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

A line, a point, and many parallelsA disc whose lines are arcs meeting the boundary at right angles, showing several lines through one point that never meet a given line.Pone line, one point off it, and 4 lines through the point that never meet itevery arc here meets the rim at a right angle, and every miss was checked for crossingsinside the disc

show: "euclid"

One line, one point, one parallel — in the planeA straight line and a point beside it, with several lines through the point and only one that never meets it.Pthe same picture in the ordinary plane: one line, one point, and exactly one parallelevery other line through the point was checked and meets the base line somewhere

show: "triangle"

A triangle whose angles come to 67.6 degreesA triangle in the disc model with sides drawn as arcs, and its three angles measured from the tangents.20.8°20.8°26.0°angles 20.8° + 20.8° + 26.0° = 67.6°, against 180° in the planethe shortfall is 112.4°, and in this model that number is the triangle's area

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.

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.

The whole library · What the figures prove