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(Yahoo)   The 11 most incredible beauties in the history of the Earth (SFW)   (news.yahoo.com) divider line 22
    More: Cool, special relativity, equations, strong forces, strong nuclear forces, quantum fluctuations, wave equation, Fordham University, physical system  
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12631 clicks; posted to Geek » on 03 Feb 2013 at 12:03 PM (1 year ago)   |  Favorite    |   share:  Share on Twitter share via Email Share on Facebook   more»



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Archived thread
2013-02-03 01:16:35 PM  
4 votes:
Was this not covered yet, or did I just miss it?
i.imgur.com
2013-02-03 12:13:30 PM  
4 votes:
img.ffffound.com
2013-02-03 01:43:37 PM  
3 votes:

Ivo Shandor: Was this not covered yet, or did I just miss it?
[i.imgur.com image 100x30]


Not covered, which is sad because it is for my money the most surprising and beautiful equation in all of mathematics. Conversely, much of that list isn't equations at all. In fact, you could probably make a better list if you restricted yourself only to equations with Euler's name attached to them.

Still, nice to see Noether getting some love (even if the explanation of her work is completely garbled). She is probably the most important physicist that most people have never heard of. If I ever write a popular book on physics, I'd probably start with her.
2013-02-03 12:38:53 PM  
3 votes:

thatguyoverthere70: List fails without 80085


so close but the real number was 5318008

the real fail was that the equations were not included in the article, or at least the version in my crappy browser

no love for navier-stokes?
2013-02-03 08:33:58 PM  
2 votes:

sxacho: 1 = 0.999999999....

Here we go again.


From some perspectives a number cannot have an infinite series of digits. In this case one can't say that 1 = .999... Instead  one has to say for the series x1 = .9, x2 = .99, x3 = .999, etc. that as n grows larger xn approaches 1 and that only the limit of the series, not a particular member of it is 1. Sure this is a fussy technical distinction but it is important in handling all sorts of different limits in other areas.
2013-02-03 04:01:10 PM  
2 votes:
So, if you want to express the quantity one-third, that is exactly one third, but you have to denote it in a decimal form, how do you do that? You write 0.3333... indicating an infinite number of decimal points that are all occupied by 3. What you have expressed in decimal form is exactly equal to the fraction 1/3. It is not almost one-third; it is exactly one-third.

Similarly, if you write 0.9999... indicating an infinite number of decimal places all occupied by 9, the number depicted is exactly 1, not some number just a hair less than one. If it were a finite number of decimal points, it would be some number that was almost 1, but since it is an infinite number of decimal points then the value is indistinguishable from 1.
2013-02-03 02:53:17 PM  
2 votes:

ds_4815: "The point is it's really very simple," said Bill Murray, a particle physicist at the CERN laboratory in Geneva.


"Back off, man", he continued.  "I'm a scientist".
2013-02-03 01:05:20 PM  
2 votes:
Beauty can often be analyzed as symmetry.

The most basic symmetries of the most commonly used numbers are:

Commutativity: A+B = B+A,  A×B = B×A

Distributivity: A×(B+C) = A×B + A×C

Usually, binary operators don't have these properties, and even if these are universally the product and coproduct within some arbitrary category they don't necessarily have to have them.

The basic numbers we use and their operations are particularly beautiful.
2013-02-03 11:48:57 PM  
1 votes:
It's true by definition. 0.999999... is a limit, specifically:

limit _{n->\infinity} ( \sum_1^n 9 * 10^-n)

and that limit is 1. That's really the only way to see it.
2013-02-03 11:42:26 PM  
1 votes:

Clockwork Kumquat: Divide 0.99999... by one. Then divide one by one. Different results.


I assume you are going like this?

