Re: Special nature of e and pi?

Keta wrote:
There are certain numbers which have very special properties on
Mathematics, such as e and pi. Why do they naturally happen in so many
equations and formulas?

The function e^x has the special property that it's derivitive is the
same as the function. It shows up in many differential equations.
Anything for which the rate is proportional to the amount present will
be exponential in nature. So it shows up in things like interest
calculations and cooling bodies, etc.

Circular, spherical, and elliptical shapes have pi as a proportionality
constant for things like volume and surface area.

What's so "natural" or "special" on them?

They turn up in lots of physical situations, and so we use them a lot.
There are other constants that have similar status, but we don't go
gaga over them as much for some reason. The digits 0 and 1 spring to
mind. Nobody is astonished that 0 and 1 turn up a lot, and -1 too, for
that matter.

Is it
because of the choice of the numeral system, or would they still appear
on other base?

Numbers do not change when you change the base, only the representation
of them. There is an interesting algorithm to calculate the Kth digit
of pi, but the answer is in hexadecimal.

I mean, would there be in a new base numbers which
retain the same properties?

The numbers pi and e are the same numbers in a different base. In base
pi, pi has the representation '1', but it will still represent the
ratio of the circumference of a circle divided by its diameter.

Is it possible to construct another algebra
based on those numbers?

This question is vague to me.
Speaking of algebra, this one is famous:

e^(i*pi) = -1

where i is the square root of -1.


Thanks in advance for your answers.

.