# Build a sheet of graph paper with rotation

I have:

Graphics[{
GeometricTransformation[
{Gray, Dashed,
Table[InfiniteLine[{k, 0}, {0, 1}], {k, -6, 6}],
Table[InfiniteLine[{0, k}, {1, 0}], {k, -6, 6}],},
RotationMatrix[π/6]]},
Axes -> True, AxesStyle -> Bold, PlotRange -> 5]


which produces this image: Can anyone share a suggestion how I might make this a full sheet of graph paper (8.5x11) to print out?

• Change the 6s to 12s and the 5 to 10? – bill s May 1 '17 at 17:00
• I think you need to make it clear how you expect to fill an 8.5 x 11 page with a square image. Also, what should be the distance between to ruled lines on the printed page? – m_goldberg May 1 '17 at 17:23
• A large variety of printable graph paper is available online (free download). You may find an isometric graph paper, an isometric dot paper or a hypometric grid paper that suits your purpose. – LouisB May 1 '17 at 18:22

Here is some code that produces a PDF file that should print something close to what you describe.

letter = {612, 792}; (* postscript point size *)
a4 = {596 , 842};
θ = ArcTan[2, 3];
vlines = Table[GeometricTransformation[
InfiniteLine[{0, 0}, {0, 1}],
{RotationMatrix[θ], {k, 0}}], {k, -16, 16}];
hlines = Table[GeometricTransformation[
InfiniteLine[{0, 0}, {1, 0}],
{RotationMatrix[θ], {0, k}}], {k, -16, 16}];
img = Graphics[{Gray, Dashed, vlines, hlines},
Axes -> True,
AxesStyle -> {{Bold}, {Thick}},
BaseStyle -> {FontSize -> 14},
PlotRange -> {{-4, 4}, {-5, 5}},
ImageSize -> letter];
Export["paper.pdf", img]


Some difference between your original code and this version are

• define letter and a4 as paper sizes
• change angle so the lines go through axis integers
• apply different axis styles, just to see the effect
• use BaseStyle to set the font size
• use ImageSize to select either letter or a4
• Export the image as a PDF

The above seems to work. That is, my PDF viewer recognizes the exported file as a letter size page. Here is what it looks like: • Thanks for the help. There are some nice things in here to learn. – David May 3 '17 at 6:00