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#1 2007-03-06 11:51:38

skymus
Member
Registered: 2007-03-06
Posts: 16

1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

Hi! Are you ready for a G A M E ? Go to Post #12 (see #s right) and have fun!roflol!
____________________________________________________

Here is a little preview:     

This was discovered by 5 year old boy who later was called Mozart of mathematics.

What's his name?

                                                              child-study-child_~u19361731.jpg

Last edited by skymus (2010-06-04 05:13:41)

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#2 2007-03-06 11:59:09

kylekatarn
Member
Registered: 2005-07-24
Posts: 445

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

Terence Tao ?

Last edited by kylekatarn (2007-03-06 11:59:28)

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#3 2007-03-06 12:05:12

Zhylliolom
Real Member
Registered: 2005-09-05
Posts: 412

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

Sounds good Kyle, I'm surprised you know of Tao. But honestly, I've heard Euler, Gauss, Erdos, and others referred to as "the Mozart of mathematics", and this "discovery" isn't something so unique that only one child would figure out, I'm sure at least one of these others realized such a thing when they were quite young.

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#4 2007-03-06 20:53:08

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

Funny thing is, even though he's Aussie, and the 'Mozart of Mathematics', go up to any average person on the street and 9/10 times they won't have a clue who he is.

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#5 2007-03-07 06:04:12

Zhylliolom
Real Member
Registered: 2005-09-05
Posts: 412

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

I would bet even as much as 9/10 math majors wouldn't know who he is, unless they are particularly interested in mathematics competitions (that is how I first learned of him). But who knows, I've never asked anyone if they know of him before.

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#6 2007-03-07 06:05:23

lightning
Real Member
Registered: 2007-02-26
Posts: 2,061

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

i don't know him


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#7 2007-03-09 10:35:46

skymus
Member
Registered: 2007-03-06
Posts: 16

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

up - good discussion!

Simple “discovery” is most often a deceptive one. It usually contains a surprise element. The magic is not in what it contains, but rather in what it doesn’t. rolleyes

1 + 3 + 5 = 3*3 … what principle does it contain and what it does not?

If  1 + 3 + 5 = 3^2, does  2 + 4 + 6 = 4^2 ?... Obviously not.

Find the play (rule/formula) for multiples a and b, which would work for both:

for


and for 
.

When you find the a * b rule, then determine if the same rule plays out for
natural, whole, integers, rational, irrational numbers X1, X2, …
in equation 

. Give some examples.

                                                     numbers-school-life_~u10761759.jpg

Now come back to  1 + 3 + 5 = 3*3 and see the hidden simplicity in it.
Mozart music also contains the highest level of deceptive simplicity,
which Albert Einstein recognized and adored in his violin journey.

Last edited by skymus (2010-06-04 05:01:51)

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#8 2007-03-12 09:16:59

skymus
Member
Registered: 2007-03-06
Posts: 16

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

... breaking down the puzzle dizzy:

                                                                                         boymath.gif

if 

,

so we have that X1 + X2 + ... + Xn = a * b for a = n and b = (X1 + Xn)/2:

Now it is your turn:
2 + 4 + 6  = _ * [( _ + __ ) / 2] = _ * _  ?

Next, may you bring an example with integers? wave

“The Lady Tasting Tea. How Statistics Revolutionized Science in the XXth Century” by David Salsburg. The book author described discovery of the five-year-old in a few sentences (p.138, Chapter 14. THE MOZART OF MATHEMATICS). It does deserve our playfull minds... let's have fun and may  even create a game on the numbers right here.

Last edited by skymus (2010-06-04 05:31:12)

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#9 2007-03-12 09:18:52

lightning
Real Member
Registered: 2007-02-26
Posts: 2,061

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

i thought mozart was a composer


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#10 2007-03-12 09:41:05

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

Right. So what do you think the 'Mozart of Mathematics' means?

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#11 2007-03-13 03:45:13

skymus
Member
Registered: 2007-03-06
Posts: 16

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

Here is an example with rational numbers:

-10.9 - 9.8 - 8.7 - 7.6 = 4 * [(-10.9 + -7.6) / 2] = 4 * [(-18.5) / 2] = 4 * (-9.25) = -37

May you bring your example with rational numbers? wave

Now come back to our original puzzle!

