Γιατί είναι η πιο όμορφη εξίσωση; What makes an equation beautiful?

Earlier this year I wrote about a psychology experiment that revealed that mathematicians appreciate beautiful equations in the same way that people experience great works of art. In the experiment, which conjures up a slightly comical scene, mathematicians were hooked up to a functional magnetic resonance imaging (fMRI) machine and asked to view a series of equations. When the subjects looked at equations they had previously rated as beautiful, it triggered activity in a part of the emotional brain associated with the experience of visual and musical beauty. The formula most commonly rated as beautiful in the study, in both the initial survey and the brain scan, was Euler’s equation, e^iπ+ 1 = 0.

Ένα πείραμα ψυχολογίας είχε δείξει ότι οι μαθηματικοί (υποθέτω και οι φυσικοί …) εκτιμούν τις όμορφες εξισώσεις με τον ίδιο τρόποι που οι άνθρωποι αισθάνονται τα μεγάλα έργα τέχνης. Μια εξίσωση που εν γένει θεωρείται όμορφη είναι η εξίσωση του Euler: e ^iπ + 1 = 0.

Ο ιστότοπος physicsworld με το infographic που ακολουθεί επιχειρεί να δικαιολογήσει γιατί οι περισσότεροι μαθηματικοί είναι ερωτευμένοι με αυτή την μικρή εξίσωση:

Inspired by this study, we have put together this infographic to dissect the Euler identity and try to understand why so many mathematicians are enamoured with this little equation.