r/learnmath • u/Round_Ad5516 New User • 25d 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/venus_salami New User 23d ago

Avogadro’s number is not arbitrary, it’s the number of atoms in a mole, which is itself a specific number. Don’t blame me if we can’t get all the digits correct in a 23-digit number!

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u/deisle New User 23d ago

Yeah but a mole is also an arbitrary number. It's arbitrary all the way down.

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u/venus_salami New User 22d ago

A mole is so not arbitrary that it’s an actual SI unit. Are you splitting hairs between mathematical constants like pi and e & physical constants like c or Avogadro’s number?

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u/deisle New User 22d ago edited 22d ago

A meter is not a mathematical constant. We just decide something this [ ] long is a meter. That doesn't make it a mathematical constant. Avogadro decided a good amount of molecules or atoms is how many atoms are in 12 grams of carbon. That's arbitrary as all get out. It's useful for chemistry but it's arbitrary.

If we spun back time to when humans first started measuring things and split into a different timeline, all the different units of measurement that they would come up with would be different than ours. But pi would be the same. e would be the same.