[math-fun] What's the proof?
On 2015-04-20 01:58, Gareth McCaughan wrote: <omitted praise for Kac monograph>
On 18/04/2015 10:16, Bill Gosper wrote:
But the cover art http://img2.imagesbn.com/p/9780883850251_p0_v1_s260x420.jpg is really stupid. --rwg
Ha. (Note in back of book: "These pictures were provided by R. William Gosper, Jr. of SYMBOLICS.")
That was back before we even had a color display, let alone a color printer. So I just sent the publisher some random color separations of Pascal's Triangle mod a couple of things. When I saw the cover, I just assumed the book designer slapped together whatever (s)he thought looked nice. But Rohan urged me to figure out what it actually was. Surprisingly, it's a coherent picture of Pascal's Triangle mod 6 (with some residues indistinguished): Graphics[Table[{EdgeForm[#], #, RegularPolygon[{4√3 (k - n/2), -6 n}, {4,π/6}, 6]} &[<|0 -> LightGray, 1 -> Red, 2 -> White, 4 -> RGBColor @@ ({74, 131, 231}/256), 3 -> Red, 5 -> Red|>@ Mod[Binomial[n, k], 6]] /. {Red ->RGBColor @@ ({250, 46, 121}/256)}, {n, 91, 161}, {k,0, n}]] Then Set Background Color to LightGray. (Not even Rohan could figure out the textual command for this.) gosper.org/kac.png --rwg
Duh, Style[Graphics[. . .], Background -> LightGray] More values, more colors: ColorData@"Pastel" Graphics[Table[{%[Mod[Binomial[n, k], 6]/5], RegularPolygon[{4√3 (k - n/2), -6 n}, {4,π/6}, 6]}, {n, 0, 105}, {k, 0, n}]] gosper.org/pastelstriangle.png --rwg On Fri, Aug 4, 2017 at 12:20 AM, Bill Gosper <billgosper@gmail.com> wrote:
On 2015-04-20 01:58, Gareth McCaughan wrote: <omitted praise for Kac monograph>
On 18/04/2015 10:16, Bill Gosper wrote:
But the cover art http://img2.imagesbn.com/p/9780883850251_p0_v1_s260x420.jpg is really stupid. --rwg
Ha. (Note in back of book: "These pictures were provided by R. William Gosper, Jr. of SYMBOLICS.")
That was back before we even had a color display, let alone a color printer. So I just sent the publisher some random color separations of Pascal's Triangle mod a couple of things. When I saw the cover, I just assumed the book designer slapped together whatever (s)he thought looked nice. But Rohan urged me to figure out what it actually was.
Surprisingly, it's a coherent picture of Pascal's Triangle mod 6 (with some residues indistinguished): Graphics[Table[{EdgeForm[#], #, RegularPolygon[{4√3 (k - n/2), -6 n}, {4,π/6}, 6]} &[<|0 -> LightGray, 1 -> Red, 2 -> White, 4 -> RGBColor @@ ({74, 131, 231}/256), 3 -> Red, 5 -> Red|>@ Mod[Binomial[n, k], 6]] /. {Red ->RGBColor @@ ({250, 46, 121}/256)}, {n, 91, 161}, {k,0, n}]] Then Set Background Color to LightGray. (Not even Rohan could figure out the textual command for this.) gosper.org/kac.png --rwg
Bill, Took the liberty of adding your pastel Pascal to https://oeis.org/A095141. Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Sat, Aug 5, 2017 at 9:38 AM, Bill Gosper <billgosper@gmail.com> wrote:
Duh, Style[Graphics[. . .], Background -> LightGray]
More values, more colors: ColorData@"Pastel"
Graphics[Table[{%[Mod[Binomial[n, k], 6]/5], RegularPolygon[{4√3 (k - n/2), -6 n}, {4,π/6}, 6]}, {n, 0, 105}, {k, 0, n}]]
gosper.org/pastelstriangle.png --rwg
On Fri, Aug 4, 2017 at 12:20 AM, Bill Gosper <billgosper@gmail.com> wrote:
On 2015-04-20 01:58, Gareth McCaughan wrote: <omitted praise for Kac monograph>
On 18/04/2015 10:16, Bill Gosper wrote:
But the cover art http://img2.imagesbn.com/p/9780883850251_p0_v1_s260x420.jpg is really stupid. --rwg
Ha. (Note in back of book: "These pictures were provided by R. William Gosper, Jr. of SYMBOLICS.")
That was back before we even had a color display, let alone a color printer. So I just sent the publisher some random color separations of Pascal's Triangle mod a couple of things. When I saw the cover, I just assumed the book designer slapped together whatever (s)he thought looked nice. But Rohan urged me to figure out what it actually was.
Surprisingly, it's a coherent picture of Pascal's Triangle mod 6 (with some residues indistinguished): Graphics[Table[{EdgeForm[#], #, RegularPolygon[{4√3 (k - n/2), -6 n}, {4,π/6}, 6]} &[<|0 -> LightGray, 1 -> Red, 2 -> White, 4 -> RGBColor @@ ({74, 131, 231}/256), 3 -> Red, 5 -> Red|>@ Mod[Binomial[n, k], 6]] /. {Red ->RGBColor @@ ({250, 46, 121}/256)}, {n, 91, 161}, {k,0, n}]] Then Set Background Color to LightGray. (Not even Rohan could figure out the textual command for this.) gosper.org/kac.png --rwg
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Neil Sloane