Final answer:
Dmitri Mendeleyev, in 1869, proposed a periodic table that represented the elements in a spiral pattern, predicting the existence of unknown elements like scandium, gallium, and germanium, which were discovered later, confirming his predictions and contributing to modern chemistry.
Step-by-step explanation:
The scientist who proposed a three-dimensional representation of the elements in a spiral pattern after Gmelin was Dmitri Mendeleyev. In 1869, Mendeleyev published his version of the periodic table, which not only illustrated the chemical relationships among the then-known elements but also predicted the existence of elements that had not yet been discovered.
His table arranged the elements in order of increasing atomic mass and left spaces for elements such as scandium, gallium, germanium, and technetium, later affirming the accuracy of his predictions when these elements were discovered. Mendeleyev's contributions significantly advanced the understanding of chemical elements and their relationships, establishing a foundation for modern chemistry.