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Power of a point: from Jakob Steiner to modern applications

Published online by Cambridge University Press:  24 February 2022

Alexandru Gîrban  and
Bogdan D. Suceavǎ
Alexandru Gîrban
Affiliation:
Christ's College, St. Andrew's Street, Cambridge, CB2 3BU
Bogdan D. Suceavǎ
Affiliation:
Department of Mathematics, California State University, Fullerton, CA92834-6850, USA
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Extract

"What should we use?" seems to be the question when one approaches a plane geometry problem. In many ways, Euclidean geometry is a laboratory in the realm of logic, an ideal place where one can see how alternative methods can be employed to solve problems. What detail might represent a hint? And from among many choices, what method could one consider? Does the geometric structure suggest a certain type of approach?

Type
Articles
Information
The Mathematical Gazette , Volume 106 , Issue 565 , March 2022 , pp. 41 - 53
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Copyright
© The Authors, 2022. Published by Cambridge University Press on behalf of The Mathematical Association

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References

Alexander Ostermann, Gerhard Wanner, Geometry by its history , Undergraduate Texts in Mathematics, Springer-Verlag (2012).Google Scholar
Steiner, Jakob, Einige geometrische Betrachtungen, J. Reine Angew. Math. (Crelle) 1 (1826) pp. 161–184.Google Scholar
Steiner, Jakob, Allgemeine Theorie über das Berühren und Schneiden der Kreise und Kugeln, manuscript from 1823-1826, published posthumously by Fueter, R. and Gonseth, F. (1931).Google Scholar
Coxeter, H. S. M. and Greitzer, S. L., Geometry revisited, Yale University Press (1967).10.5948/UPO9780883859346CrossRefGoogle Scholar
Aubert, P. and Papelier, G., Exercices degéométrie analytique, Vuibert (1930).Google Scholar
Suceavǎ, Bogdan D., Problem 11006, Amer. Math. Monthly, 110 (2003), p. 340.Google Scholar
Adam Glesser, Matt Rathbun, Isabel Marie Serrano, and B. D. Suceavǎ, Eclectic illuminism: applications of affine geometry, College Math. J. 50 (2019), no. 2, pp. 82-92.Google Scholar
W. G. Boskoff and B. D. Suceavǎ, A projective characterization of cyclicity, Beiträage zur Algebra und Geometrie 49 (2008), No.1, pp. 195-203.Google Scholar
Lalescu, T., La géometrie du triangle (2nd edn.) Librairie Vuibert (1952)Google Scholar
Andreescu, T. and Gelca, R., Mathematical Olympiad Challenges, Birkhäuser (2000).10.1007/978-1-4612-2138-8CrossRefGoogle Scholar
Vâjiac, A. I., Vâjiac, M. B., and B. D. Suceavǎ, The power of a point for some real algebraic curves, Math. Gaz. 92 (March 2008) pp. 22–29.Google Scholar