latin
latin 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: "transversal"
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.
- and once in each column of the first square ×1
- and once in each column of the second square ×1
- every ordered pair of symbols occurs exactly once ×1
- every symbol appears once in each row of the first square ×1
- every symbol appears once in each row of the second square ×1
- the cyclic square has transversals exactly at odd orders ×1
- the drawn order agrees with the table ×1
- the multiplier of the second square is a whole number between 1 and 7 ×1
- the neighbouring orders are shown or not ×1
- the order of the square is a whole number between 3 and 7 ×1
- the order of the squares is a whole number between 3 and 8 ×1
- the pair is built from a prime order, where the construction works ×1
- the second square uses a multiplier that makes it a different square ×1
- the size of the permuted set is a whole number between 1 and 8 ×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.
Seven points, seven lines
A geometry with seven points, in which every two points lie on exactly one line and every two lines meet in exactly one point. There are no parallels, the whole thing is built out of the two-element field, and one of its lines has to be drawn as a circle.
ComputationThe thirty-six officers
Six regiments send six officers each, one of every rank. Arrange all thirty-six in a square so that each row and each column holds every rank once and every regiment once. Euler could not, guessed why, and was wrong about the reason.