[math-fun] Neat Dragon question
What is the longest line segment inscribable in the Dragon linking 0+0i to 1 + 0i via (1+i)/2? "Hint": If the segment be t z2 + (1-t)z1, with 0<t<1, then every point on it is (empirically, at least) a triple point of the spacefill whenever t is a dyadic rational! —rwg (This impacts OEIS A260747, etc.)
Sorry, subject should have been Neat Dragon *puzzle*. Partial SPOILER: A picture of the answer <http://gosper.org/maxdragseg.png>, with ℵ₀ "ruler function" ticks at the dyadic rationals indicating the triple points. The segment appears to graze the Dragon boundary, which has no triple points. It must be that the grazing points are not tick points. There remains the puzzle of finding|guessing the endpoints. —rwg There is another alef in my font collection: א . It somehow screws up succeeding subscripts and superscripts, and makes my cursor-right key move left! Does this happen for you? On Sun, Jan 26, 2020 at 12:32 AM Bill Gosper <billgosper@gmail.com> wrote:
What is the longest line segment inscribable in the Dragon linking 0+0i to 1 + 0i via (1+i)/2? "Hint": If the segment be t z2 + (1-t)z1, with 0<t<1, then every point on it is (empirically, at least) a triple point of the spacefill whenever t is a dyadic rational! —rwg (This impacts OEIS A260747, etc.)
Hebrew is written from right to left. I am guessing that the first alef is from a set of Unicode points that are all math symbols, and the second alef is just the ordinary one from the Hebrew alphabet. It's guessing that you are going to type a Hebrew word that starts with alef, so the "Forward" action would naturally go to the left. But I do find it surprising that they interpret right-arrow to mean "move forward", not the more literal "move right". On Sun, Jan 26, 2020 at 9:07 PM Bill Gosper <billgosper@gmail.com> wrote:
Sorry, subject should have been Neat Dragon *puzzle*. Partial SPOILER: A picture of the answer < http://gosper.org/maxdragseg.png>, with ℵ₀ "ruler function" ticks at the dyadic rationals indicating the triple points. The segment appears to graze the Dragon boundary, which has no triple points. It must be that the grazing points are not tick points. There remains the puzzle of finding|guessing the endpoints. —rwg There is another alef in my font collection: א . It somehow screws up succeeding subscripts and superscripts, and makes my cursor-right key move left! Does this happen for you?
On Sun, Jan 26, 2020 at 12:32 AM Bill Gosper <billgosper@gmail.com> wrote:
What is the longest line segment inscribable in the Dragon linking 0+0i to 1 + 0i via (1+i)/2? "Hint": If the segment be t z2 + (1-t)z1, with 0<t<1, then every point on it is (empirically, at least) a triple point of the spacefill whenever t is a dyadic rational! —rwg (This impacts OEIS A260747, etc.)
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On Sun, Jan 26, 2020 at 7:07 PM Bill Gosper <billgosper@gmail.com> wrote:
There is another alef in my font collection: א . It somehow screws up succeeding subscripts and superscripts, and makes my cursor-right key move left! Does this happen for you?
Of course: it's Hebrew. -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
Dividing the maximal inscribed segment into 32 equal lengths produces 31 triple points with a total of 93 preimages in (0,1). Restoring 0 and 1 results in 94 intervals. Coloring their images using a cycle of six colors produces gosper.org/dragtripsonmaxseg.png. Images of intervals under the Dragon function appear improbably straight-sided. But closer inspection reveals the "straight" edges are on unions of several images. —rwg On Sun, Jan 26, 2020 at 6:06 PM Bill Gosper <billgosper@gmail.com> wrote:
Sorry, subject should have been Neat Dragon *puzzle*. Partial SPOILER: A picture of the answer <http://gosper.org/maxdragseg.png>, with ℵ₀ "ruler function" ticks at the dyadic rationals indicating the triple points. The segment appears to graze the Dragon boundary, which has no triple points. It must be that the grazing points are not tick points. There remains the puzzle of finding|guessing the endpoints. —rwg There is another alef in my font collection: א . It somehow screws up succeeding subscripts and superscripts, and makes my cursor-right key move left! Does this happen for you?
On Sun, Jan 26, 2020 at 12:32 AM Bill Gosper <billgosper@gmail.com> wrote:
What is the longest line segment inscribable in the Dragon linking 0+0i to 1 + 0i via (1+i)/2? "Hint": If the segment be t z2 + (1-t)z1, with 0<t<1, then every point on it is (empirically, at least) a triple point of the spacefill whenever t is a dyadic rational! —rwg (This impacts OEIS A260747, etc.)
participants (3)
-
Allan Wechsler -
Bill Gosper -
Mike Stay