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Teachers' Lounge Discussion: Volume of a sphere

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From: Loyd <loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2002110214:06:54
Subject: Re: A division pattern in Pascal's Triangle

On 2002110204:39:07, John wrote:
>I am a math student and I'm having difficulty solving the following
>math problem:
>
>Construct another triangle by replacing every number in Pascal's
>triangle by its remainder when divided by two.
>
>(A)  What special property is shared by row 1 and 3 of Pascal's
>triangle?  What are the numbers of the next two rows that share the
>same property?  Describe the pattern.
>	
>

        11^0 =                        1
        11^1 = 11                   1   1
        11^2 = 121                1   2   1
             etc                1   3   3   1
                              1   4   6    4  1
                           1    5   10   10  5  1
                          1   6   15   20  15  6   1
HERE IS THE REMAINDER TRIANGLE:
                                      1
                                    1   1
                                  1   0   1
                                1   1   1   1
                              1   0   0    0  1
                            1   1   0    0   1  1
                          1   0   1   0    1   0  1

Maybe this will help you see the property you are seeking. I am not
sure what your teacher had in mind.  

In Pascals triangle, each element (after the first) is the some of the
two elements diagonally above.  In the remainder triangle, if the two
diagonal elements are the same, then you have zero below and in
between.  If they are different, then you have a "one."


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