Describe a geometric connection with a generalization of the decimal expansion of a number

by RoRi

February 29, 2016

We may generalize the decimal expansion of a number by replacing the integer 10 with any integer $b> 1$ . If $x > 0$ , let $a_0$ denote the greatest integer greater than $x$ . Assuming the integers $a_0, a_1, \ldots, a_{n-1}$ have been defined, let $a$ , denote the largest integer such that

$\sum_{k=0}^n \frac{a_k}{b^k} \leq x.$

Describe a geometric method for obtaining $a_0, a_1, a_2, \ldots$ .

Instead of dividing the real line into segments with 10 subintervals and taking the greatest integer number of intervals, we divide the line into $b$ subintervals.

Stumbling Robot

Describe a geometric connection with a generalization of the decimal expansion of a number

Related

Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment): Cancel reply