Celebrating e-day
Tomorrow 2/7 is e -day. e or Euler's number is a number that is approximately 2.718281828, so that is why someone chose 2/7 as an e-day. But e is an irrational number, so its decimal expansion is never-ending and never-repeating. Why is this number e so important that people have even named a day after it? If you've studied calculus, you already know at least part of the story. But even if you haven't, I'll try to unravel at least the most basic feature of e . Consider the exponential function e x . It is graphed below. It has one remarkable property: when you draw a tangent to it at any particular point, the SLOPE of that tangent is always the value of the function e x at that point. See below two examples: A tangent at 0.69 with slope 2 A tangent at -0.69 with slope 0.5 This feature is usually expressed this way: e x is its own derivative, or the derivative of e x is e x . There exists NO other function with that property! Here's also an interesting explanat...