A very special repeated division

A decrease with geometric progression is characterized by a divisor and how often the divisor is applied. Smaller steps with roots of the divisor (fractioned exponents) are ignored here. If the start concentration c0 is set to 1, all results with any divisor will be within 1 and the border 0. For a division by 2 or by 3 well-known expressions exist in different languages, but not for a division by e, although such an expression would give a better understanding:

	c0 /2 /2 /2 /2	bisections	c0 * 2-4
	c0 /3 /3 /3 /3	trisections	c0 * 3-4
	c0 /e /e /e /e	"e-sections"	c0 * e-4
	c0 /10 /10 /10 /10		c0 * 10-4

In the following special cascade with different vessels the concentration 1 g/L in vessel A will be bisected after filling of the smaller vessel B and again bisected after filling of the smaller vessel C. But the disadvantage of such a cascade is: A "unit vessel" is no longer valid. The great advantage of e are equal-sized vessels in the dilution model. A lot of mathematical formulas are simplified, too, by using e, although it is possible to use any other value (base) on principle.