Geometry PDFs Are a Mess if You Don't Know What to Look For
You grab a geometry PDF from the internet expecting clean diagrams and readable notation. More often than not you get something where the triangles are rendered as blurry blobs, the LaTeX symbols didn't compile right, and the page numbers reference a table of contents that doesn't exist. I've spent years collecting and building geometry resources, and the people who actually understand what makes one PDF worth keeping versus one that just sits in a folder never to be opened tend to share a few specific habits. It starts with vector-based diagrams rather than embedded raster images. A diagram drawn with TikZ, Asymptote, or even a well-exported SVG becomes crisp at any zoom level. Raster screenshots of GeoGebra or Desmos look fine on your monitor and then turn into pixelated garbage when someone prints them on A4 paper for an exam review session. I learned this the hard way back in 2019 when I compiled a 60-page Euclidean geometry workbook with screenshots from my tablet and tried to use it for a study group. Three people couldn't read the angle marks on page twelve. I rewrote every figure using Asymptote and the whole thing became usable. Searchable text is non-negotiable. If the PDF doesn't have selectable text underneath the equations, you can't find a specific theorem by keyword. That sounds obvious until you're hunting for Ptolemy's theorem in an 80-page document and the author embedded everything as images because their conversion tool swallowed the text layer.
Building a Geometry PDF That Actually Works
The workflow most people skip over is the diagram production step. Here's how it actually plays out in practice. Create your figures in Asymptote or TikZ inside a standalone TeX document first. Render them to EPS or PDF directly. Then import those into your main LaTeX file using the graphicx package. This keeps every diagram as a vector object in the final PDF. If you need to change a single angle or relabel a point, you edit the Asymptote source, re-render that one figure, and replace the imported PDF. You don't reopen a screenshot from three months ago and try to guess which program made it. For coordinate geometry and computational problems, I use a Python script with matplotlib set to backend 'pdf' and export directly. The output is vector-based and integrates cleanly into LaTeX. People who export to PNG from matplotlib and then embed those get burned eventually when line thicknesses vanish on certain printers or when the resolution looks bad at 200 percent zoom.
Set your document class to standalone or article with a4paper and a 10pt or 11pt base font size. Geometry textbooks that stick to 9pt or smaller are painful to read with dense proofs. I once compiled a collection of contest geometry problems in 9pt to fit more on each page and ended up spending more time adjusting margins than anything else. Going to 11pt with reasonable margins and a comfortable line spacing of 1.15 actually fit more content because the diagrams didn't need to be crammed into narrow columns.
Get the Full Details
The Things PDFs for Geometry Get Wrong Regularly
The most common failure point is not the text or the layout. It's the theorem numbering and cross-referencing. When a PDF has five chapters and you reference theorem 3.7 from section 4.2, every hyperlink needs to resolve correctly. I found this out after distributing a comprehensive inequality geometry PDF to a small group and having half of them report that clicking theorem references jumped to completely unrelated sections. The issue was that I'd merged content from two separate compilations without re-running after the merge. Cross-reference labels get orphaned during merges if you aren't careful. Always do a full rebuild after combining files. Another problem I see constantly is color dependence in diagrams. A configuration that relies on red and blue lines to distinguish between two different cevians becomes impossible to follow in black-and-white print. I switched to using dashed versus solid line styles combined with distinct labels and never looked back. It costs nothing in production time and saves the document from becoming unreadable the moment someone prints it without color. There's also the issue of embedded fonts. If your PDF uses custom or obscure fonts without embedding them properly, readers on different systems get substitution glyphs. Greek letters turning into Latin characters is a frequent complaint in geometry PDFs because packages like unicode-math or newtxmath sometimes behave inconsistently across TeX distributions. I settled on using the standard lmroman and lmodern font families with amsmath for consistent rendering everywhere.
Where This Approach Falls Short
No geometry PDF is going to be perfect. Vector diagrams are fragile. A single missing semicolon in an Asymptote block will break the entire compilation. If you're not comfortable debugging TeX errors, your timeline explodes. I've spent entire afternoons chasing a missing brace in a figure definition that had nothing to do with the actual content I was trying to produce. Large PDFs with many high-resolution figures also become slow to open on older machines. A 200-page geometry compendium with dozens of vector diagrams can take 15 to 20 seconds to load on a standard laptop, and scrolling becomes choppy. If your audience includes people on older hardware, consider splitting large documents into themed volumes rather than producing one massive file. There's also no substitute for actual mathematical rigor in the text itself. A beautifully typeset PDF with incorrect or incomplete proofs is worse than a poorly formatted one with correct content because it builds false confidence. I've seen this repeatedly in competition geometry materials where the author assumes the reader will fill in the gap, but the gap is the entire useful part of the argument. Always verify each step, especially when adapting known results from other sources.
Where to Find Solid Geometry PDFs
The most reliable sources are university course pages, competition training materials from recognized programs like the IMO shortlist archives, and publications from mathematical societies. AoPS publishes several geometry PDFs that follow good typographic standards. The Geometry Revisited text by Coxeter and Greitzer is widely available in public domain form and typeset correctly. For contest-level material, check the Chinese GM training notes that circulate through math olympiad communities, though these vary in quality depending on who converted them to PDF. When you evaluate a geometry PDF, check these things before investing time in it: the diagrams are vector-based, the theorem references work when you click them, the notation is consistent throughout, and the proofs contain complete logical steps rather than skipping to conclusions. Most free geometry PDFs fail at least two of those checks.
