific American: Jan 1995)

phive

to the power of point phive

times point phive

plus point phive

equals phi

1.618033988749 squared = 2.618033988749 = phi +1

1 / 1.618033988749 (the reciprocal) = .618033988749 = phi -1

.618033988749 x .618033988749 + .618033988749 = 1

n phibonacci x 5 to the power of .5 = n lucas

eg: phibo #19 = 4181

4181 x2.2360679775

Nature is replete with this ratio in the proportions of area, volume

and the palisading growth of crystals and spirals.

( see: Ian Stewart. Mathematical Recreations, Scientific American: Jan 1995)

__The Number Phive__phive

to the power of point phive

times point phive

plus point phive

equals phi

1.618033988749 squared = 2.618033988749 = phi +1

1 / 1.618033988749 (the reciprocal) = .618033988749 = phi -1

.618033988749 x .618033988749 + .618033988749 = 1

__The Power of Point Phive__n phibonacci x 5 to the power of .5 = n lucas

eg: phibo #19 = 4181

4181 x

*= 9349.0002 = phi to the 19th*

= 9349 ( #19 Lucas )

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 are 5 numbers centered on 500 :

191 / 500 = .382

309 / 500 = .618

500 / 500 = 1

809 / 500 = 1.618

1309 / 500 = 2.618

The sum of these phive = 3118

= 9349 ( #19 Lucas )

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 are 5 numbers centered on 500 :

191 / 500 = .382

309 / 500 = .618

500 / 500 = 1

809 / 500 = 1.618

1309 / 500 = 2.618

The sum of these phive = 3118