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

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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 , .


Contributed by: Izidor Hafner (August 2017)
Open content licensed under CC BY-NC-SA



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].


[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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