Generator
8 multiples of φ in 7 boxes
A generator in the number library, called 5 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.
approx 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: "error"
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.
- |qα − p| comes out below 1/N ×1
- and every convergent from the first onward breaks a record ×1
- every record-breaking fraction is a convergent ×1
- neighbouring convergents differ by a determinant of one ×1
- so p/q is within one over qN of the number itself ×1
- the constant is one this figure knows ×1
- the largest denominator is a whole number between 8 and 200 ×1
- the number of boxes is a whole number between 3 and 14 ×1
- there are record-breaking denominators to mark ×1
- two of the N + 1 points share a box, as they must ×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.