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## #1 Re: Dark Discussions at Cafe Infinity » The Prophecy » 2010-11-26 21:36:40

The power is maintained by getting information on the population at first, hence this will done more and more through machines, and so the latter should slowly go to the power. (?)

## #2 Re: Help Me ! » polynomial » 2010-11-08 04:32:16

I have a similar problem but over real numbers : P(x) = 2x^4 + x^3 - x^2 - x

i can get x(2x^3 + x^2 - x - 1), but then i cannot find the next real root with 3rd degree formulas

and cannot find another method. thanks.

## #3 This is Cool » Numerical basis change » 2010-09-27 01:47:42

jk22
Replies: 1

If taken a number in basis 10, let say 10(10)

in basis 4 it is : 10=4*2+2=22(4) (notation)

hence the number in a smaller basis is bigger if it were in basis 10

however let say we had 2.5(10) in basis 10, then

2.5=2+1/2=2+2/4=2.2(4)

this time the number in the smaller basis is smaller than if it were in basis 10

## #4 Re: Dark Discussions at Cafe Infinity » Where am I? » 2010-08-19 08:29:07

Hi dave and bobby,

about this topic I thought that about the case of a blind person, If I close the eyes for example,  I could not see 3d dimension, but feel them locally, the touching sense, and hence could never be sure/globally that suddenly a "passage" would not exist in an other dimension, by following a certain trace ?

Or what about if we moved in a 3d "tunnel", how to know if this tunnel itself were more than in 3 dimensions ?

thanx.

## #5 Re: Puzzles and Games » Bubble Sum » 2010-08-15 08:24:58

Hi John,

thanks for your info. Did you get 29% from a calculation ? I have a video about but I can't up load it, maybe it's seeable at : https://docs.google.com/leaf?id=0B9pGxyM9yy2fNDMxMjgyYWQtNjQ0Ny00NGYzLTllOTUtMzFkNmIwNGY1MTky&hl=en

## #6 Re: Puzzles and Games » Square screw & hexagonal key » 2010-08-15 03:45:33

Hi bob and heirot,

what about the reverse case : a hexagon in a square ? Only eccentric case exist ? I suppose it's possible to unscrew.

## #7 Re: Puzzles and Games » Square screw & hexagonal key » 2010-08-11 23:03:12

Hi Bob,

yeah it's dumb, it's a link to google docs I have, but only me can see them.

Does there exists a 4-point eccentric case ? I cannot figure it out.

bye.

## #8 Puzzles and Games » Bubble Sum » 2010-08-11 05:27:45

jk22
Replies: 2

Hi all,

I have a small problem I would like to solve :

Suppose 2 same soap bubbles on a table :

a) glued at each other with a plane separation, what is the volume and shape ?

b) if the separation is made away, forming a unique bubble, what is the final volume ? (note : Vfinal>V1+V2)

Bye.

## #9 Re: Puzzles and Games » Square screw & hexagonal key » 2010-08-10 22:18:00

Hi, bob,

i thought there was a domain, but couldn't figure it out with geometry. Maybe it's the first case i fell upon, I used the sine theorem.
d/sin(60)=b/sin(180-60-45) [hope you can see the pics]

Do you think other possibilities with 3 touching spots are not possible ? I mean this would imply non concentric centers, and I don't know if it's possible to (un)screw in this eccentric case ? ( I could manage to upload pictures) :

I'll look at the equation and tell you if i manage to understand these.

cya.

## #10 Re: Puzzles and Games » Square screw & hexagonal key » 2010-08-09 21:43:23

Hi heirot, nice to meet you,

I think I found a case with a=2*sin(60)*sin(45)/sin(75)*b ?

cya.

## #11 Re: Help Me ! » Deriving an operator basic complex analysis » 2010-08-09 09:17:28

Hi, nice to meet you,

we could start like : d/dx=d/dz*dz/dx+d/dzbar*dzbar/dx=d/dz+d/dzbar

## #12 Re: Help Me ! » 1=2 proof » 2010-08-08 02:07:30

Hi,

yes, or 0^0.

Studying false proof can help not making them. Some pitfall are :

a) right deduction, but hypotheses aren't (Sometimes proven after),    hence we can deduce nothing

b) the proof uses the result to be proven

## #13 Re: Help Me ! » 3d Rotations » 2010-08-07 07:34:21

Hi bob,

f you find 24 elements in a closed set (ie. no more elements generated by those 24 in any combination) you've got your result.

I finally got the 24, but with a computer program, after 100 multiplication, only 24 were different. Anyway, Thanks for your explanation of why it was not 48.

I haven't found yet the dimension, taken this 9 element function of 24 variable, how many are independent : it should be 4 or 8, but i need to write a code again (could it be that there were 9 linearly independent matrices in this set ?)

almost, I read we put complex numbers in the form of real matrices, but this "isomorphism" is maybe already too descriptive of the symbol i ?

