Abstract
The problem title comes from a famous proverb “To have a cake and eat it too,” which in my early American years I could not understand. Surely you have to “have a cake” in order “to eat it”! A better formulation of this folk wisdom would have been “To keep a cake and eat it too,” which is obviously impossible, hence a moral of the proverb. But that is not what I would like to share with you here. A version of what follows first appeared in the second, 2009 Springer edition of my book “How Does One Cut a Triangle?” [Soi6]. But it fits here so well that I am including its new updated and expanded 2016 version.
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At the same time, I was a “Long Term Visiting Scholar” at Rutgers University, Piscataway, but there I was involved in totally different problems, jointly with the genius Saharon Shelah. Read about it in my “The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of Its Creators” [Soi3].
References
Chung, F., & Graham, R. (2009). Packing equal squares into a large square. Journal of Combinatorial Theory Series A, 116, 1167–1175.
Conway, J. H., & Soifer, A. (2005). Covering a triangle with triangles. The American Mathematical Monthly, 112(1), 78.
Conway, J. H., & Soifer, A. (2004). Cover-up. Geombinatorics, XIV(1), 8–9.
Erdős, P., & Graham, R. L. (1975). On packing squares with equal squares. Journal of Combinational Theory Series A, 19, 119–123.
Karabash, D., & Soifer, A. (2005). On covering of trigons. Geombinatorics, XV(1), 13–17.
Karabash, D., & Soifer, A. (2008). Note on covering square with equal squares. Geombinatorics, XVIII(1), 13–17.
Soifer, A. (2005). Cover-up squared. Geombinatorics, XIV(4), 221–226.
Soifer, A. (2009). The mathematical coloring book: Mathematics of coloring and the colorful life of its creators. New York: Springer.
Soifer, A. (2009). How does one cut a triangle? (2nd expanded edition). New York: Springer.
Soifer, A. (2015). The scholar and the state: In search of Van der Waerden. Basel, Switzerland: Birkhäuser Springer.
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© 2017 Alexander Soifer
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Soifer, A. (2017). E21. Cover-Up with John Conway, Mitya Karabash, and Ron Graham. In: The Colorado Mathematical Olympiad: The Third Decade and Further Explorations. Springer, Cham. https://doi.org/10.1007/978-3-319-52861-8_13
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