I am going through the paper, Energy of a Knot by Jun O'Hara. Let me quote from the Definition 1.1 of Section 1 on the first page:
Let $f:S^1 = \mathbb{R}/\mathbb{Z} \to \mathbb{R}^3$ be an embedding of class $C^2$ such that $|f'(t)| = 1$ for all $t \in S^1$, where $|.|$ denotes the standard norm of $\mathbb{R}^3$.
What is the definition of standard norm of $\mathbb{R}^3$?
Presumably, the Euclidean norm: $$ {\large||} (x, y, z) {\large||} = \sqrt{x^2 + y^2 + z^2} $$