THE FOUNDATIONS OF FORM
THE FOUNDATIONS OF FORM
“The form of the volume unit can change into a multitude of variations. And correspondingly, a multitude of varying surface areas will result. Thus, surface changes are really variations of the volume’s form. Volume always remains the same.”
A unit of volume transforming by dividing its surface into two equal units of the same form as the original’s surface, regardless of form. . . will always have to eject the exact same amount of “excess volume” in the process of dividing into two such forms. This excess volume is so scaled that packaged as two tetrahedrons makes their triangular faces congruent to the circular cross-section of the spherical equivalent of the volume unit. In The Geometry of Form these transitional tetrahedra are called “Transit-tetrahedrons”. The volume of any of these second generation forms, if packaged as a sphere, will have its diameter equal to the height of this tetrahedron.
The form of the volume unit can change into a multitude of variations. And correspondingly, a multitude of varying surface areas will result. Thus, surface changes are really variations of the volume’s form. Volume always remains the same.
TRANSFORMING SURFACE AND VOLUME UNITS
Even though a given volume unit can take on an infinite variety of differing shapes with a wide range of surface areas associated with each, when any one of these various forms divides its surface into two equal units (identical in form to the original unit), in each case the amount of the original’s volume that cannot be accommodated within the surface of the two new forms will always be the same. This excess volume, packaged as two equal regular tetrahedrons, is so scaled that the tetrahedron’s face is congruent to the cross-section of a sphere equal in volume to the original volume quantity.
From the illustrations above it is clear that “form” is a function of surface area. The form of the volume can change into a multitude of variations. And correspondingly, a multitude of varying surface areas is possible. Thus, surface changes are really variations of the volume’s form. Volume always remains the same.
~Paul Kasprzycki
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