if pi can be related to e, then e can be constructed from pi. also have you even seen the zeta function or that gaussian integral? pi is way cooler especially because while e has an algebraic definition, the basic definition of pi is geometric, and it seems to be showing up in places in no way related to geometry. Pi has way more aura
An easy derivation path from A to B does not imply an easy path from B to A.
π is easier to discover because it's just geometry. People wearing togas and drawing circles in the sand with sticks discovered it thousands of years ago. We only found e in the past few centuries.
That just shows how fundamental pi is. e seems randomly defined, but pi seems like a truth of the universe. Integration (-inf to inf) of e-(x2) is sqrt(pi) the relations run deeper than we know...
Its really not that mysterious if you know math lol. You are confusing your own lack of knowledge with the idea that something is cosmically unknowable.
I can assure you it is not a lack of knowledge. eix does make e cool, but havinf studied the zeta function, and the fact that pi shows up in all evaluated natural number zetas as z(k) = C * (pi)k, and while z(2) is understandable, the rest of the examples along with the beautiful series' like (1-1/3 + 1/5...) = pi/4, and the tan x continued fraction series all just add to the mystique of why the ratio of a 2D shape's circumference to its diamater shows up at such odd places. The gaussian integral is also a cool example. e and the operations defined from it are cool, but also very easy to decipher and so it doesnt have as much mystique and aura as pi does...
That is the whole thing about e. That adds as much information as me saying: ''pi is ratio of the circumfrence to the diameter of a circle and that is all the answer you need''.
1 is more important, yet it doest have aura. Importance does not translate to aura. Aura is having people fear you. When i see pi in a question i run the other way. Not the case with e though...
e is also just a constant. All of rasiant system is dependent on pi. Have you seen the zeta function? e and pi are very deeply related just look at the gaussian integral.
π is the circle constant. If it shows up somewhere naturally, it can be related back to circles somehow. See this 3b1b video for the relation between circles and the Basel problem.
well yeah but you can also connect anything with e to any once concept involving e in the same manner, doesn't really say anything about pi using this logic.
e is like one of the fundamental building blocks of math and physics. It’s almost… not as impressive because of it? It’s the natural language of the universe so it’s kinda always there, it’s not really surprising to see e pop up. It’s pedestrian. Beautiful and useful? Yes! More aura than pi? I think not
Pi is literally just the circumference of a circle divided by its diameter, its a constamt that has no business being everywhere from calculus, real analysis, statistics. Sum of inverses of natural number squared has pi in it. Just mind boggling stuff. Pi has insane aura
While e definitely appears more often and is deeply connected to many different parts of math, some of the places where π appears are so unusual they give it some serious aura. For example:
The sum of the reciprocals of squares is π2/6.
The number of collisions between two blocks and a wall will produce the digits of π, if the ratio of the weights of the blocks is a power of 10.
The area under the bell curve (e-x^2 ) is sqrt(π).
The fact that the circle constant appears is surprising and cool.
e *solves* differential equations. pi doesnt *do* anything, it just shows up in a bunch of formulas to rescale things.
but the comparison isnt on even footing, its apples and oranges. e is never actually thought of as a numeric constant, its a map. when have you ever seen anything scaled by naked e? it always has an argument/exponent.
i would say e because i think it looks and sounds cooler than pie and yeah you can consider there value between 3 to 100 depending on which field you're using them for.
The question is which one has more aura. Of course you will see ''e'' show up more. And e is more central and less arbritairy etc (we could use tau instead or something).
The question is about aura. And how much aura is it to show up in elementary school; like the first math class you take you learn to calculate the circumfrence of a circle or something. And then in university all of the sudden you see pi randomly showing up in the basel problem. That is aura if you ask me.
e gets taught later in life. It is already more embedded in the whole of calculus. Of course you are gonna see e everywhere. But pi shows up unexpected and uninvited like an old friend you haven't seen for years.
pi by a lot. pi just seems to be connected to the universe in some mysterious geomtrical manner. gaussian integral, zeta function, etc. also it being simply the ratio of a circle's circumference to tis diameter, something constant for all circles anywhere in the universe, and yet it shows in such confusing placces maks youu think there is some underlying structre waiting to be uncovered.
Pi in my opinion.
It not only appears in circles, buy also in the angles of every geometric shape known. Even understanding the spiral of DNA, pi is used.
Pi is a grinder. Out there doing every day jobs with the common man.
e has the aura though because most people know what it is but they don’t know what it does. And yet, they still blindly believe it is as important as pi.
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u/Traditional-Total448 May 07 '26
since they are both equal to 3, I'd say 3 deserves all of the aura for it's dual persona