# Minkowski's Question Mark Function

Minkowski's Question Mark Function

Minkowski's question mark function is a purely singular odd function of a real argument. If is the simple continued fraction representation of the positive number , then . The value of the question mark function on the integers, rationals, or irrational quadratic numbers is rational. This Demonstration visualizes Minkowski's question mark function on the interval .

[;,,…]

a

0

a

1

a

2

x

?(x)+2(-1)+…+

a

0

n-1

Σ

n≥1

a

1

a

n

2

(,+δ)

x

0

x

0