Harmonic net — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
The bays that are not equal
The diagonal repeats a bay exactly and forever, and what it reaches is the whole multiples of that bay and nothing else. An arcade of 1:1.5:2 is 250 mm short of its boundary with no halving, exact after one, and an arcade of 1:1.333:2 is out of reach at every depth whatever. A measuring point lays out all three to 6e-14 px.
What a straightedge reaches on a receding line
Three marks on a receding line fix a coordinate, and everything a straightedge builds from them is a ratio of whole numbers. Three complete quadrangles put 1655 marks on the unit interval with no gap above 0.0038, a third costs two quadrangles where repeated halving never reaches one at all, and the same net built on a line that does not recede arrives at the identical 30 coordinates.
Named alongside it
The objects these essays reach for when they reach for this one.
Complete quadrangleCross-ratioDyadic rationalHarmonic conjugateStraightedge constructionVanishing pointAffine structureFixed pointGround lineIncidenceMeasuring pointPavement