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Mark Saul Program Director Elementary, Secondary, and Informal Education National Science Foundation. Embroidery…. …Or Fabric?. Bronxville High School (ret.) Bronx High School of Science (ret.). 1974. 2004.

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Mark Saul

Program Director

Elementary, Secondary, and Informal Education

National Science Foundation


Embroidery…

…Or Fabric?


Bronxville High School (ret.)

Bronx High School of Science (ret.)


1974

2004


There are 22= 4 subsets of the set {a,b}. Arrange these in a sequence so that each subset differs from the previous one in having exactly one new element added or exactly one old element deleted.


Examples (reading down):

Ø Ø {a} {b}

{a} {b} {a,b} {ab}

{a,b} {a,b} {b} {a}

{b} {a} Ø Ø


Ø

a

b

ab


There are 23=8 subsets of the set {a,b,c}. Arrange these in a sequence so that each subset differs from the previous one in having exactly one new element added or exactly one old element deleted.


  Ø Ø Ø

a b c

ab cb ab

b c a

bc ac ab

c a b

ac ab bc

abc abc abc


bc

abc

c

ac

b

ab

Ø

a


“Characteristic Functions”

a b c

0 0 0 (0,0,0)

{a} 1 0 0 (1,0,0)

{b} 0 1 0 (0,1,0)

{c} 0 0 1 (0,0,1)

{a,b} 1 1 0 (1,1,0)

{b,c} 0 1 1 (0,1,1)

{a,c} 1 0 1 (1,0,1)

{a,b,c} 1 1 1 (1,1,1)

Ø


Binary Counting

0 000

1 001

2 010

3 011

4 100

5 101

6 110

7 111


Binary Gray Code

0 000

1 100

2 110

3 010

4 011

5 001

6 101

7 111



Tower of Hanoi

Chinese Rings

Space-Filling Curves

Campanology (Bell-ringing)


Subsets

Counting

Geometry

Dimension

Characteristic function

Coordinates

Graph theory

Hamiltonian Circuits

Symmetry

Induction

Recursion

What else?




Funding? Check out:

  • NSF 04-600

  • EMSW21 (Enlarging the Mathematical Science Workforce for the 21st Century)

  • MCTP (Mentoring Through Critical Transition Points)

Or talk to:

John Conway, DMS: [email protected]

Liz Teles, DUE: [email protected]


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