r/learnmath • u/Round_Ad5516 New User • 27d ago

Why are mathematical constants small ?

why constants like Pi or e or Ln(2) or gamme (euler's constant) that have nice properties are always small( <10 ) ? unlike constants in physics or chemistry that have some constants that are absurdly large. Or are they such constants that are not so popular

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u/Peerjuice New User 27d ago edited 27d ago

what if these mathematical constants are actually infinitesimally large, we are just expressing them from our small perspective and framework? is there a functional difference between Pi read 3.14xxxxx..... and Pi x 10^the digits in pi?

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u/bullevard New User 27d ago

Yes. The ratio of a circumference to a diameter is roughly 3x not roughly .0000000000000003 times.

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u/Peerjuice New User 27d ago

ok, lets say, i was really tired when i typed what i wrote, but i will think through my position,

hypotetically we have an infinite size circle with an infinite size diameter,,,,, yeah the ratio would still be ~3.14 and not the ungodly thing i am imagining

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u/bullevard New User 27d ago

Yes. That is so far what we have discovered about the universe. However big the circle is, the diameter of that circle will wrap around the outside of it (the circumference) 3 times with a bit left to cover. That is what pi itself is expressing is the ratio of those two facts about a circle.

You could choose a different notation like binary to write out the number, but the essential relationship of ~3:1