Geometric Properties
I thought the geometric relationships are interesting and worth thinking about. ( Primarily, put the standard deviation between .2222 and 1,2,3,4,5 to see the relationship between the Tan, Z values, Normal Probabilities )
1) - PrN1 (Purple) - Tan of an Angle
2) - Z ( Blue ) - Sum of Two Tangents
3) Equations of the Green and Red Parallel Lines - Slopes - x and y equal the probabilities of the Normal Curve.
4) Purple Triangle - Normal Probabilities
5) Gold Triangle - Standard Deviations
6) Blue Triangle - Z values which correspond to the Standard Deviations and the Normal Probabilities