# Aesthetic Old Geometry

### by Donald Daniel, 2019

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I appreciate the aesthetic value of some very old gothic
architecture more than modern architecture. A case in point is
Durham cathedral. There is a covered walkway outside the base
of the building that impressed me for some mysterious
subconscious reason. I first noticed it about 38 minutes into
the second Harry Potter movie, but you can find pictures of
Durham cathedral on the internet.

The walkway has repeated identical sections. I made a guess
at the geometric construction of one of the sections, shown in
this figure.

The geometric construction proceeds as follows. The points
1 through 6 are equally spaced on a straight horizontal line.
The arc from 2 to 7 pivots about 5 as the center of the arc. 2
is the center of the arc 5 to 7. The arcs that rise out of
points 3 and 4 to meet the previously mentioned arcs are
centered at 1 and 6. The small arcs connecting 2,3,4,5 are an
embellishment that the architect added. I guessed that the
angle of these arcs at each end was 50 degrees above the
horizontal.

This figure was drawn using the software described at this
website here.

A gothic revival design appeals to me. While circular
trefoils seem blandly romanesque to me, triangular trefoils
seem decisively gothic. Below is a triangular gothic trefoil
drawn with the same software as before. The sides of the
triangle are not straight, they are arcs. The center of each
arc is the vertex of the triangle opposite the arc. Inner and
outer arcs are drawn to make a curved bar. Both use the same
center. The inner arc is decorated with a cusp in the center
half of the arc. The cusp is made with a pair of small arcs.
Cusps like this are a major feature of gothic revival
design.

For a long time string instruments related to the violin
have had artistic holes in the wooden body of the instrument.
The holes in all such instruments are very similar, but not
identical. There seems to be no exact procedure for
constructing the geometry of the hole. I used the previously
mentioned software for my attempt at making the hole geometry.
The drawing consists only of simple arcs and lines. It is
drawn with 6 lines and 8 arcs:

up one level

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