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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:
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