### 17 equations that changed the world

By Vasos L Pavlika, on 15 November 2021

I have read this book by Ian Stewart and it is wonderful. It is strange that Newton’s second law of motion is omitted but as the Navier-Stokes equation (which is just this law) is included I will not object. Of course, there are some misnomers here namely Pythagoras’ theorem as the result was known numerically to the Babylonians computing triples in sexagesimal (base 60, which we still have remnants of in the measurement of time), furthermore Euler was not the first to be led to the square root of -1, this was first done by the great Italian algebraist Cardano (1501-1576) in solving cubic and quartic equations. I am not sure which one of these beautiful equations is my favourite but the one that caused the most fascination was Euler’s polyhedral formula which amazed me as I suppose on looking at geometric figures (normal Mathematicians) do not notice that V+F=E+2, where V=the number of vertices (nodes), F=the number of faces, E=the number of edges (lines) and from here he spawned the geometric discipline now known as topology (named after the Greek for place). We all know of a topological map (most train networks are topologically accurate but not geometrically accurate) i.e. the position of a node relative to another is important but not its distance or angular orientation.