Occurence of fundamental mathematical constants

[Loren Booda]

0, 1, phi (the Golden ratio), e, pi, delta (Feigenbaum's constant) and comparatively many other fundamental, dimensionless mathematical constants occur on the interval 0 to 5. With a potential infinity of numbers to choose from, why does such a confluence exist?

 

[Sangoku]

For the physical constant.. perhaps they lie on [0,5] due to the strength of the interactions (weak, strong) in many cases using 'Natural units' you can set them equal to value '1'

 

[Nesk]

For the physical constant.. perhaps they lie on [0,5] due to the strength of the interactions (weak, strong) in many cases using 'Natural units' you can set them equal to value '1'

But physical constants are in no way limited to [0,5] like mathematical constants appear to be. Just consider Planck's constant and Avogadro's number in SI units.

 

[CRGreathouse]

0, 1, phi (the Golden ratio), e, pi, delta (Feigenbaum's constant) and comparatively many other fundamental, dimensionless mathematical constants occur on the interval 0 to 5. With a potential infinity of numbers to choose from, why does such a confluence exist?

Maybe small ones are easy to discover. Maybe our idea of 'small' is tied to the size of these constants (no, really -- 1 is the measure by which we count, so if it were 'larger' so would be our concept of 'small').

Maybe it's just easier to find and work with small constants -- perhaps the order of the Monster group is just as fundamental, but less has been done with it since it's so large.

 

[Blouge]

Maybe it's because the infinite sums that start off involving small numbers like 1, 2, 3, .. or 1!, 2!, 3!, etc. yield the most interesting and general constants:

e=1+1+1/2+1/6+1/24+1/120+... approx = 2 + 1/2 = 2.5
pi= 4 - 4/3 + 4/5 - 4/7 +... approx = 4 - 4/3 = 2.66666...
phi = (1 + 1/phi) = (1 + 1/(1+1/phi)) = ... approx = 1 + 1 / (1 + 1) = 1.5
euler mascheroni gamma = (1 - ln 2/1) + (1/2 - ln 3/2) + (1/3 - ln 4/3) + ...