27 lines on a cubic
Here's the best thing I know about the number 27. Any smooth surface described by a cubic equation has 27 lines on it!
In general this is true only for complex
surfaces, where we look at complex solutions of the cubic equation. For these it takes two complex numbers (rather than two real ones) to say where you are. So they're kind of hard to visualize.
But for this particular surface, drawn by Greg Egan, we can see all 27 lines even if we only look at the real
surface formed by the real
This is the tip of an iceberg I'm just starting to drill down into. For more, visit:http://blogs.ams.org/visualinsight/2016/02/15/27-lines-on-a-cubic-surface/#geometry