## #14 Re: Help Me ! » 1=2 proof » 2010-08-06 08:19:29

Hi,

we have not 1=2, except if units are e.g. \$ and £ in the year (to find, e.g. in the y 1976, or 1978 http://www.miketodd.net/encyc/dollhist.htm)...1£=2\$ were at some time of the story of humanity.

but we were allowed to write

2 is equivalent to 0 (modulo 2)

divide by 2 and

1 is equivalent to 0 (modulo 1).

## #15 Re: Help Me ! » 3d Rotations » 2010-08-06 01:23:48

Hi, ok.

By dimension I meant : the minimal number D of elements, so that a linear combination of these independent elements (now with a sum) give all the elements.

Anyhow in this case the field of coefficient cannot be continuous, but maybe

which were not so interesting.

## #16 Re: Help Me ! » 3d Rotations » 2010-08-04 07:09:47

Hi, thanks for the explanation.

Now that I have the number of elements, I tried to find the concept of dimension, but I don't know how to find it, it should of course be <=9.

For the second question I found :
[1 -1]
[2 -1] has determinant 1 and square to -1, but it's not a good example, since this 3 axes were broken at origin (x->(1,2), y->(-1,-1))

## #17 Re: Help Me ! » 3d Rotations » 2010-08-03 07:25:50

Hi, thx.

I had another question : Suppose we find 2 linearly independent i=sqrt(-1), with 2x2 matrices, let say I1, I2. I don't know If their product is spanneable by {1,I1,I2}, but if it were the case, were this a sufficient condition to build an algebra ?

----------------------------------

(there is more time than patience, but the world is imaginary small)

## #18 Re: Help Me ! » 3d Rotations » 2010-07-31 10:28:47

Hello bob,

yes it is, however i couldn't find the cardinality of the group of rotation of 90 around xyz which i suppose to be 48.

## #19 Re: Help Me ! » polynomial » 2010-07-25 23:35:19

Hi, nice to meet you.

I looked at the Kronecker's method, but don't understand how it goes

for example : f(x)=x^8-x^7+x^5-x^4+x^3-x+1

I have f(0)=1, f(2)=151, f(-2)=331

if I look for a polynomial g(x)=ax^2+bx+c, fitted with the values above, got :
g(0)=1=>c=1
and a=60, b=-45.

and the following of it would be : if the coefficient are integer, and the discriminant <0 it should be dividable ?? (which here is not the case, since delta>0)

## #20 Help Me ! » 3d Rotations » 2010-07-25 03:47:06

jk22
Replies: 10

Hello,

If I consider 2 rotations in space : Rx(90°) and afterwards Ry(90°) of the vector (1,1,0)

it gives : (1,0,-1) (as by matrix multiplication Ry*Rx)

but considering that the first rotation, Rx, turns the y-axis, leads to (0,1,1)

Is there an easy way to get the latter with matrix operations, can it be shown generally, that it will be Rx*Ry, hence :

Is it that the resulting rotation of two rotations rotating the axis too, were the inverse order matrix product, is it the same as Euler-angles ?

b) do you know how many elements the group of all composition of rotations of 90° around x,y,z axis contains  ?

Thx.

## #21 Re: Puzzles and Games » Selling apples » 2010-07-21 22:01:13

Hi, nice to meet you.

can we say : to be sold 60 apples at 25\$,

6 apples at 2.50\$ (or 5 at 2.083\$, since 25\$/12 non equals 2)

3 at 1.25\$ but then w/o caring about the sort of apples.

## #22 Dark Discussions at Cafe Infinity » Stock market prediction » 2010-07-20 08:48:18

jk22
Replies: 2

Hi all, I'm new to this forum,

suppose that by telepathy it could be found if the price would be lowered or increased, so that a stability on some domain can be found,

what will the effect of a rat running on the keyboard ? It could not be predicted by telepathy, and could induce chaos

## #23 Re: Coder's Corner » Programming Joke » 2010-07-05 05:10:29

programmers have noticed it's much easier to program an automatic insult generator than a worship generator.

and that death of people was always the same : enough money was put in the bet, that it was worth programming the death of with certainty : take bill with the more money corresponding, say the cause.

## #24 Re: Help Me ! » Abstract Algebra, COOL Homework :D » 2010-07-01 21:25:31

Hi, nice to meet you.

for #1 could we write :

let c=0 :

let a=0 :
, the square of any number is 0

-------

from

:

right-multiply with a :

let a=1,

but since the square of b is 0 :

, which can be written :

## #25 Re: Coder's Corner » Complex Number Representation » 2010-07-01 21:12:22

Hi, nice to meet you.

i think it works as distributing r1 i1 on comp2 :

comp1*comp2=(r1+i*i1)*(r2+i*i2)=r1*(r2+i*i2)+i*i1*(r2+i*i2)
=r1*r2+i*r1*i2+i*i1*r2+i*i1*i*i2=
=(r1*r2-i1*i2)+i(r1*i2+i1*r2)., since i*i=-1

or

realpart(comp1*comp2)=real1*real2-imag1*imag2
imagpart(comp1*comp2)=real1*imag2+imag2*real2

cya.