Favorite Equation...
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Favorite Equation...
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Hard work never killed anybody, but why take a chance? -- Charlie McCarthy
They missed a biggie! (Score:5, Interesting)
No variables, though...
Re:They missed a biggie! (Score:4, Insightful)
The above is NOT an equation.
But this is an equation: e^(i*pi)+1 = 0
Re:They missed a biggie! (Score:4, Informative)
e^(i*pi)+1 = 0
is an equality. An equation is something like F=ma.
Re:They missed a biggie! (Score:3, Funny)
Euler's Identity (Score:5, Interesting)
It comes from the fact that e^(i * theta ) can be expressed in terms of the taylor series for e^(x): the sum of all terms x^n/n! for each integer value of n from one to infinity.
Plug in i * theta for x - you get:
i*theta^1 / 1 - theta^2/2 - i*theta^3/3 + theta^4/4
if you separate out the terms with i in them, you get the taylor series for cos(theta) and i times the taylor series for sin(theta), and you get Euler's relation:
e^(i*theta) = cos(theta) + i*sin(theta) [planetmath.org]
plug in pi for theta, and you get cos(pi) + i*sin(pi). cos(pi)=-1 and sin(pi)=0, so you get -1+0, or -1. e^(i*pi) = -1, or:
e^(i*pi)+1 = 0
Mathematicians like that last form more, because it is the equation that simply relates the five most fundamental constants of mathematics; pi, e, i, 1, and 0. Really amazing, when you think about it.
Re:Euler's Identity (Score:4, Insightful)
I've never understood the fascination with "e" -- Wow, we found this fudge factor that makes our math come out even, and look, we can invent all these problems where it also makes the math come out even! "e", the magic fudge factor. I grant that it's useful, but I find PI much more interesting, as it's based on a physical object I can grasp (the circle). "e" may be the basis for "natural" logarithms, but I find it all artificial and never got the "natural" part.
E isn't just some "fudge factor" (Score:4, Interesting)
What are you thinking? They didn't just sit down and guess numbers ("hmm, 2.9? no, smaller than that. 2.6? nope..."). e isn't just some magic smear of decimal places. Read that comment the other guy posted. e comes into play in a _lot_ of different, seemingly unrelated fields.
Also, here's a definition of e that you might find interesting:
Think of the number one. What's 1^2? What's 1^9? Still 1.
How about 1.1^2? Just a little bigger than 1.1
How about 1.01^2? Still bigger than the starting 1.01, but by a lot less.
What about (1 + 1/1000)^2?
What about (1 + 1/1000)^500?
The bigger the exponent, the more the number grows
but the smaller the initial number is compared to 1, the less the number grows
What happens if the base number is infinitely close to 1, but the exponent is infinitely large?
The limit as x approaches infinity of (1+1/x)^x =
e
Interested in e now?
Re:They missed a biggie! (Score:5, Informative)
Incidentally, here's a quote from Benjamin Peirce, a Harvard mathematician in the 19th century:
(I yanked that quote out of WMCF).Let's not forget Orwell's Equality! (Score:4, Insightful)
Re:i? That's Current! (Score:3, Funny)
I know! As we all know i is for iurrent and j is for jmaginary.
Oh wait...no it's not!
Re:i? That's Current! (Score:3, Informative)
what's |S|?? (Score:2, Interesting)
Re:what's |S|?? (Score:4, Informative)
This is one of the forms of the the Cantor [wikipedia.com] theorem, meaning that the cardinality of the power set of the set S is greater than the cardinality of S itself.
|S| is defined as the cardinality [wikipedia.com] of the set S (its size) if the set S is finite. This designation can be also be conveniently used for infinite sets with several more definitions.
2^|S| is the cardinality of P(S), the power set [wikipedia.com] (set of all subsets) of S. Since the expression 2^|S| is defined only for finite S, before it can be used for infinite sets, one should prove that if card(S)>card(T), card(P(S))>card(P(T)) as well. Since this syntax requires the Cantor theorem, the theorem is usually not written down using it.
PI R SQUARED??! (Score:4, Funny)
(trollin for jesus)
-Tim
Re:PI R SQUARED??! (Score:4, Funny)
Re:Vol=Pi*D^2/4*H (Score:4, Funny)
Hey, my car gets 40 rods to the hogshead, and that's the way I like it!
