Reality → Base → Tools → Constants
Euler’s famous identity ei π + 1 = 0 combines the three numbers in a beautifully simple equation, a masterpiece of mathematical genius.
Jacob Bernoulli was first to calculate the approximate value of e based on a relatively simple example of compounded interest calculation (see Sheet). The number e is also the limit of an infinite convergent series of the reciprocals of factorials and occurs frequently in probability theory and calculus. The function y = ex is its own derivative, making it the 'natural' exponential function.
Euler’s formula e i x = cos x + i sin x makes a wonderful connection between exponential and trigonometric functions.
Mathematical operations with alternating currents (or voltages) of different frequency, amplitude, and phase become relatively easy when the sin/cos functions are converted to exponential form with the help of complex numbers.
The number π not only occurs frequently in geometrical and trigonometrical formulas, but also in normal distribution, and in classic and modern physics.
The energy-like product of pressure p and volume V is proportional to absolute temperature T and amount of substance N, with the constant R constituting the factor of proportionality.
The product of energy and time is called action (Wirkung in German) and has the same dimension (J s) as angular momentum.
In quantum mechanics, ħ is often preferred to h because it simplifies many formulas. The Planck length is a very curious constant denoting the incredibly small length of 1.6 × 10-34 meter which has no known physical meaning. It was computed by Planck from ħ, G, and c0 as part of an effort to create a system of units of measurement solely based on natural constants.
For instance, the speed of light is reduced by 0.03% in air and by 25% in water.