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.

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.

- 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.

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.

                                                     

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 (2010-06-05 03:01:51)

i thought mozart was a composer

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?

Now come back to our original puzzle!

                                                               
                                                                                      Pascal Triangle

Last edited by skymus (2010-06-05 05:01:30)

gives... 6

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

1 + ... = 6 * 6

Last edited by skymus (2007-04-03 03:04:58)

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.

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

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

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

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

1 + ... = 3 * 3
_______________________________________

      
Now let us have even more fun!

Let's say that gives...

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

First, count Roll# = __

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

Have fun

Last edited by skymus (2007-04-27 08:16:48)

       
ok, ok. Let's do it together!

      
Find:
               1
Roll # = (∫x³dx)-¹
               0
                                             
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

                       

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

      
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 (2010-06-02 03:42:53)

            

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

1 + 3 + 5 + 7 = 4 * 4

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

Ok, now is your turn.

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

      

Last edited by skymus (2007-07-26 02:25:17)

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

           
Rabbit: No, NOBODY!

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

Winnie:
Can Anybody Roll the Dice?

      

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

Until this moment  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, !

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

            

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

Last edited by skymus (2010-06-05 02:53:01)