Crappy of options! (Score:5, Insightful)
e^(i*pi) + 1 = 0
Re:Crappy of options! (Score:3, Interesting)
If you're wondering how calculus figures into it, look at the derivation of Euler's equation. It uses MacLaurean (I think) series.
Re:Crappy of options! (Score:5, Funny)
'Cause I couldn't see how it was done,
Now Euler's my hero,
For I now see why zero,
= e ^ (i pi) + 1
-- Anonymous
Re:Crappy of options! (Score:3, Funny)
The great mathematician Von Blecks
Devised an equation for sex
Having proved a good fuck
Wasn't patience or luck
But a function of y over x.
Magnus.
Re:Crappy of options! (Score:3, Funny)
I wanted that equation to be an option too. I settled for 'e^x' in despair.
Re:Crappy of options! (Score:3, Insightful)
i^i = e^(-pi/2).
Which is incredibly impressive to me. It basically states that if you take the square root of -1, (i), to it's own power, the result is not complex, imaginary or completely whacked, but a real number!
The only problem with current mathematics is it's inadequate treatment of infinities. Heck, we can get integers, fractions, zero, negative numbers and even imaginary numbers, but infinity is still too slippery to grasp.
Only problem is, according to Go:del (o with an umlaut), once we iron out one deficiency in maths, another one will pop up.
Just my (i^i) cents...
Re:Crappy of options! (Score:5, Interesting)
0 = Identity under addition.
1 = Identity under multiplication.
e = Base of the natural logarithm; the unique number such that d/dx e^x = e^x.
pi = Ratio of circumference to diameter of a circle.
i = The number such that i^2 = -1 in the complex field.
One could probably engage in endless philosophical and theological debate about the implications of the fact the most fundamental elements of our understanding of truth are so related.
Re:Crappy of options! (Score:5, Insightful)
0 = Identity under addition.
1 = Identity under multiplication.
e = Base of the natural logarithm; the unique number such that d/dx e^x = e^x.
pi = Ratio of circumference to diameter of a circle.
i = The number such that i^2 = -1 in the complex field.
Not only does the equation include the five most important (or at least most-used) numbers, it also includes the three most important operations: addition, multiplication and exponent (that's why it must be written e^(pi*i)+1=0, not e^(pi*i)=-1).
Addition and multiplication are bound up in the axioms, and the exponent is neccessary for exponential growth (ie. f(x)=k*f(x+a) for all x). Together you can approximate any smooth-enough function to arbitrary precision using Taylor polynoms.
The equation simply contains all the fundamental building blocks of mathematics, in one simple, true statement.
(I immediately started scanning the poll options for this one. As it isn't there, I think I won't bother voting at all. The others simply pale in comparison.)
Re:Crappy of options! (Score:5, Insightful)
And beyond that, it has to do with the fact that these constants originally came from widely different fields of mathematics:
"0" and "1" come from simple arithmetic and counting.
"e" comes from analysis (calculus), originally from studying the primitive function of 1/x.
"pi" comes from a geometric ratio.
"i" comes from algebra, and is simply an algebraic extension of the real numberline to solve certain polynomial equations (like x^2 = -1 - it turns out it solves all polynomial equations, but that is another amazing theorem.)
After one has studied mathematics for a while, one starts to recognize it as almost a fractal landscape, where every theory grows infinitely complex in itself, but where everything comes together to a greater pattern. A lot of the time, when one is bogged down on particular subjects, it is difficult to see the forest for all the trees, but every once in a while one comes across something that ties things together, and one catches a glimpse of the greater picture, in all its divine and stunning beauty. I think that for many people, Euler's equation is their first such epiphany, which is why it holds a special place in the heart of almost every mathematician.
Re:Crappy of options! (Score:5, Funny)
(e^pi-i)^0=1
My favorite equasion (Score:5, Funny)
Proof that .9999(rep) = 1 (Score:3, Interesting)
Set x = 0.99999999...
Then 10*x - x = 9*x
But 10*x = 9.9999999...
So 10*x - x = 9.999... -
So 9*x = 9 => x = 1
Another way to think of this... (Score:4, Informative)
2 * x = 0.666666...
3 * x = 0.999999...
However, 3 * x is also equal to 3/3, which is 1.
IANAM, so I don't know if this constitutes actual proof, but it does seem to make sense.
Lendrick
Re:Proof that .9999(rep) = 1 (Score:3, Interesting)
In step one of your proof, you're taking 9*x to equal 9.0000.
