[Verse 1] In ancient Greece, a theorem born A squared plus B squared equals C The triangle's secret, mathematical dawn Distance formula, plain to see Right angles hiding truths so deep This pattern makes the cosmos speak [Chorus] One equation, many faces Distance measured through all spaces A squared plus B squared, that's the key Sine squared plus cosine makes it one Complex numbers, vectors run The heartbeat of geometry [Verse 2] Draw a circle, radius one Sine and cosine dance around Their squares will add to always sum To unity, forever bound Unit circle tells the tale Pythagorean truth prevails [Chorus] One equation, many faces Distance measured through all spaces A squared plus B squared, that's the key Sine squared plus cosine makes it one Complex numbers, vectors run The heartbeat of geometry [Bridge] Complex plane with X and Y Magnitude is Z times Z-bar Vector length we calculate Dot product shows us how far Infinitesimal DS squared Differential forms declared [Verse 3] When this breaks, the space will bend Einstein's relativity Curved spacetime where straight lines end But flat space lives eternally In this simple, pure design Mathematical paradigm [Final Chorus] One equation, many faces Distance measured through all spaces Sum of squares in every tongue From triangles to space and time This eternal, perfect rhyme The first song that math has sung [Outro] A squared plus B squared equals C The heartbeat of reality
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