proposed in the 18th and 19th centuries describe them as using red, yellow and blue pigments as chromatic primaries. Tobias Mayer (a German mathematician, physicist, and astronomer) described a triangular bipyramid with red, yellow and blue at the 3 vertices in the same plane, white at the top vertex and black and the bottom vertex in a public lecture in 1758. There are 11 planes of colors between the white and black vertices inside the triangular bipyramid. Mayer did not seem to distinguish between colored light and colorant though he used vermilion, orpiment (King’s yellow), and Bergblau (azurite) in partially complete colorings of planes in his solid. Johann Heinrich Lambert (a Swiss mathematician, physicist, and astronomer) proposed a triangular pyramid with gamboge, carmine, and Prussian blue as primaries and only white at the top vertex (since Lambert could produce a mixture that was sufficiently black with those pigments). Lambert's work on this system was published in 1772. Philipp Otto Runge (the Romantic German painter) firmly believed in the theory of red, yellow and blue as the primary colors (again without distinguishing light color and colorant). His color sphere was ultimately described in an essay titled Farben-Kugel (color ball) published by Goethe in 1810. His spherical model of colors equally spaced red, yellow and blue longitudinally with orange, green and violet in between them and white and black at opposite poles. Red, yellow, and blue as primary colors Numerous authors have taught that red, yellow, and blue (RYB) are the primary colors in art education materials since at least the 19th century, following the ideas tabulated above from earlier centuries. A wide variety of contemporary educational sources also describe the RYB primaries. These sources range from children's books and art material manufacturers to painting and color guides. Art education materials often suggest that RYB primaries can be mixed to create all other colors. Criticism Albert Munsell, an American painter (and creator of the Munsell color system), referred to the notion of RYB primaries as "mischief", "a widely accepted error", and underspecified in his book A Color Notation'', first published in 1905. Itten's ideas about RYB primaries have been criticized as ignoring modern color science with demonstrations that some of Itten's claims about mixing RYB primaries are impossible. See also Color vision RGB color model References