No.
In step one he said "10*x - x = 9*x".
Ten things minus one thing is nine things. Basic arithmetic.
He's saying 9*x to equal 9*x.
10* x is 9.99999... with infinite nines. No rounding.
and x is 0.99999... with infinite nines. No rounding.
Subtract and you get:
9 * x is 9.00000... with infinite zeros. No rounding.
The infinite nines all matched up and canceled. No rounding anywhere.
-
Re:Proof that .9999(rep) = 1 (Score:3, Informative)
.9999999999999... = sum(x=1,infinity)(9*10^(-n))
10*sum(x=1,infinity)(9*10^(-n))
= sum(x=1,infinity)(9*10^(-n)*10)
= sum(x=1,infinity)(9*10^(-n + 1))
= sum(x=0,infinity)(9*10^(-n))
= 9*10^(-0) + sum(x=1,infinity)(9*10^(-n))
= 9 + sum(x=1,infinity)(9*10^(-n))
= 9 +
= 9.9999999999999999999999999999999999999999...
For further enlightenment, consult any book on infinite series or analysis.
Re:My favorite equasion (Score:3, Funny)
2 does not equal 3, even for large values of 2.
Equations? (Score:2)
(pi)r^2 -> which is the area of a circle, but the way it's written it's not an equation, more like a formula.
e^x -> again, not an equation, it could have been a function if it was written f(x) = e^x, but it's not an equation.
2^|S| > |S| -> almost there, except that's an INequality.
Most beautiful equation ever... (Score:2, Redundant)
Re:Most beautiful equation ever... (Score:2)
e^(pi*i)+1 = 0
This ties together all the big (and seemingly unrelated) constants in math (e, pi, i, 1, 0). This was used as a proof that there must be a God, if i recall.
Re:You can't invert a periodic function (Score:3, Informative)
Here is another fallacious argument that uses the same trick yours does:
-1 = -1
(-1)^2 = 1
sqrt((-1)^2)= sqrt(1)
but sqrt(x^2)=x
so
-1=1
See, the fallacy lies in saying sqrt(x^2)=x, ie that the inverse of the squaring function is the square root function. But the squaring function can not have an inverse, since it is a two-to-one function. Similarly, e^z cannot have an inverse on the complex plane, since it is periodic, and is thus an infinity-to-one function.
Re:Most beautiful equation ever... (Score:2)
Re:Most beautiful equation ever... (Score:2)
--Jim
Better written as (Score:2)
------ = e^x
dx
what about (Score:3, Interesting)
for non zero integers a,b,c and n > 2
known as Fermat's last theorem [mbay.net].
Re:what about (Score:3, Informative)
Mandelbrot? (Score:5, Interesting)
I know, I know - don't complain about the options.
You missed a biggie: (Score:3, Interesting)
I just wish I could reproduce it here.
Here it is: (Score:3, Informative)
The derivitive f'(x) of the function f(x) is equal to the limit as h goes to zero of:
f(x+h)-f(x) / h [planetmath.org]
H represents a horizontal distance along the graph of f(x), and f(x+h) - f(x) represents the vertical difference. The ratio of one to the other becomes increasingly accurate as h approaches zero, but to determine exactly what the ratio is when h equals zero, you have to do some math.
While we're on the subject of calculus, I also nominate the first fundamental theorem: [planetmath.org]
The integral from a to b of f(x) = the antiderivative of f(x) evaluated at b - the antiderivative of f(x) evaluated at a [planetmath.org]
Re:Here it is: (Score:3, Interesting)
This one is old, yet... (Score:4, Funny)
GIRLS = TIME * MONEY
but if "time is money"
TIME = MONEY
we have that
GIRLS = MONEY^2
and if "money is the root of all evil"
MONEY = SQRT(EVIL)
this implies that
GIRLS = EVIL
Q.E.D
(quod erat demonstrandum)
So sloppy! (Score:5, Interesting)
GIRLS = TIME * MONEY
Surely anyone with any mathematical sense must be cringing at such sloppy usage. We all know that requiring something is not the same thing as being equal to it. Here's an alternate way of looking at things:
Denote Girls by G. Girls require time t and money M, so we can write:
G(t,M).
