Journal of Applied & Computational Mathematics

Solar Power Tower technology requires accurate techniques to ensure the optical performance of the heliostats both in commissioning and operation phases. This paper presents a technique based on target reflection to detect and correct canting errors in heliostat facets. A camera mounted on the back of a target heliostat sees an object heliostat and the target facets in reflection. The pixels difference between detected and theoretical borders determines the canting errors. Experiments in a lab scale testbed show that canting errors can be corrected up to an average value of around as low as 0.15 mrad. Experiments were also performed on a real heliostat at Plataforma Solar de Almería. As a result, canting errors (up to 5 mrad) have been reduced below 0.75 mrad. Mirror slope errors, which can be noticeable in large facets, becomes the largest source of inaccuracy in the presented method.

In light of current psychological and educational research, I examine two of L.E.J. Brouwer's hypotheses regarding the origin of mathematical intuition in this article. Processes related to the perception of formal properties of sensory stimulation, attention, and memory that emerge in early infancy, it is argued, can be understood as the unfolding of the fundamental intuition of mathematics, the abstraction of the relation of n to n + 1. In addition, I contend that over the course of a person's lifetime, these fundamental processes facilitate the creation of more intricate mathematical entities. Mathematical entities constructed from the abstract properties of perceptual activity are expressed and communicated, albeit imprecisely, through language and logic. Last but not least, I think about what the intuitionistic perspective means for teaching mathematics.