Is it turquoise + fuchsia = purple or is it turquoise + fuchsia = blue?

The first step in communicating color is to name it. The second step is color semiotics. The third step is introducing structure in the set of colors. In color education at all levels, this structure often takes the form of formulæ, like red + green = yellow, or turquoise + red = black. In recent times, Johannes Itten's color theory and its associated color wheel have been very influential, mostly through its impact on Bauhaus, although a number of color order systems and circles have been introduced over the centuries. Students get confused when they are trying to formulate the color name arithmetic using the structure of color order systems and concepts like complementary colors and opponent colors. Suddenly turquoise + fuchsia = purple instead of blue; purple and violet become blurred, and finally the student's head explodes under the epistemological pressures of Itten, Albers, Goethe, Runge, Newton, da Vinci, and all the other monsters of color structure. In this contribution we propose a systematic presentation of structure in color, from color theories to color naming. We start from the concept of color perception introduced by da Vinci and work ourselves through color measurement, color formation, and color naming, to develop the basis for a robust system based on table lookup and interpolation. One source of confusion is that color naming has been quite loose in color theory, where for example red can be used interchangeably with fuchsia, and blue with turquoise. Furthermore, common color terms are intermingled with technical colorant terms, for example cyan and aqua or fuchsia and magenta. We present the evolution of a few color terms, some of which have experienced a radical transition over the centuries, and describe an experiment showing the robustness of crowd-sourcing for color naming.