Now suppose that we can write
G(t,M)=f(t)h(M)
Now recall that money is power, and power is work/time. This means our equation above becomes:
G(t,M)=f(t)h(w/t)
Now we need only apply dimensional analysis to get an idea of the general functional form of G. Since many girls tend to have best friends of the same gender, and diamonds are a girl's best friend (*), we can conclude that women are some sort of precious stone. This means that girls have units of Joules. The general form is then obvious. The only way to get units of energy from the above is if
f(t) ~ t
h(M) ~ w/t
Therefore, we see that
G ~ w, or in other words, girls are work (to some constant factor). I'm sure this comes as a surprise to nobody.
(*) Ugh, I really hate quoting deBeers. Bastards.
Re:This one is old, yet... (Score:3, Funny)
Many guys have worked out that GIRLS can also be obtained with imaginary MONEY. In this case, it turns out that GIRLS=-EVIL, which is quite a counter-intuitive result when you think about it.
So does that mean... (Score:2)
RMN
~~~
Zero to the power of zero (Score:4, Funny)
Absolute Values? (Score:5, Funny)
GIRLS=sqrt(EVIL^2)=|EVIL|
or in your terms,
Girls = Absolute Evil
(Types a quick Ctrl-Tab to other dekstop as girlfriend walks in...)
Oh come on! (Score:2)
V=IR
It's all about the greeks... (Score:2)
the equation that started it all (Score:2, Funny)
After that, mathematics seemed to multiply like rabbits (no pun intended).
V=IR . I=V/R . R=V/I . P=IV . P=I^2R . P=V^2/R ... (Score:2)
-Adam
technically, e != mc^2 (Score:2, Informative)
E = sqrt( (mc^2)^2 + (pc)^2 )
Just setting the record straight on that one.
Success (Score:3, Funny)
A = X + Y + Z
Where
A = Success
X = Work
Y = Play
Z = Keeping your mouth shut
Old T=$ related joke (Score:5, Funny)
After applying some simple algebra to some trite phrases and cliches a new understanding can be reached of the secret to wealth and success.
Here goes.
Knowledge is Power
Time is Money and as every engineer knows,
Power is Work over Time.
So, substituting algebraic equations for these time worn bits of wisdom, we get:
K = P (1)
T = M (2)
P = W/T (3)
Now, do a few simple substitutions:
Put W/T in for P in equation (1), which yields:
K = W/T (4)
Put M in for T into equation (4), which yields:
K = W/M (5).
Now we've got something. Expanding back into English, we get:
Knowledge equals Work over Money.
What this MEANS is that:
1. The More You Know, the More Work You Do, and
2. The More You Know, the Less Money You Make.
Solving for Money, we get:
M = W/K (6)
Money equals Work Over Knowledge.
From equation (6) we see that Money approaches infinity as Knowledge approaches 0, regardless of the Work done.
What THIS MEANS is:
The More you Make, the Less you Know.
Solving for Work, we get
W = M x K (7)
Work equals Money times Knowledge
From equation (7) we see that Work approaches 0 as Knowledge approaches 0.
What THIS MEANS is:
The stupid rich do little or no work.
Working out the socioeconomic implications of this breakthrough is left as an exercise for the reader
2^|S| > |S| (Score:2)
For those who don't know, the equation 2^|S| > |S| is what implies that there are different levels of infinity.
There is a 1-1 correspondence between the reals and the power set of the natural numbers (I forget how it's done off the top of my head, but there is). Since the power set of the natural numbers has 2^|N| elements, |R| > |N|. Eric [wolfram.com] has some things to say on the subject.
And then, you take a course in set theory and you're warped forever. :-)
FYI - explanations (Score:5, Informative)
F = ma : Newton's 2nd Law of motion, relating force (F) with mass (m) and acceleration (a).
Originally, written as: F = (d2)/(dt2)[ms] (2nd derivative of displacement with respect to time). Yes, m was left in the derivative, which jives today with relativistic motion (mass increases with velocity).
a^2 + b^2 = c^2 : Pythagoras' theorem, stating the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Actually, it is misnamed, since the relation was know to envery surveyor/engineer/builder worth his salt 1000 years before Pythagoras was born.
(pi)r^2 : Formula for the area of a circle
For those interested in the historical attempts to calculate pi, I might recommend A History of Pi [amazon.com] by Petr Beckmann. Be warned: the author makes no bones about his strong opinions on history, but it's an interesting read nonetheless.
e^x : exponential formula. Euler's number (2.7182...) raised to the x power.
