Coordinate grid, four quadrants to 10

What is printed on this sheet

A coordinate grid with all four quadrants on it. Each axis runs from -10 to 10, which is twenty units across and twenty down, and that makes 400 cells on the sheet. Forty-four lines are drawn in all, and two of them, the axes themselves, are drawn heavier than the rest.

The axes cross at the origin and the origin is at the middle of the drawing rather than in a corner. That is what four quadrants means here, and it is the reason the sheet arrives with its numbering already printed: a grid whose origin is somewhere particular has to be drawn knowing where that somewhere is.

Square cells, and why that is not a detail

The cells are square by construction. The horizontal unit and the vertical unit are set to the same length when the grid is drawn, rather than each taking whatever space happens to be left over in its direction.

This matters more than it sounds. A grid whose cells are slightly taller than they are wide looks perfectly reasonable and quietly misrepresents everything put on it. A circle plotted on it comes out an ellipse. A shape counted out ten across and ten down is not a square. A figure drawn and then reflected does not match its reflection. Nothing on the sheet warns of any of that, because the sheet has no way of knowing what was intended, and by the time it shows it has been on every drawing made on that paper.

Changing the span, and printing it true

The span is a setting: the grid can be numbered further out than 10 or brought in closer, and the number of quadrants goes with it, a single-quadrant sheet putting the origin in the corner instead of the middle. Paper is set to A4, Letter, Legal or A5, the ink to grey, blue or black, and name-and-date lines can be added at the head. The file comes out as PDF, PNG or SVG, drawn in the browser and sent nowhere.

Print at 100 per cent, or Actual size, and then check the bar in the foot margin: it is drawn 50 mm long and labelled with that length. A Fit to page print of A4 onto Letter scales at 94.1 per cent and brings the bar back at about 47 mm.

Note that scaling shrinks both directions equally, so the cells stay square while getting smaller. Squareness is no test of the print size. The bar is.