What are universal constants in mathematics

Constants of Mathematics

Numbers with a certain universal meaning that appear in many contexts in mathematics and nature, sometimes astonishing at first glance, such as the circle number π & equals; 3.14159…, Euler's number e & equals; 2.71828 ..., the number τ & equals; 1.61803 ... the golden section, the Euler-Mascheroni constant (Euler's constant) γ & equals; 0.57721… and the Feigenbaum constant δ & equals; 4.66920 ...

So can π as the ratio of the circumference of the circle to the diameter of the circle (whereby it is not a matter of course, but a fact worth proving that this ratio is constant, i.e. the same for all circles) or as double the smallest positive zero of the cosine function, and e completely independent of this as the value of the exponential function at position 1, i.e.

The two numbers are, however, by the Euler formula e + 1? 0 with each other and with the basic numbers 0, 1, i connected and sag, for example, via the Euler Γ function

together. For e the surprising relationships \ (e = {\ mathrm {lim}} _ {n \ to \ infty} {(1+ \ frac {1} {n})} ^ {n} \) and \ (e = { \ mathrm {lim}} _ {n \ to \ infty} \ frac {n} {\ sqrt [n] {n!}} \), and \ (\ frac {1} {e} \) is the probability for this that given a random distribution of N Elements on N Places no element ends up in a given place.

is the limit value of the ratio of two consecutive Fibonacci numbers, which Leonardo of Pisa (called Fibonacci) introduced in his reflections on the reproduction of rabbits, and which can also be observed in botany in the growth of leaves and flowers.

Euler's constant