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Mathematical extension
Extend the line segment AB to C, so that BC= one-third AB, that is, the length of AC is 1(AB)+

1/3(AB)=4/3(AB) extend BC to point d, so that CD= one-third BCCD= one-third BC, that is, CD= one-ninth AB( 1/3

X

1/3) Now the length of this line segment is 1+

1/3

+

1/9(AB)= 13/9(AB) Extend the CD to point E, so that DE= one third of CDDE= one third of CD, that is, DE= one ninth of BC (1/3

X

1/3)= one seventh AB( 1/3

X

1/3

X

1/3) Now the length of this line segment is 1+

1/3

+

1/9

+

1/27

(AB)= 40/27(AB)CE = CD+DE = 8cm = 1/9

+

1/27(AB)= 4/27(AB)4/27(AB)= 8 cmab = 8/(4/27)= 54(CM)