Angles are inherently neither length ratios nor dimensionless

2019/06/07 by Paul Quincey, Peter J Mohr, William D Phillips · 2 citations
Decision Sciences · Engineering · Physics and Astronomy · #Advanced Measurement and Metrology Techniques #Radioactive Decay and Measurement Techniques #Scientific Measurement and Uncertainty Evaluation #physics.gen-ph

paper · pdf · doi:10.1088/1681-7575/ab27d7

published as Metrologia 56 043001 (2019)

openalex publication_date 2019/06/07 · openalex created_date 2019/07/12 · arxiv created 2019/09/13 · arxiv updated 2019/09/19 · openalex updated_date 2026/07/28

Abstract

The status of angles within The International System of Units (SI) has long been a source of controversy and confusion. We address one specific but crucial issue, putting the case that the idea of angles necessarily being length ratios, and hence dimensionless, is not valid. By making a clear distinction between the definition of a quantity and the process of making a measurement of that quantity, we show that the usual arguments for angles being length ratios are problematic. An appreciation of this point should clear away a major obstacle preventing a more proper treatment of the angle problem.

Citations

• Dimensionless units in the SI
• Angles—Let’s treat them squarely
• Plane and Solid Angles. Their Pedagogic Value When Introduced Explicitly
• A clearer approach for defining unit systems

Cited by

• On the dual nature of a plane angle
• Radian [wikipedia]

Related

• On the dual nature of a plane angle
• On the dimension of angles and their units
• On the status of plane and solid angles in the International System of Units (SI)
• Implications of adopting plane angle as a base quantity in the SI
• Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)