Incidentally, how is e^(i*pi) + 1 = 0 not in the poll? It only related the 5 most important numbers in mathematics! You actually could have put e^(i*x) = cos(x) + i * sin(x), of which e^(i*pi) = -1 is a special case.
E = mc^2 : Energy (E) is equal to mass (m) multiplied by velocity of light (c) squared (yes, a very large constant).
Einstein's famous relation which follows from his work on special relativity. Most obvious demonstation is nuclear weapons, whereby a very small amount of mass is converted into a great deal of energy.
2^|S| > |S| : inequality (not an equation) which states that exponential functions are larger than linear for any non-negative number. |S| means abs(S) ie. abs(-5) = abs(5) = 5
T = $ : not sure what this is
CowboyNeal, Q.E.D. : ask Jon Katz
Re:FYI - explanations (Score:4, Informative)
F=ma (Score:2)
F=dp/dt
Using the change in momentum you then can do:
F = d(m*v)/dt
F = vdm/dt
This is the "thrust equation", generall speaking.
Check out this [nasa.gov]
Having a degree in aersopace engineering (Yes! I am a rocket scientist) mean that I know and love this equation.
F=ma (Score:3, Interesting)
The reason I chose F=ma is because mechanical physics is one of the few equations out there that you can 'see' and think about; you are able to apply it in a useful manner to a variety of physical situations.
When I started college, I thought about double majoring in Computer Science and Physics (I loved both at the time, and was quite good at Physics in high school (5 on the AP)), but once the Physics moved out of the realm of mechanics (pretty much anything related to F=ma) into the area I term 'magic' (a.k.a. anything dealing with electromagnetic waves), I couldn't wrap my head around it anymore :( So Computer Science it was :)
One must never forget this chemical compound (Score:4, Funny)
Commonly found on fire hydrants
Favorite derivation (Score:5, Funny)
X = Y
X^2 = XY
X^2-Y^2 = XY-Y^2
(X+Y)(X-Y)= Y(X-Y)
X+Y = Y
2Y = Y
2 = 1
what happened?
Re:Favorite derivation (Score:4, Informative)
You divided by zero. (X-Y) is a root of the equation, at least one solution of which is X=Y=0. After dividing by zero, you can pretty much prove anything, regardless of whether or not it is true.
Re:Favorite derivation (Score:4, Informative)
Re:Favorite derivation (Score:3, Interesting)
If x is the largest integer, x=x+1, and similary, x=x+2:
x = x + 2
Square both sides:
x^2 = (x + 2)^2
x^2 = x^2 + 4x + 4
Subtract x^2:
0 = 4x + 4
4x = -4
Divide by 4:
x = -1
Pythagorean Theorem has a solution? (Score:2)
"My game is like the Pythagorean theorem, no one has an answer," O'Neal said.
After beating the Nets in 1999 [sportsline.com].
Now that's gold.
Re:Pythagorean Theorem has a solution? (Score:3, Insightful)
ph33r (Score:2)
Correction (Score:2)
E^2=(mc^2)^2
IIRC, this has implications for things like anti-matter (particles with negative mass). IANAPP (I Am Not A Physics Professor).
Interesting for a computer scientist... (Score:2)
0!=1
n!=(n-1)!*n
Anyway, anything that has to do with recursion in mathematics is fun, e.g. infinite rows (I don't know if this is the correct english term for it), the b_1 + b_1*q + b_1*q^2 +
Pi (Score:2)
MC^2 (Score:2)
Expressions (Score:2)
The others are just expressions.
0=0 (Score:2)
One with all the important constants (Score:2)
That's got a 1, a 0, and a bunch of good constants.
The obligatory explanations (Score:3, Informative)
a^2=... : Elementary mathematics. Pythagoras's theorem. For high flighers you can say it is a special case of the triangle inequality for the usual metric in R^2.
pi r^2: area of circle embedded in R^2 using above metric.
e^x : exponential growth/ decay (depending on you level of paranoia)
E=mc^2 : Pakistan vi India (basically)
2^|S|>|S|: set theory. the cardinality of functions from a set S to the set {0,1} is `bigger' than the set S
T=$ : Finance, but more usual written as e^x or called `interest'.
CowboyNeal, QED : Not my area of expertise, but probably a major area of research.
