Second geometrical introduction of Napier's e
by Hessel Pot (posted 8/25/11)

An exponential curve in polar coordinates is a logarithmic spiral. For all points on such a spiral curve, the angle between the direction of the curve and the direction to the center is the same. Choosing 45 degrees for this constant angle, the logarithmic curve has the following property: moving (outward) along the curve corresponding to an increase of the polar angel by ONE RADIAN, the factor by which the distance to the center increases is NAPIER’S CONSTANT.