F12.00012. Transform as a vector? Tying functional parity with rotation angle of coordinate axes
Presented by: Sayak Bhattacharjee
Abstract
A vector is defined as a quantity which remains unchanged under a rotation of coordinate axes. This definition is associated with the phrase 'transform as a vector'; however, students are frequently confused about the meaning of the phrase and seldom realize its significance. To remedy this, an exposition to this definition is pursued. As a central notion, quantities (triplets) of the form C ≡ (Φ(x), Φ(y), Φ(z)) (where x, y and z are coordinate points and Φ is a real valued function) are investigated using the definition. This novel approach employs elementary mathematics to determine possible value(s) of rotation of axes angle θ at which C may transform as a vector, even if it does not for all θ. A notable correspondence between the parity of function and rotation angle(s) is observed. The analysis, initially carried out in an orthogonal coordinate system, is subsequently generalized for skew coordinate systems. This work was accepted for publication in the European Journal of Physics in October 2019 [1]. [1] Sayak Bhattacharjee Transform as a vector? Tying functional parity with rotation angle of coordinate axes 2019 Eur. J. Phys. in press https://doi.org/10.1088/1361-6404/ab4d64
Authors
- Sayak Bhattacharjee
