Tree problem
What fractional part is filled by the black stars in
the "tree" picture? What part by the white rhombi?
NOTE: This problem came to me from Erich Wittmann / Dortmund University In a mathe 2000
hnichun:.
There are many ways to find the answer, and at'ter tindinl,! the answer, mathematks be�s ... ( 1)
there are many ways to find the answer, some more mathematically rich than others; (2) thne are
patterns to ohscrve und to think fmm; (.l) there is a generul rule to determine if the " Tree " is
continued downwards, keeping the triangular shape; (4) it can he "taken to the limit;' yit>lding
a
result not expel'tt'd by studt>nts; (.5) thP problPm may bl' relatt"d to tht> SiPrpinskl T1;angle
(Sierpinski Gasket). lThe triangular shapt> of tht> three rhomi form the logo of Mitsubishi motor
vehicles, so we cull them MRI.s.l Our lhunks to Ms. Elllz Mi Jmmg 11 grnduutc student at SH1C for
assisting in prcpurlng the figures in the paper.
.Terry P. Becker
Southern Tllinoi.., University Carbondale