---
Math proof (Score:3, Interesting)
e^(pi*i)=-1
Square both sides and you get:
e^(2*pi*i)=1
Take the natural log of both sides:
2*pi*i=0
Have fun killing your brain over that result
-
Re:Math proof (Score:3, Informative)
e^(j*k*theta) is probably one of the most beautiful things in the world once you understand it. Every period function can be written in terms of it. And that's where the "trick" comes from on your puzzle.
e^x is a one to one function for all real values of x.
However, e^x is not one to one for x a member of the complex numbers. In fact, it's periodic. Period functions don't have a inverse. So the natural log of e^x doesn't necessarily equal x if x is a complex number.
Kinchin's Constant (Score:3, Interesting)
Lim {n->infinity} (Qn)^(1/n) = exp(pi^2/(12 Ln 2)).
That's my favorite equation.
Ummmm...pie! (Score:3, Interesting)
Electrical Power is equal to Voltage times the Amperage.
Generalized Stokes' theorem (Score:3, Informative)
This equation has everything you need to know about integral calculus. It's the fundamental theorem of calculus, Gauss' theorem, Green's theorem and every other integral related theorem you've ever seen in one equation.
None of them. (Score:3, Interesting)
M = (Q, sigma, delta, q0, F)
A deterministic finite state machine, made of Q (the finite set of valid state),
sigma (the set of valid tokens), delta (the partial mapping function), q0 (the initial
state, aka S) and F (the set of final states, a subset of Q)
Life = L(M); the proof is left as an excercise to the reader (Hint: you need to have debugging
scars on your forehead to appreciate this.)
The d/dx joke (Score:4, Funny)
The constant "c" is wandering around town, very upset because he heard that the big, bad "d/dx" is also in town. The anxious "c" meets up with another character who's very relaxed.
"How can you be so relaxed? d/dx is going to come around and wipe us all out!" said c.
"Because I'm 'e^x'. Stick with me, c, and you'll be okay."
So c and e^x joined hands, and became c*e^x. Shortly after, a nasty derivative walks up to them. c*e^x stays very calm.
"Aren't you afraid of me?" the derivative asked.
c*e^x coolly replied, "We're c*e^x. You can't do anything to us, you derivative!"
"OH YEAH?" replied the derivative. " WELL, I'M d/dy!!!"
e^x (Score:5, Funny)
E to the X dy dx,
E to the X dx,
Tangent Secant Cosine Sine,
3.14159,
Square roots, cube roots, Poisson brackets,
Dis-integrate 'em Yellow Jackets!
Line, Circle, Sphere, Hypersphere and beyond in 1! (Score:3, Interesting)
[(pi)**(d/2) / (d/2)!] * R**d
Folks, you need to keep in mind first the following:
You all know that Factorial of n ("n!") is a product PI but since most of you are programmers I'll define it recursively:
n! = (n-1)! * n
Okay, that's simple enough.
Next, remember n! = Int(x**n / e**x dx, 0, [Inf]) which is a messed up way of expressing an integral, so let's just skip that step and cut to the chase:
Define the base case for your Recursive Function Factorial:
0! = 1
Now, since a line (d=1) or 3D space (d=3) are odd, you get for each:
[sqrt((pi)) / (1/2)!] * R
and
[pi * sqrt((pi)) / (3/2)!] * R**3
Yes, it's not 4/3 * (pi) * R**3 but be patient, we're almost there!!
Now let's write a special base case for half-factorial. We can evaluate the integral above at n=-1/2 and by rearranging to create a Gaussian curve, we find that:
(-1/2)! = sqrt((pi))
With our recursive definition, we see:
(1/2)! = (-1/2)! * 1/2 = sqrt((pi))/2
(3/2)! = (1/2)! * 3/2 = [3 / 4] * sqrt((pi))
...And So On
So, given that, we can solve d=1 and d=3 and any odd d, e.g.
d=1 => [sqrt(pi) * 2 / sqrt(pi)] * R = 2*R
d=3 => [(pi) * sqrt(pi) * 4 / (3 * sqrt(pi))] * R**3 = 4/3 * (pi) * R**3
Now for your slashdot option, you are SO 2-dimensional!!! Please consider:
[(pi)**(2/2) / (2/2)!] * R**2 = (pi) * R**2
And for you Four-Dimensional, Quaternian or simply Einstienian Space-Time Centrics, the Hyper-Volume of a HyperSphere in 4D is:
[(pi)**2 / 2] * R**4
And for Steven Hawkin and other String-Therory subscribers:
[(pi)**5 / 120] * R**10
Or if you like Membranes like me and are into M-Theory:
64/10395 * (pi)**5 * R**11
And it's all thanks to:
[(pi)**(d/2) / (d/2)!] * R**d!!
