fixed-point
fixed-point 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: "hairy"
show: "index"
show: "disc"
What it checks while it draws
Collected by running the family and listening to lib/verify.js, not written
here. The count is how many separate times this build put that claim to the test.
- and has no direction to choose there ×1
- and it lies inside the disc ×1
- and sits on it ×1
- at the left end the map moves the point right or not at all ×1
- at the right end it moves it left or not at all ×1
- dipole has the index it claims ×1
- every arrow is tangent to the sphere ×1
- every orbit runs into the fixed point ×1
- saddle has the index it claims ×1
- source has the index it claims ×1
- the field is one the figure knows ×1
- the field vanishes at the pole ×1
- the fixed point is unique ×1
- the map is one the figure knows ×1
- the map keeps the interval inside itself ×1
- the map sends the disc into itself ×1
- the point found really is fixed ×1
- the solved point is fixed, first coordinate ×1
- the solved point is fixed, second ×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.
Nothing on a sphere can be combed flat
Point an arrow along the surface at every place on a sphere, continuously, and somewhere an arrow has to vanish. On a doughnut it can be done. The difference between the two is a number that was already known from counting corners.
TopologySomething always stays put
Stir a cup of coffee however violently and let it settle. Some molecule is exactly where it started. Crumple a map and drop it on the region it depicts, and one point lies over the place it names.