Generator
disc-model
A generator in the logic library, called 7 times across 1 essays. Below: what it draws at its defaults and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.
disc-model is one function. Everything below came out of it during this
build, at parameters taken from the essays rather than invented for this page — so a figure
here is the same figure a reader meets in an essay, and if the generator changes, this page
changes with it.
At its defaults
show: "euclid"
show: "triangle"
What it checks while it draws
Collected by running the family and recording what it asserted, not written here. The count is how many separate times the claim was put to the test while these drawings were made.
- a line drawn as parallel was checked and does not meet the base line inside the disc ×1
- a triangle has three vertices ×1
- each crossing point was computed and lies on both lines ×1
- every angle of the triangle is positive ×1
- every geodesic arc meets the boundary circle at a right angle ×1
- every vertex is inside the disc ×1
- exactly one of the lines through the point never meets the base line ×1
- more than one geodesic through the point misses the base line ×1
- the angles of a triangle in this model add to less than a straight angle ×1
- the defect is a positive area ×1
- the number of lines tried through the point is a whole number between 3 and 9 ×1
- the number of parallels drawn is a whole number between 1 and 9 ×1
- the outside point is inside the disc ×1
- the point is off the base geodesic ×1
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.