                                                               PascalTriangleAnimated2.gif
                                                                                      Pascal Triangle

Last edited by skymus (2010-06-04 07:01:30)

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#12 2007-03-21 04:14:56

skymus
Member
Registered: 2007-03-06
Posts: 16

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

Let's now play a little game: !roflol!

Come back to our original formula:

                                       1 + 3 + 5 = 3*3

How many numbers are on the left side of the above equality? That's right: 3 !

Follow the same reasoning for other numbers as it is done below:

Example: roll a 6-sided dice to receive amount of number participants in the game:

e.g., Roll #1 = 5 and you make equality of 5 members. Always start from 1 and add 2 to get next number:
                                                                1 + 3 + 5 + 7 + 9 = 5*5
next: Roll #2 = 2, then 1 + 3 = 2*2
Roll #3 = 6, then 1 + 3 + 5 + 7 + 9 + 11 = 6*6
Roll #4 = 4, then 1 + 3 + 5 + 7 = 4*4
Roll #5 = 1, then 1 = 1*1
Game: roll 5 times and count the sum of all 5 rolls. The highest sum wins. swear

Let's count our 5 rolls: 25 + 4 + 36 + 16 + 1 = 82.

Roll your dice 5 times and try to reach that 82.

Your turn...give me your Roll #1 = ___ wave

Last edited by skymus (2007-03-22 09:29:31)

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#13 2007-04-02 04:59:12

skymus
Member
Registered: 2007-03-06
Posts: 16

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

dunno

touched gives... 6

for Roll # = 6, write down the equality here:

1 + ... = 6 * 6

up

Last edited by skymus (2007-04-02 05:04:58)

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#14 2007-04-02 05:23:19

lightning
Real Member
Registered: 2007-02-26
Posts: 2,061

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

1+5=6 there you got all figured out and it only took me............................1 hour nah i'm joking it actully took me 0.01 secs to figure that out! lol


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#15 2007-04-02 05:31:38

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

He said write an equality, and plus it would be wrong if that wasn't even asked, anyway. It isn't basic mathematics, you'll get taught about equalities and inequalities in later years.

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#16 2007-04-02 05:35:47

lightning
Real Member
Registered: 2007-02-26
Posts: 2,061

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

i'm in year 7 not the high school but a couple of days soon and i will be in 1st year whooooo hoooooo!!!!!!!!!!!


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#17 2007-04-26 10:08:05

skymus
Member
Registered: 2007-03-06
Posts: 16

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

For previous case of Roll # = 6, the equality is:

1 + 3 + 5 + 7 + 9 + 11 = 6 * 6

Next, let us say touched gives... Roll # = 3:

for Roll # = 3, write down the equality here:

1 + ... = 3 * 3
_______________________________________

roflol   roflol   roflol
Now let us have even more fun!

Let's say that touched gives...

                   1
... Roll # = (∫x³dx)-¹
                  0

First, count Roll# = __

Then, write down the equality here:   _ + _ + ... = _ * _

Have fun dizzy

Last edited by skymus (2007-04-26 10:16:48)

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#18 2007-05-16 07:46:20

skymus
Member
Registered: 2007-03-06
Posts: 16

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

wave   wave   wave

For Roll # = 3 the equality is: 1 + 3 + 5 = 3 * 3.

up   up   up

________________________________________________

faint   dunno   faint   rolleyes   faint

Use the table to find what :
               1
Roll # = (∫x³dx)-¹
               0

roflol Anybody give it a try?.. touched

Last edited by skymus (2007-05-17 11:31:58)

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#19 2007-06-09 11:42:17

skymus
Member
Registered: 2007-03-06
Posts: 16

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

sleep    sleep    sleep
ok, ok. Let's do it together!

