For me math is hard. But these look much fun than hard.
For me math is hard. But these look much fun than hard.
If we take a to be any number in the complex plane then 1^a is not always 1.
proof:
1^a = exp(a*log 1)
and log z is the complex natural log for z = x + i y defined as
log z = ln |z| + i arg z
and arg z = atan(y / x) + 2 n pi for n = 0,1,2...
Thus,
1^a = exp(a)*exp(ln |1| + i arg 1)
=exp(a)*exp(0 + i*(pi/4 + 2 n pi)
=exp(a)*exp(i*(2n+1)*pi/4)
=exp(a)*[cos((2n+1)*pi/4) + i*sin((2n+1)*pi/4)] by Euler's Formula
=exp(a)*[sqrt(2)/2 + i*sqrt(2)/2] for n = 0
=exp(a)*[-sqrt(2)/2 + i*sqrt(2)/2] for n = 1
=exp(a)*[-sqrt(2)/2 - i*sqrt(2)/2] for n = 2
=exp(a)*[sqrt(2)/2 - i*sqrt(2)/2] for n = 3
...
Last edited by lvleph; April 18th, 2009 at 01:53 PM.
Do any math problems on Google, Google will give you the answer.
2 * 5 ^ 6 = 31250 according to Google.
9 Times tables.
9 x 1-10
subtract the number you're multiplying by from 10. And the number that is needed in the ones column is what makes the first number equal 9. (9x6 is 54, 10-6=5, 9-5=4 9x6=54)
This will help third graders with remember their times tables. I figured this out in third grade and made me love the 9's
9x10=90
9x9=81
9x8=72
9x7=63
9x6=54
9x5=45
9x4=36
9x3=27
9x2=18
9x1=09
Only after disaster can we be resurrected. ~Fight Club
I have this condition. ~ Memento
A young girl believed in the brain in a vat theory. And when she tried to get everyone to believe her, they didn't and she was sad.
Not sure if this counts but its too intersting. I am always baffled by the huge numbers you get when you measuse distances in space. Closest Neighbor star Vega is about 25 light years away, or 1.5837x10^14 miles, or one hundred and fifty eight million, three hundred and seventy THOUSAND million miles. To put it simply its really far. So if you scaled it down, you are standing in Los angeles, and vega is in New York city, you only move 7 millimeters and you just reached the moon.
source from http://www.rocketroberts.com/astro/howfar.htm
Don't get me started, I just finished astronomy a couple months ago. SPACE is so large, that when 2 Galaxies collide/combine/mix NOTHING HITS!!! there is such vast space that if the Milkyway galaxy collided with the Andromeda galaxy in the next 2 weeks. nothing would be different, more large stars in our sky sure, but no new light penetrating to our planet.
And we estimated the size of the universe, based on light speed and estimated age of the univere. 14.7 billion light years...
2.7 septillion light years
thats 2.7x10^24
or
2,700,000,000,000,000,000,000,000 Miles across APPROX. and growing every second.
Last edited by quirkification; July 6th, 2010 at 08:34 PM.
Only after disaster can we be resurrected. ~Fight Club
I have this condition. ~ Memento
A young girl believed in the brain in a vat theory. And when she tried to get everyone to believe her, they didn't and she was sad.
and it is estimated that there are as many stars in a galaxy as sand on our beaches. and the same goes for the number of galaxies.
Are we alone?
Only after disaster can we be resurrected. ~Fight Club
I have this condition. ~ Memento
A young girl believed in the brain in a vat theory. And when she tried to get everyone to believe her, they didn't and she was sad.
And its also possible that just after the big bang that space might have been expanding faster than the speed of light so therefor could be many many more galaxies that we will never see because its moving away to fast in the opposite direction that we are. So basically Space could be bigger than the visible space we can see.
are we alone? there answer is simple **** (whats up with this lame chat filter and cant type in the nick name for richard) Cheney was brought here by aliens.
Last edited by chiliman; July 6th, 2010 at 10:57 PM.
the infamous MIB clip
I guess we kinda turned this into an Astronomy thread for a bit.(but astronomy is just math. We cannot touch in this science field.)
I for one vote on the re-collapsing universe. Where it expands for billions and billions of years and then contracts for billions and billions once all the stars burn out and the universe contracts because of the cold. and then that is where the big bang came from.
The way I always looked at the big bang, was infinite heat and density became so hot and dense that the density surpasses a infinity finite point and imploded.
Explains the size and rapidness of the expansion a bit better.
O o . o O o . o O o .
is a way cooler idea than
. o O O O
And on the faster than speed of light bit, that is because the 4 laws were not created yet. Or as much as we know thus far.
Only after disaster can we be resurrected. ~Fight Club
I have this condition. ~ Memento
A young girl believed in the brain in a vat theory. And when she tried to get everyone to believe her, they didn't and she was sad.
necro-bump
...here's one... what kind of equation might we see - like a replacement for E=mc2 (or a variant/development off of it) - if it is absolutely proven that muon neutrinos can travel faster than the speed of light?
I came across the published paper/PDF of the research. Here is an excerpt that addresses the 2 speeds compared:
(the +0.34 is superscript and -0.24 is subscript; and the -5 is superscript)"The corresponding relative difference of the muon neutrino velocity and the speed of light is:
(v-c)/c = (2.37 ± 0.32 (stat.) +0.34 -0.24 (sys.)) ×10-5,
with an overall significance of 6.2 σ."
Last edited by Th3Professor; December 6th, 2011 at 10:29 AM.
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