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Suggested Reading and References Suggested Reading and References For further reading, consider College Geometry by Nathan Altshiller Court and Ruler and Compasses by Hilda P. Hudson. These books have been reprinted in inexpensive editions by Chelsea Publishing Company. If you read German, seek out the book by L. Bieberbach; if you read French, seek out the book by Henri Lebesgue. Also, you may find a lot of interesting geometry in Foundations of Geometry by David Hilbert. For biographies of mathemati­ cians and scientists, enjoy wandering among the eighteen volumes of the Dic­ tionary of Scientific Biography, edited by Charles Coulston Gillispie. The following list of references includes only those references on geomet­ ric constructions that the author has seen. For each entry, the name of the author is as it appears on the cited work. A complete bibliography would be much longer than this entire book. Many more references to the sub­ ject, especially references at an elementary level, may be found in various bibliographies by William L. Schaaf. 190 Suggested Reading and References Aaboe, Asger, Episodes from the Early History of Mathematics, New Math­ ematical Library Vol. 13, Mathematical Association of America, 1964. Adler, August, Theorie der Geometrischen Konstruktionen, Goschen, 1906. Altshiller Court, Nathan, College Geometry, Barnes and Noble, 1952. Altshiller Court, Nathan, See Court, N. A. Archibald, R. C., Constructions with a double-edged ruler, American Math­ ematical Monthly 25 (1918) 358-360. Archibald, R. C., Gauss and the regular polygon of seventeen sides, Amer­ ican Mathematical Monthly 27 (1920) 323-326. Archibald, R. C., Malfatti's problem, Scripta Mathematica 1 (1932) 170- 17l. Ball, W. W. Rouse and H. S. M. Coxeter, Mathematical Recreations fj Essays Twelth Edition, Toronto University Press, 1974. Becker, Jerry P., On solutions of geometrical constructions utilizing the compasses alone, Mathematics Teacher 57 (1964) 398-403. Bell, E. T., The Development of Mathematics, McGraw-Hill, 1940. Berggren, J. L., Episodes in the Mathematics of Medieval Islam, Springer­ Verlag, 1986. Bieberbach, L., Theorie der geometrischen Konstruktionen, Birkhauser, 1952. Birkhoff, Garrett and Saunders MacLane, A Survey of Modern Algebra Third Edition, Macmillan, 1965. Bishop, Wayne, How to construct a regular polygon, American Mathemat­ ical Monthly 85 (1978) 186-188. Bold, Benjamin, Famous Problems of Geometry and How to Solve Them, Dover (reprint), 1982. Bos, H. J. M., Arguments on motivation in the rise and decline of a mathe­ matical theory; the "construction of equations", 1632-ca.1750, Archive for History of Exact Sciences 30 (1984) 331-380. Boyer, Carl B., A History of Mathematics, Wiley, 1968. Breidenbach, Walter, Die Dreiteilung des Winkels, Teubner, 1951. Breidenbach, Walter, Das Delische Problem, Teubner, 1953. Breidenbach, W. and W. Suss, Geometric constructions IN Fundamentals of Mathematics Vol. 2 (Geometry), (H. Behnke, F. Bachmann, K. Fladt, and H. Kunle, eds.), pp 198-237, MIT, 1974. Brocard, H., Note sur la division mecanique de l'angle, Bulletin de la Societe Mathematique de Prance 5 (1877) 43-47. Bunt, Lucas N. H., Philip S. Jones, and Jack D. Bedient, The Historical Roots of Elementary Mathematics, Prentice Hall, 1976. Suggested Reading and References 191 Bussey, W. H., Geometric constructions without the classical restriction to ruler and compasses, American Mathematical Monthly 43 (1936) 265-280. Cajori, Florian, A forerunner of Mascheroni, American Mathematical Monthly 36 (1929) 364-365. Cannon, Larry, Geometry of the rational plane, College Mathematics Jour­ nal 17 (1986) 392-402. Carnahan, Walter H., Compass geometry, School Science and Mathematics 32 (1932) 384-390. Carnahan, Walter H., Geometrical