Fun with Math!

[ssdt]

For me math is hard. But these look much fun than hard.

[lvleph]

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
...

[lkjoel]

Do any math problems on Google, Google will give you the answer.
2 * 5 ^ 6 = 31250 according to Google.

[quirkification]

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

[chiliman]

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

[quirkification]

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.

[quirkification]

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?

[chiliman]

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.

[quirkification]

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.

[Th3Professor]

What interesting mathematical things can you share?

Here's one...

Kaprekar’s Constant.

Take any four-digit number except an integral multiple of 1111 (i.e., don’t take one of the nine numbers with four identical digits). Rearrange the digits of your number to form the largest and smallest strings possible. That is, write down the largest permutation of the number, the smallest permutation (allowing initial zeros as digits), and subtract. Apply this same process to the difference just obtained. Within the total of seven steps, you always reach 6174. At that point, further iteration with 6174 is pointless: 7641–1467 = 6174.

Example: Start with 8028. The largest permutation is 8820, the smallest is 0288, and the difference is 8532. Repeat with 8532 to calculate 8532–2358 = 6174. Your own example may take more steps, but you will reach 6174.

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 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."

(the +0.34 is superscript and -0.24 is subscript; and the -5 is superscript)