The Hyperbolic Geometry Song. Hyperbolische Geometrie, also die Geometrie von Flächen mit Krümmung = -1, wird in den nächsten Folgen der "Topologie von Flächen"-Reihe noch häufiger vorkommen. Hier heute nur ein Song zum Thema von Jasmerrin. The Hyperbolic Geometry Song Lyrics by Jason Merrin Song parody of "Superman" by Five for Fighting Geometric lines In negatively curved space Can curve in all different directions In this strange but common case Not a regular line on a regular plane As it goes farther out it increases in length It's hyperbolic geometry Hyperbolic geometry's not strange In fact it is just fine Especially for a person Who wants three or more parallel lines I think it's right, I think it's a hit That outside of the Poincare disc is infinite And riding a horse is a tough battle Without a pseudosphere disc shaped saddle It's hyperbolic geometry The closer to the edge a segment gets The longer it is This will be on the quiz The closer it gets To infinity Hyperbolic triangles Which sort of look like trees Are always curved strangely So that they're less than 180 degrees Not a regular line on a regular plane Shaped like a potato chip on a subway train Not a regular line on a regular plane A complicated challenge for the human brain The human brain The human brain The human brain It's hard for the brain Not a regular line or a regular plane Shaped like a potato chip on a subway train Not a regular line on a regular plane And it's hyperbolic Hmm hmm hmm It's hyperbolic... geometry...