Civil Engineering Reference
In-Depth Information
To describe an octagon is not quite so direct. h e face angles of an octagon are
each 1 ½ right angles. h eorem: the interior angles of a regular polygon equal twice
the number of right angles as the i gure has sides minus 4, i.e. 2n - 4. h us the
face angles of an octagon = 16 - 4 = 12 right angles, and each face angle = 12/8 =
1½ right angles, i.e. the face angles of an octagon are 135°. h is is easily obtained
by erecting a perpendicular at the desired point and bisecting the exterior right
angle to give two angles of 45°. h e supplementary (internal) angle to 45° is 90° +
45°, i.e. the desired 135°. h e simple proceedure for setting out an octagon is then
to mark out a side of the desired length on the desired orientation. Construct an
angle of 135° at each extremity. Bisect these angles to give the centre of the cir-
cumscribing circle. Mark out this circle with the radius so obtained, and step of
round its circumference the 8 sides of the desired octagon.
Although simple hexagonal and octagonal plans are straight forward to set out,
they depend upon angular (geometric) construction. h us if they are of complex
development with internal compartments, then almost inevitably a regular design
will involve irrational linear measurements. Complex designs of this nature occur
in later antiquity, e.g. h e Church of h eotokos, 484 AD on Mt Gerizim (Krau-
theimer, p. 151, i g 118) and the analysis of these plans is very complicated. Such
plans are clearly concerned with numbers and proportions. h ey are products
of the intellectual idealism of Neo-Platonism—expressions of the mystique and
symbolism of numbers in quest of the “perfect”. h ey are thus more properly
concerned with design rather than setting out.
Regular
polygons
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Curvilinear (Oval) Buildings
Buildings on curved plans other than round buildings are virtually all oval or
ovoid in form, and they are of Roman date. It is the plan adopted by the Romans
for their amphitheatres.
h e oval is generated as a conic section, a strong point of Greek mathematics.
However the oval form never seems to have been adopted into Greek architectural
design. h e oval curve (or ellipse) is dei ned as the path traced out by a point
moving so that the sum of its distance from two i xed points (the foci) remains
the same. h e curve varies in appearance from rotund to virtually parallel sided
depending on the distance apart of the foci. h e limiting forms are a circle and
a straight line. When the foci are identical in position (no distance apart) then
the curve is a circle (the major and minor axis are identical). When the foci
are an ini nite distance apart, it is a straight line (the major axis ini nite and no
minor axis).
h ere is a well known practical method of drawing an ellipse. Locate the foci
as desired. Take a length of cord equal to the combined distance of any point on
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