11479

Lill's Method for Calculating the Value of a Cubic Polynomial

This Demonstration shows Lill's graphic method for calculating the value of a cubic polynomial using the Horner formulas:
,
,
,
,
,
and finally,
.
This is true by Thales's side-splitter theorem. For instance , .

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This method is attributed to the French engineer Eduard Lill (1867).
The side-splitter theorem states: If a line parallel to one side of a triangle intersects the other two sides in different points, it divides the sides in the same ratio [2. p. 354].
References
[1] D. Kurepa, Higher Algebra (in Croatian), Zagreb: Skolska knjiga, 1965 pp. 1071–1073.
[2] H. R. Jacobs, Geometry (2nd ed.), New York: W. H. Freeman and Company, 1987.
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