points out uniformity of construction and variety of external
forms. The sections are unavoidably triangular, running from
the middle of the wall till the ridge. The baseline equals
the internal diameter of the space plus two halves of the
walls thickness and is measured from the entrance as the walls'
thickness plus the internal depth of useful space. The
height of the triangle is the root of three halves, but
can also be composed from three equally long sticks used as
toys by shepherds during pasture. Thus theory coupled with
mathematics joins with practice of the simple builders' development
that uses theoretical principles although not even being aware
of their existence.
Corbelling is a construction more
than six thousand years old: the Hypogeum in Malta shows it
in the carved subterranean sanctuary built more than four
thousand years ago.
and proportions: man's proportion is golden
section, and is in use at the stone shelters, but
for shelter is equilateral triangle typical
Hereby the most important element
affecting composition and its recognisable order is the relation
of dimensions. Relations vary, from simple to highly complex
ones, but the most effective ones are those, which can be
easily constructed; these are the most distinct and easily
From the circle and derived square
(internal or external) the relation with square root of
two emerges. The square root of two is the diagonal of
a square whose baseline is one. Paper used in day-to-day practice
The gold section is a limitless
relation, both in enlargement and reduction. It is built
on the human scale, thus is easily acceptable. It is however
difficult to express, by using two squares and the diagonal
of two squares, which equals the square root of five. The
gold section is seen in nature, both in detail and in whole
entities, even in space.
The sides of an Egyptian triangle measure 3, 4 and 5 and it
has one right angle. In times primeval Egyptians determined
right angles with it when working in the desert. Today we
know it as the relations of a television screen.
in practice: triangle, inscribed on the top
stone simple shepherds play with three sticks: triangle,
left: Grans (Provence), France
The corbelling construction brings
a new relation: the equilateral triangle. It's height equals
the baseline multiplied by the half of the square root of
three, as was proven by Pythagoras.
Shepherds played with wooden sticks:
from three equally long sticks they composed the only possible
form: the equilateral triangle.
By using three sticks we can also determine the half of the
square root of three. This is the height of corbelling up
till the ridge.
The principle isn't only an aid
in construction: by opposite use we can determine the height
of construction built by corbelling quite accurately. Theoretical
analysis is proven even in practice.