Sequences Extrapolation and the Moser Problem

Polynomial extrapolation of a moser_1.gif length sequence

moser_2.gif

moser_3.gif

moser_4.gif

moser_5.gif

Exemple  : polynomial extrapolation of  the sequence 1, 2, 4, 8, 16

moser_6.gif

moser_7.gif

moser_8.gif

moser_9.gif

moser_10.gif

moser_11.gif

moser_12.gif

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moser_14.gif

Mathematica is able to generalize the polynomial extrapolation to all degrees :

moser_15.gif

moser_16.gif

m
moser_17.gif
moser_18.gif
moser_19.gif
moser_20.gif
moser_21.gif

moser_22.gif

{1,2,3,4,5,6,7,8}
{1,2,4,7,11,16,22,29}
{1,2,4,8,15,26,42,64}
{1,2,4,8,16,31,57,99}
{1,2,4,8,16,32,63,120}
{1,2,4,8,16,32,64,127}

moser_23.gif

The Moser problem

One point is marked at the top of a circle. Six other points are marked at random. Chords are drawed. Points are successively removed one at a time : the figures are modified appropriately.

In[1]:=

moser_24.gif

Out[1]=

moser_25.gif

moser_26.gif

moser_27.gif

moser_28.gif

moser_29.gif

moser_30.gif

moser_31.gif

moser_32.gif

moser_33.gif

moser_34.gif

moser_35.gif

moser_36.gif

moser_37.gif

moser_38.gif

moser_39.gif

moser_40.gif

moser_41.gif

moser_42.gif

moser_43.gif

Out[2]=

moser_44.gif

moser_45.gif

The Pascal triangle

moser_46.gif

moser_47.gif

moser_48.gif

moser_49.gif

Spikey Created with Wolfram Mathematica 8.0