Calculating e

--[[

This program attempts to approximate the value of
the mathematical constant e, which is about 2.718

This method uses Euler's method for solving
differential equations to approximate the function
defined by the differential equation dy/dx = y,
which if solved analytically is e^x. So, as x
approaches 1, we get closer and closer to e.

With xStep at 0.00001, it is accurate to 4 decimals

While there are much better and more accurate ways
to calculate e, this is most likely the simplest.

]]

local xStep = 0.00001 -- Smaller = more accurate

-- Give the initial condition, when x = 0, y = 1
local ypos = 1
local lslope = 1

for i=1, 1/xStep do
    ypos = ypos + (lslope)*xStep
    lslope = ypos
end

print(ypos)