Source: https://www.york.cuny.edu/~malk/utopia.html
Timestamp: 2019-04-25 08:49:31+00:00

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With the widespread triumph of symbolic algebra software in revolutionizing the way that symbolic calculation can be accomplished, mathematicians are getting greater respect for the subtlties of geometric phenomena. It is still not possible to get a computer to "scan" an image and "describe" what it sees!
In light of this, and the fact that unlike many other parts of mathematics, geometry often requires relatively little background to get started, it is sad how little awareness there is either within the mathematics community and certainly outside of it of the vast domains of geometry. At a time when rote excercises still are the hallmark of mathematics teaching in the lower grades, few students who leave the 6th grade have seen much geometry, though it would be quite reasonable for them to have done so.
Geometry can be thought of as being built up from many parts (not all incorporated below) even though these parts overlap greatly. You may also want to look at some of my ideas about mathematics with geometrical content which I think should be taught in grades K-12. Here is a very small sample of the kinds of problems that could be looked at.
This bibliography, an expanded version of Geometry in Utopia (which appeared in Geometry's Future, COMAP, Arlington, 1991), adds a few new categories (including journals that have significant treatment of geometry) but more importantly fills in many old and newer sources. (Nearly all references are to books in English, with occassional references to journal articles.) Some of the sections have very detailed lists while other sections are not as thoroughly covered. My goal is to encourage mathematicians at all levels to explore the exciting world of geometry and show more of its wonders to their students. Our students and the public deserve to be more broadly aware of geometric phenomena and applications of geometry.
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Baragar, A., A Survey of Classical and Modern Geometries, Prentice-Hall, Upper Saddle River, 2001.
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Berger, M., Geometry I, Springer-Verlag, Berlin, 1987.
Berger, M., Geometry II, Springer-Verlag, Berlin, 1987.
Berger, M., and P. Pansu, J. Berry, X. Saint-Raymond, Problems in Geometry, Springer-Verlag, New York, 1982.
Bix, R., Topics in Geometry, Academic Press, San Diego, 1994.
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Davis, C. and B. Grünbaum, F. Sherk, The Geometric Vein, Springer-Verlag, New York, 1981.
Guy, R. and R. Woodrow, (eds.), The Lighter Side of Mathematics, Mathematical Association, Washington., 1994.
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