Explore fundamental concepts of quantum physics through orientations and angles in the plane, illustrated by linear polarizations of light in this 59-minute seminar. Delve into the Euclidean plane as a Hilbert space paradigm, identifying orientations with pure quantum states. Examine the association between quantum orientations and linear light polarizations, providing a tangible illustration of the presented formalism. Investigate the dynamics of quantum states, with pure states forming a unit circle and mixed states a unit disk. Learn how rotations in the plane govern time evolution through Majorana-like equations for both closed and open systems. Discover intriguing probabilistic aspects and revisit light linear polarization as an example of quantum measurement using Stokes parameters. Gain insights from speaker Jean-Pierre Gazeau of Université de Paris in this ICTP Mathematics presentation, supported by references from the Brazilian Journal of Physics and recent arXiv submissions.