In 1912, Laue spots were discovered in x-ray scattering 'photograms' of crystals, which were amongst the most consequential experimental findings of the 20th century. Inter alia, spots established the x-ray waves and crystal lattice; plus, for the first time ever, revealed atoms as real physical objects. Laue, a protégé of Planck and a wave-optics expert, had theoretically predicted these spots, and promptly won the Physics Nobel Prize for 1914. The prize did not come easy: executing his experimentum cruces, over the judgments of Sommerfeld and Wien, required force of will and a certain amount of diplomacy. Besides, his explanation for missing spots and x-ray diffraction were proven wrong by Moseley, Darwin and the two Braggs. Traditionally, Laue's three-dimensional diffraction model is reconciled with Bragg's reflection formula by Ewald's construction using reciprocal lattice space. Laue had overlooked that his fundamental equations violate Euclidean length invariance. This article shows that implementation of invariance consolidates Laue's system of three (multi-parameter) equations into a single formula containing one integer, one angle and two distances; plus validating Bragg's conjecture of reflection. This new derivation demonstrates that the mechanism of Laue spots is akin to the anti reflection coating the colour-plays in soap bubbles and oil slicks-reflection and interference not diffraction. Yet, Laue stimulated countless breakthroughs: Nobel Prizes and scientific innovations, with an enduring legacy of inspiration a century later.