Here I have done a complex geometric analysis of the Normal Curve.
1) Take the Time to Look at the Diagram and explore it's values - Pick a value - Study entire diagram - Make slow changes or Specific changes of Values via the slider.
2) The Math at the Bottom right is only for reference of those values shown which will come up in the geometry.
3) The Main thing to take away from this is how these values are " Golden " in this Geometry: 1 , 1.08, 1.16 , 1.35 , 1.64 , 1.79 , 2.83 , 1.41 , 3.14 , 3.81 - See Point (M)
4) Take a slow pace and look at all tangent Lines and Points that are Listed and Find all Values shown above at each "slider value" measurement.