Devo Andare,
Jeffrey.
P.S. Because Slashdot.org does not recognize the need for mathematical formulae to be contained on separate lines and this serious post of bone-fide content is consider spammy because it originally got an 18.6 characters per line count, this disclaimer is included to let you, the reader enjoy this thoughtful commentary. That first sentence brought me up to 22.0 but I must continue with this rightly ignored gibberish in order to create something the Slashdot.org engine considers worth your time. I will continue writing until I reach the magic threshold. Sorry again for the added bandwidth of this silly post script, but after all, it would be VERY hard to read this if I didn't put all my mathematical formulae on separate lines, eh? Now, with 26.9 characters per line I still have a ways to go with my run-on sentences and endless paragraph, so shall I tell you a story? Would you like to know more about me? Like that my favourite television programme is Doctor Who, or that for some reason I perfer F=m*a over E=m*c**2 because the later is SO cliché and the former so cute because Einstein ended up proving in General Relativity that as you approach the speed of light, m goes to infinity really messing up the Newtonian calculation. And don't get me started on how you can't know the position and velocity at the same time to an order below Plank's Constant, but Heisenberg's Uncertainty Principal really doesn't enter into this, as I'll I'm interested in is expounding on the beauty of the universal HyperSphere formula for HyperVolume. Ta Da! Now it is long enough! Sorry you had to read this paragraph but I did warn you it was not worth it.
Physical graffiti (Score:3, Funny)
F does not always equal ma (Score:5, Informative)
F = dp/dt
where p is momentum = mv. This makes:
F = d(mv)/dt
and by the prodcut rule of differentiation:
F = m*dv/dt + v*dm/dt
and we all know that dv/dt = a, so we get:
F = ma + v*dm/dt
Now, the change of mass with respect to time of some object is usually zero, so the last term usually dissapears and the equation becomes F=ma, but in referential cases, when some object is moving closer and closer to the speed of light, the mass may grow as a function of velocity, so the last term might not be zero!
The famous limerick (Score:4, Funny)
3 _
\/3
| 2 3 pi 3 _
| z dz X cos(------) = ln (\/e )
| 9
/
1
The integral of zee squared dee zee,
From one to the cube root of three,
Multiplied by cosine
of three pi by nine
Is the log of the cube root of e.
Re:high school (Score:2, Funny)
But isn't your tone both condescending and self important?
Re:high school (Score:2)
e=mc^2 might be fun and all, but I don't use it day to day. Although I know that some other professions do use it on a regular basis (physicists, etc.)
I do regularly use (pi)r^2 and a^2+b^2=c^2, but they're quite boring to use.
But right know, it's a system of differential equations with an unknown function that is causing me some problems (optimization by using Pontryagin Maximum Principle if you must know).
Re:high school (Score:4, Interesting)
Interesting, yes. Very much so. But my favorite? No. F=m*a is my favorite of the bunch, mostly because it's so much more useful for mechanical engineers like me.
I would amend the poll to make the equation a bit more general: F=d(p)/dt which is the derivative of momentum with respect to time. Substituting p=m*v and differentiating you get F=m*a + v*d(m)/dt the second term being the velocity times the change in mass over time; quite handy when calculating forces in rockets which burn substantial fractions of their mass every second.
Enough of this physics. Now back to your regularly scheduled computer geekiness.
Re:high school (Score:2)
engineers, not high schoolers (Score:2)
It is more likely to mean that most
I'm actually partial to the equation:
love(out)-love(in)=0 @t=tf
implying that "in the end, the love you take is equal to the love you make"
Re:high school (Score:5, Funny)
Those should be "substantial" and "consent"; you can start being condescending when you learn how to spell -- until then, go back to kindergarten.
Re:high school (Score:4, Insightful)
That's definitely top-5 interesting *and* useful material in my book.
Of course, this is a poll about favorites so there is no correct answer, but I think you're shortchanging the readership just a little.
Re:My personal favourite ... (Score:2)
Re:favourite equation (Score:5, Funny)