Making Necklaces

embedding dimension

2

3

necklace length

1

2

3

4

5

6

bead colors

1

2

3

4

necklace number

bead diameter

with neck

There are

-1

n

∑

d|n

ϕ(d)

n/d

b

ways to make a necklace using

n

beads of

b

colors, with

ϕ(d)

being the totient function. Build and wear them all!

External Links

Necklace (Wolfram MathWorld)

The Mathematica Guidebook for Numerics (Wolfram Store)

Totient Function (Wolfram MathWorld)

Permanent Citation

Michael Trott, Michael Trott

"Making Necklaces"
http://demonstrations.wolfram.com/MakingNecklaces/
Wolfram Demonstrations Project
Published: September 28, 2007