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NCB Deposit # 46

Alexander M. Mitchell
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Pascal's Triangle

in needlepoint
Rutgers Alumni magazine cover

When he retired, William H. Mitchell joined his wife in a hobby of needlepoint.  As a 1925 graduate of Rutgers University, Mitchell chose to create original designs based on a life long love of his undergraduate major, mathematics.  His son, Alexander M. "Sandy" Mitchell of Joppa, Maryland, asked the NCB to honor his father's memory by displaying one of his projects.

Needlepoint Pascal's triangle 

In Mitchell's design, prime numbers ( 2, 3, 5, 7, 11, 13, . . . ) are designated by a single colored square.  For example, the prime numbers 2, 3, 5, and 7 are represented respectively by the solid colors red, yellow, blue and green.
triangle code
triangle code
The composite number  6  is represented by its prime factor colors of red and yellow, or ( 2 x 3).  The number 4, or 22  is represented by red with a tiny square.  For larger composite numbers, requiring several factors, Mitchell chose to use the colors of the prime factors in modified patterns. 
row of triangle

Note that 126 =  2 x 32 x 7  is composed of two parts yellow (3) and one part each of red (2) and green (7).  He finished his triangle with the 32nd row, or  25, or red with a tiny blue square.  In addition, the project contains math operation symbols, Rubic's Cube, Sierpinski's Triangle and other mathematical memorabilia.

Mitchell's mathematical needlework required great patience spread over several years.  From a technical view point, each individual block required 120 stitches.  There are over 500 blocks of colors.

In Spring, 1984, Rutgers University honored their former math major by featuring his creation on the cover of their alumni magazine, 1766.

Another version of the triangle
Pascal's version of the triangular array.
Pascal's triangle in early Greek

From a very early Greek manuscript found in the Vatican Library by the great classical scholar from Denmark, Johan Heiberg.

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