0.99999.../1 = 0.99999...
              1/1 = 1

In this case they  are the same result. Just with different notation. Try dividing by 3 (or 9):

0.99999.../3 = 0.33333...
              1/3 = 0.33333...
Therefore:
0.99999.../3 = 1/3

And if a/x=b/x, then a=b. Therefore:

0.99999... = 1

Based on that, if we refer back to the original statements,

0.99999.../1 = 1/1

And we are all happy.
2013-02-03 08:24:54 PM  
1 votes:

GoldDude: 0.999999999999 is like a "tease" of 1.
You're infinitely close to it, but can't actually reach it.

Another similar way of looking at this is as follows:
Say you are standing 10 feet away from a line painted on the sidewalk.
Every minute, you walk half the distance remaining to the line... so 5.0 feet the first minute, 2.5 feet the second minutes, 1.25 feet the third minute, 0.625 feet the fourth minute, etc.
How long before you cross the line?
Never.  Because you are just infinitely moving closer to it, without ever reaching it.


You don't understand the difference between a statement of equality and a limit "as it approaches" statement.

What you're missing is a precalc class that would fix this in about two class lessons. Or rereading through the first chapter of any calculus textbook.

Bottom line - you're showing you don't know what you're talking about by using an "approaching" analogy to disprove an equality statement.
2013-02-03 04:15:43 PM  
1 votes:
It would have been a cool story with Mandelbrot.

/coded that thing in HS on a trash-80.  The pixels were enormous and you couldn't see sh*t, but you could tell without a doubt what it was.
2013-02-03 03:56:07 PM  
1 votes:

sxacho: 1 = 0.999999999....

Here we go again.


But will it take off if Monty Hall opens one of the doors first?
2013-02-03 03:35:55 PM  
1 votes:

McGrits: no love for navier-stokes?


Came here to ask about Navier-Stokes.  See that I am not needed.

/one should never use "Navier-Stokes" and "beautiful" in the same sentence
2013-02-03 03:02:14 PM  
1 votes:

DeltaPunch: Article is incredible misleading. They mention E=mc2, then proceed to say that it was formulated as part of Einstein's theory of General Relativity, which is incorrect. It's part of Special Relativity -- GR came later. To top it off, the article fails to mention that the scientists they interview are discussing Einstein's Field Equations, which is not at all E=mc2.


agreed, and
....it's not even the complete equation, which is E=mc2 + pc
....E=mc^2 doesn't apply to photons. For those, E=hν
2013-02-03 02:54:36 PM  
1 votes:

GoldDude: 1 = 0.99999999...  X
Way wrong.
If this is probability, 1 is absolute certainty and anything less than 1 is not.
The sun will rise tomorrow?  Yeah, I'd give that 0.9999999999.... probability given that it is very unlikely the world will end, the earth will stop turning, the sun will burn out, etc. within the next 24 hours.  But it is not absolutely certain.


The probability that you don't understand what 0.99999999... means is 0.99999999...
2013-02-03 02:34:51 PM  
1 votes:
Article is incredible misleading. They mention E=mc2, then proceed to say that it was formulated as part of Einstein's theory of General Relativity, which is incorrect. It's part of Special Relativity -- GR came later. To top it off, the article fails to mention that the scientists they interview are discussing Einstein's Field Equations, which is not at all E=mc2.
2013-02-03 02:11:43 PM  
1 votes:
i2 = j2 = k2 = -1
2013-02-03 12:47:28 PM  
1 votes:
HΨ = EΨ
2013-02-03 12:43:12 PM  
1 votes:

GoldDude: If this is probability, 1 is absolute certainty and anything less than 1 is not.


Sorry, they said it was MATH. Not probability, which is by definition, not math.
2013-02-03 12:36:40 PM  
1 votes:
newspaper.li

I think this covers both the article and misleading Fark headline.
2013-02-03 12:33:15 PM  
1 votes:
1 = 0.99999999...  X
Way wrong.
If this is probability, 1 is absolute certainty and anything less than 1 is not.
The sun will rise tomorrow?  Yeah, I'd give that 0.9999999999.... probability given that it is very unlikely the world will end, the earth will stop turning, the sun will burn out, etc. within the next 24 hours.  But it is not absolutely certain.
 
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