Hah. The real hidden question was actually “How does one arrive at e specifically by looking at the universe, and why does it work like that?”, I think.
I agree that they’re not the most clear stuff, but I’ve listed them as the most accessible wonder-inducing mathematics-related points of interest.
That’s an interesting question, and I have no idea about the answer.. If aliens asked me to define e, I’d start talking about exponential functions that were their own derivative. But I have no idea if that’s the historical motivation for noticing e.
Pi is obviously much easier, since it is part of the ratios linking circle diameter to circle perimeter and circle area.
Pi is obviously much easier, since it is part of the ratios linking circle diameter to circle perimeter and circle area.
If I had to explain Pi to real aliens that somehow understood English but not our mathematics, I would start with straight lines of a fixed length (radius) that share one (fixed) endpoint and where the other (movable) endpoints get gradually closer and closer.
Some multiple of pi is the ratio you apparently get as you compare those lengths and extrapolate for infinitely-closer-and-closer lines.
Sounds simple enough, as far as explaining abstract concepts to real aliens goes.
In my imagination, I have a chalkboard, but no other ability to communicate. So, lots of drawing circles (with emphasis on diameters and circumferences).
Hah. The real hidden question was actually “How does one arrive at e specifically by looking at the universe, and why does it work like that?”, I think.
I agree that they’re not the most clear stuff, but I’ve listed them as the most accessible wonder-inducing mathematics-related points of interest.
That’s an interesting question, and I have no idea about the answer.. If aliens asked me to define e, I’d start talking about exponential functions that were their own derivative. But I have no idea if that’s the historical motivation for noticing e.
Pi is obviously much easier, since it is part of the ratios linking circle diameter to circle perimeter and circle area.
If I had to explain Pi to real aliens that somehow understood English but not our mathematics, I would start with straight lines of a fixed length (radius) that share one (fixed) endpoint and where the other (movable) endpoints get gradually closer and closer.
Some multiple of pi is the ratio you apparently get as you compare those lengths and extrapolate for infinitely-closer-and-closer lines.
Sounds simple enough, as far as explaining abstract concepts to real aliens goes.
In my imagination, I have a chalkboard, but no other ability to communicate. So, lots of drawing circles (with emphasis on diameters and circumferences).