If you plot pairs of successive digits occurring in 1/n (zero-extended for finite decimals) as points, there are actually many n for which the points uniquely determine an ellipse. I found these: 7, 16, 39, 63, 88, 91, 143, 160, 202, 240, 264, 273, 369, 429, 505, 540, 606, 675, 693, 740, 819, 1355, ... For the above n, I plotted the points and determined by inspection that the point set consists of either - 5 points at the vertices of a convex pentagon - 6 points at the vertices of a convex hexagon with 180-degree rotational symmetry or symmetry about a line. I did not look at n generating more than 6 points that might happen by chance to lie on an ellipse. I assume that 4 or fewer points cannot determine a unique ellipse (is this true?) I assume that 5 points at vertices of a convex pentagon always determines a unique ellipse (is this true?) Call these (base-10) ellipse numbers. To accurately decide which integers are ellipse numbers, requires an algorithm to decide if n distinct points in Z^2 lie on a unique ellipse. I wouldn't know how to write such an algorithm. There are also hyperbola numbers, e.g. 13 is a base-10 hyperbola number.
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Simon Plouffe Sent: Wednesday, June 08, 2016 2:37 PM To: math-fun; Paul Simon; Sylvain Lambert; Louis Plouffe Subject: [math-fun] unusual things
Hello math-funsters,
there is an interesting site here,
http://www.futilitycloset.com/?new=true
a representation of 1/7 in decimal on an ellipse.
the other pages are interesting as well,
quite amusing,
in the same vein ,
that one is original, very original, I counted at least 100000 original images and pages.
http://www.laboiteverte.fr/?s=math
like this 'etch-a-sketch' on a sphere :
http://www.laboiteverte.fr/le-doodle-dome-de-tyco-lardoise-magique- spherique/
and with Pi digits here ??:
http://www.laboiteverte.fr/le-doodle-dome-de-tyco-lardoise-magique- spherique/#jp-carousel-68129
This is what I call original.
one drawback : the whole site is in french, not the images.
Have fun.
Cheers.
Simon Plouffe
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