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• Post #2704907

  #Polyhedron #Polygons #tiles #opticalillusion #MathArt #MathsArt The youtube video by Ooqui, linked to in this Mathstodon post by @graveolensa https://mathstodon.xyz/@graveolensa/115885487505867437 is about people with 4 color cones having a sphere's worth of hues. I find it fascinating but, being a trichromat, i don't fully understand it or know if its correct. Here is a mathematically simple but scientifically crude analogy between trichromaticity and tetrachromaticity. A...

• Post #2704906

  #Polyhedron #Polygons #tiles #opticalillusion #MathArt #MathsArt The set of all \((r,g,b)\) values for monochromatic light is the color cube \([0,1]^3\) shown in the figure. More generally each \((r,g,b)\) in the color cube generates some color experience or qualia. The norm of \((r,g,b)\) represents the subjective brightness of the color. When \(r=g=b\) the color is black, white, or a shade of gray, depending on its brightness. The \(r=g=b\) diagonal is the achromatic axis. The saturation...

• Post #2704905

  #Polyhedron #Polygons #tiles #opticalillusion #MathArt #MathsArt The visible spectrum is a line segment in frequency space for light. It is naturally embedded in 4 edges of the hue hexagon. This is shown in the previous figure. We let the frequency of monochromatic light, \(\nu\), vary across the visible spectrum to get the curve. Its image is the 4 edges from \((1,0,0)\) to \((0,0,1)\). This is the spectral locus in the color cube. The remaining 2 edges is the "line" of...

• Post #2704904

  #Polyhedron #Polygons #tiles #opticalillusion #MathArt #MathsArt The achromatic axis is the diagonal connecting \((0,0,0,0)\) to \((1,1,1,1)\). The color tesseract has 2 achromatic vertices and 14 chromatic vertices. The saturation of a \((\chi_1,\chi_2,\chi_3,\chi_4)\) color is its distance from the achromatic axis. Maximum saturation occurs at the 14 chromatic vertices Removing the achromatic vertices and their edges from the tesseract leaves behind a nonconvex square dodecahedron. The...

• Post #2704903

  #Polyhedron #Polygons #tiles #opticalillusion #MathArt #MathsArt The spectral locus is the image of the quadruple of spectral sensitivity curves, \((\chi_1(\nu), \chi_2(\nu), \chi_3(\nu), \chi_4(\nu))\), where \(\nu\) varies across the visible spectrum. Its image is 6 edges from \((1,0,0,0)\) to \((0,0,0,1)\). The path of length 2 connecting \((0,0,0,1)\) back to \((1,0,0,0)\) is the "line" of purples, the hues stimulated by mixtures of \(\chi_1\) and \(\chi_4\) light....

• Post #2704902

  #Polyhedron #Polygons #tiles #opticalillusion #MathArt #MathsArt The hue octagon is symmetric under a rotary reflection by a quarter turn (the symmetry of a tennis ball seam) like here @GerardWestendorp https://mathstodon.xyz/@GerardWestendorp/116489390390156043 The rotation axis passes through the 2 nonspectral secondary hues. The color complement of each tetrachromatic hue is the point on the opposite side of the square dodecahedron. Complementary colors remain antipodal in the rhombic dod...

• Post #2479520

  On the fortieth anniversary of Calvin and Hobbs. Based on this strip from 1992. https://www.reddit.com/r/calvinandhobbes/comments/u51he5/what_story_would_you_like_tonight/#lightbox

• Post #2479518

  The youtube channel Tibees recently posted a nice half-hour video titled "Fibonacci slop is out of control". It discusses the difference between being inspired by Fibonacci numbers to study math and making myths with Fibonacci numbers. https://www.youtube.com/watch?v=LWJzirlCv8I Here is the citation to a good paper that she refers to. Markowsky, George, 1992. "Misconceptions about the Golden Ratio", The College Mathematics Journal, 23(1), pp. 2-19. http...