We have number like pi and √2 that are problematic in some cases.
Does it exists a branch of math that uses them as units and recalculate every number in that scale to simplify some calculus?
Like
-π, 0,π,2π,3π and so on.
In: 2
We like our scale because we can count 1, 2, 3 on our fingers. And there’s a one-to-one correspondence between our fingers and the apples we’re counting. 3 fingers = 3 apples. I’ll let others opine about having a second scale as you suggest.
There’s a wikipedia page that covers this: https://en.wikipedia.org/wiki/Non-integer_base_of_numeration#Base_%CF%80
We can use a different _base_ to make certain solutions more elegant within that base, but its utility is limited if you need to convert to another base.
For Pi you’re talking about radians, where 2PI radians represents the 360 degrees to go around a circle. This is used in a large number of applications – trigonometry, geometry, representations of cyclical/oscillating motion, and solutions to a number of equations.
You cant really do that as π is a ratio between a circles circumference and its diameter.
You could say a value of π is equal to say 1 but then the diameter of the circle will just be 1/π because that ratio would not change becauseyou made π an integer now the diameter isn’t an integer
What this means is you could create a number set for π like you suggested 1π, 2π etc but when you go back to the source, the diameter to circumference ratio, it will always be the same.
Trigonometry comes to mind. Basically anything that has to do with circles/sections of circles uses radians; 2π radians = 360 degrees
You can, but it pretty much requires using pi(or a multiple of pi) as a base, and it would make a lot of other numbers be as irregular as pi.
it would simplify some calculus, that’s why we use this scale (it’s called radians) but it makes most other – and more importantly most of our day-to-day – calculations A LOT more complex and difficult
Yes. For specific applications we do. Angles are (or can be) expressed in fractions of pi. Complex numbers have a fraction of sqrt(-1) aka i component. Distance between celestial bodies is described in light years. Mass of celestial bodies is described in masses of Jupiter/the sun…
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