What's the most badass mathematical constant? I gotta give the award to pi, followed very closely by e, with a distant third going to phi. Just look at some of the mind-blowing identities and formulas derived by Ramanujan to see why pi and e are most certainly badass to the extreme. These two constants are just so versatile and they are related to practically everything, even the most abstract mathematical ideas that seem to be completely unrelated to pi or e. So what do you think about these amazing constants? And if you have any mind blowing formulas or anything like that involving constants in cool ways that you'd like to share, this is the place. Word.
But is time really constant? I know little about relativity, but doesn't it say that time varies with, among other things, speed, for example? Time is badass, but I wouldn't say that it's constant, no?
I personally would put e in first place and pi in second. Of course they are tied together by e^(j pi)=-1, so you can always get one from the other. But I think it is easier to use that formula to solve for pi given e than vice versa. -Dale
Hum, the Fine Structure Constant, alpha, includes pi, and is even more messed up. http://en.wikipedia.org/wiki/Fine_structure_constant
Haha I'm assuming DaleSpam must be a EE or something of the sort. j is the same as "i" or sqrt(-1). Normally people working with electronics use j, since i is reserved for current.
I think that e is probably the coolest constant. Working with derivatives, e is the derivative of itself...which is quite weird since it models itself...haha. Going into physics, the Universal Gravitational Constant (Newton's Law of Gravitation) as well as Coulombs Constant (Electric Forces) are also pretty cool. These two make the world what it is today, which I think a few might appreciate. B)
Hehe, yes on both accounts: i = j = sqrt(-1) and I am an engineer. I use i and j fairly interchangably and not very consistently either way. But I generally prefer j for exactly the reason you mentioned. -Dale
Backing up my assertion that pi is the most amazing constant: The sum of (1/n)^2 from n=1 to infinity equals (pi^2)/6. Holy crap. And the sum of (1/n)^4 is (pi^4)/90. There is actually a closed form for all even powers that follow a similar pattern. However, no one has been able to come up with a closed form for odd exponents. Now come on, how can you argue with that? OK but then for every sweet pi formula there's an equally sweet formula for e...so maybe e is equally badass. Who knows?
I never really thought of a favorite constant, but pi and e seem pretty interesting mathematically. In physics, I seem more intrigued by G from it's peculiarly low value.