roflolrolleyes   dunno   rolleyesroflol
Find:
               1
Roll # = (∫x³dx)-¹
               0
                                             what
Use the table to find it:
       1
for (∫x³dx)-¹:  (x^4/4)-¹ = 4/x^4  ???  Nope! See Mr. Franklin's corrective post below
       0
It is:
       1
for (∫x³dx)-¹ we plug 0 and 1 into formula as follows:
       0
                           (x^4/4)-¹ ol¹ = [(1^4)/4 - (0^4/4)]-¹ = (1/4 - 0/4)-¹ = (1/4)-¹ = 4

faint      rolleyes      faint      rolleyes      faint

Therefore:
  1
(∫x³dx)-¹ = 4 and thus Roll # = 4
  0

up   touched   up
PS I've got too much pre-occupied with placing correct math symbols as x^4 and ∫
to miss on the flow of the calculation itself.
It is interesting that we have x³ ready to use here, which is x^3, but not the same for x^4.
Thank you, John, for interaction.

Last edited by skymus (2010-06-01 05:42:53)

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#20 2007-06-11 06:56:40

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,561

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

Right, the integral from 0 to 1 is (1^4)/4 - (0^4)/4, which is 1/4 - 0/4, which is 1/4.
Then you flip 1/4 over to 4/1.


igloo myrtilles fourmis

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#21 2007-07-25 04:04:11

skymus
Member
Registered: 2007-03-06
Posts: 16

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

roflol   roflol   roflol   roflol   roflol

For previous case of Roll # = 4, the equality is:

1 + 3 + 5 + 7 = 4 * 4

dizzy  Do you remember?  dizzy
  1
(∫x³dx)-¹ = 4 and thus Roll # = 4?
  0
______________________________________

Ok, now is your turn. big_smile

May you roll a dice to give me your Roll #?

wave   up   wave

Last edited by skymus (2007-07-25 04:25:17)

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#22 2007-10-02 12:51:24

skymus
Member
Registered: 2007-03-06
Posts: 16

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

So, Post #12 defined the game out of 5 rolls.       
The number to reach and overcome is = 82.

Until this moment touched gave us the following rolls:
6: 1 + 3 + 5 + 7 + 9 + 11 = 6 * 6 in Post #13
3: 1 + 3 + 5 = 3 * 3 in Post #18
4: 1 + 3 + 5 + 7 = 4 * 4 in Post #19

                                                   We need two more rolls!

faint  wave  faint  wave  faint  CAN anybody ROLL the DICE?.... ANYBODY ? . . . .   faint  wave   faint  wave  faint 

              Let's do the deal: you will roll the dice and I will count the numbers! 

Last edited by skymus (2007-10-04 06:47:06)

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#23 2007-11-23 13:23:41

skymus
Member
Registered: 2007-03-06
Posts: 16

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

wave   wave   wave
Winnie the Pooh: Hellooooooo.... Is anybody at home??????

        shame   shame
Rabbit: No, NOBODY!

...
             dunno
Winnie (to himself): if somebody says NOBODY, than it means there should be somebody.
_______________________________________________________________

Winnie:
Can Anybody Roll the Dice?

touched   touched   touched

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#24 2007-11-23 14:50:28

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

Winnie is philosophical thinker

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#25 2008-01-28 09:29:02

skymus
Member
Registered: 2007-03-06
Posts: 16

Re: 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2 etc.

sleep
So, Post #12 defined the game out of 5 rolls.       
The number to reach and overcome is Total = 82.

Until this moment  touched gave us the following rolls:
Roll #1 = 6: 1 + 3 + 5 + 7 + 9 + 11 = 6 * 6 in Post #13
Roll #2 = 3: 1 + 3 + 5 = 3 * 3 in Post #18
Roll #3 = 4: 1 + 3 + 5 + 7 = 4 * 4 in Post #19
Total = 36 + 9 + 16 = 61
                                                   We need two more rolls!

Today we will Roll #4 = ...

Ready, Set and Ready, Go: . . . 5

Thank you, touched!

Thus, Roll #4 = 5: 1 + 3 + 5 + 7 + 9 = 5 * 5
Total: 61 + 25 = 86

wave   roflol   roflol   roflol   wave

Can Anybody roll the dice for the last Roll #5? sleep

Last edited by skymus (2010-06-04 04:53:01)

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