Didactical Modeling, Vol. 7, pp. 21-29

HILBERT’S THIRD PROBLEM AND THE TEACHING OF GEOMETRY

Kiril Bankov
Faculty of Mathematics and Informatics, Sofia University “St, Kliment Ohridski”
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
kbankov@fmi.uni-sofia.bg

Abstract  

During the Second International Congress of Mathematicians held in Paris in 1900, David Hilbert presented 23 unsolved mathematics problems. Only one of them, the third, is related to teaching of mathematics. The article examines the prerequisites that led to Hilbert’s third problem, its solution, and its implication to the teaching of geometry – in particular, the similarity and difference between theoretical study of area and volume.

Keywords: Hilbert’s third problem, polygons of equal area, polyherdas of equal volume, equidecomposable figures.

REFERENCES

[1]     Aigner, M., G. Ziegler. Proofs from THE BOOK (Fourth Edition). Springer, 2010. 

[2]     Банков, К., Т. Витанов. Geometry, Anubis, Sofia, 2003.

[3]     Болтянский, В. Г. Третья проблема Гилберта. Наука, Москва, 1977