Generator
algebra-tiles
A generator in the algebra library, called 8 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.
algebra-tiles 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: "solve"
show: "identity"
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 the reassembled rectangle has the same area ×1
- the four tiles are the square ×1
- the larger length is larger ×1
- the length really solves the equation ×1
- the missing corner is (b/2)² ×1
- the negative root solves it too ×1
- the picture is about positive lengths ×1
- the positive root is the one a length can be ×1
- the square tile is x² ×1
- the strips are bx however they are cut ×1
- the three pieces and the corner make a square of side x + b/2 ×1
- the two pieces are what is left of a² after b² is removed ×1
- which is completing the square, as arithmetic ×1
- which is the identity ×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.