constructions without the compass, School Science and Mathematics 36 (1936) 182-189. Cheney, Wm. Fitch, Jr., Can we outdo Mascheroni?, Mathematics Teacher 46 (1953) 152-156. Coolidge, Julian Lowell, A History of Geometric Methods, Dover (reprint), 1963. Coolidge, Julian Lowell, A Treatise on the Circle and the Sphere, Chelsea (reprint), 1971. Courant, Richard and Herbert Robbins, What Is Mathematics?, Oxford, 1941. Court, N. A., Mascheroni constructions, Mathematics Teacher 51 (1958) 370-372. Court, N. A., The problem of Apollonius, Mathematics Teacher 54 (1961) 444-452. Court, N. A., See Altshiller Court, Nathan. Croft, H. T. and T. W. Korner, Constructions with a rigid compass, Math­ ematical Gazette 62 (1978) 85-89. Dantzig, Tobias, The Bequest of the Greeks, Scribner, 1955. Davis, David R., Modern College Geometry, Addison-Wesley, 1949 Dawson, T. R., "Match-stick" geometry, Mathematical Gazette 23 (1939) 161-168. Dayoub, 1. M. and J. W. Lott, What can be done with a Mira?, Mathematics Teacher 70 (1977) 394-399. Dedron, P. and J. Itard, Mathematics and Mathematicians (2 vols.), Trans­ world, 1974. Dennis, David, Rene Descartes' curve-drawing devices: experiments in re­ lations between mechanical motion and symbolic language, Mathematics Magazine 70 (1997) 163-174. DeTemple, Duane W., Simple constructions for the regular pentagon and heptadecagon, Mathematics Teacher 82 (1982) 361-365. Dickson, Leonard Eugene, New First Course in the Theory of Equations, Wiley, 1939. 192 Suggested Reading and References Dickson, L. E., Constructions with Ruler and Compasses; Regular Poly­ gons IN Monographs on Topics of Modern Mathematics Relevant to the Elementary Field (J. W. A. Young, ed.), Dover (reprint), 1955. Dorrie, Heinrich, 100 Great Problems of Elementary Mathematics, Dover, 1965. Dudley, Underwood, What to do when the trisector comes, Mathematical Intelligencer, 5 (1983) 20~25. Dudley, Underwood, A Budget of Trisectors, Springer-Verlag, 1987. Duncan, Donald and \Villiam Barnier, On trisection, quintisection, ... , etc., American Mathematical Monthly 89 (1982) 693. Eidswick, Jack, Two trisect rices for the price of one rolling coin, College Mathematics Journal 24 (1993) 422~430. Emert, John W., Kay 1. Meeks, and Roger B. Nelson, Reflections on a Mira, American Mathematical Monthly 101 (1994) 544~549. Eves, Howard, An Introduction to the History of Mathematics, Rinehart, 1953. Eves, Howard, A Survey of Geometry (2 vols.), Allyn and Bacon, 1965. Euclid, Elements, See Heath, Sir Thomas L. Fraleigh, John B., A First Course in Abstract Algebra, Addison-Wesley, 1967. Gardner, Randolph Scott, Instmments for the Enrichment of Secondary School Mathematics, Edwards, 1951. Geiselmann, Harrison A., Have you tried this? An alternate construction of a regular pentagon, New York State Mathematics Teachers' Journal 31 (1981) 56~58. Gertschliiger, Robert, Euclidean constructions and the geometry of origami, Mathematics Magazine 68 (1995) 357~371. Gibb, Allan A., There are more ways than one to bisect a segment, Math­ ematics Teacher 70 (1977) 390~393. Gleason, Andrew M., Angle trisection, the heptagon, and the triskai­ decagon, American Mathematical Monthly 95 (1988) 185~194. Glotin, De quelques moyens pratiques de diviser les angles en parties egales, Memoires de la Societe des Sciences Physiques et Naturelles de Bordeaux 2 (1863) 253~278 and plates. Goldberg, Michael, On the original Malfatti problem, Mathematics Maga­ zine 40 (1967) 241~247. Goldberg, Michael, The converse Malfatti problem, Mathematics Magazine 41 (1968) 262~266. Hadlock, Charles Robert, Field Theory and its Classical Problems, Carus Mathematical Monographs Vol. 19, Mathematical Association of America, 1978. Suggested Reading and References 193 Hallerberg, Arthur E., The geometry of the fixed compass, Mathematics Teacher 52 (1959) 230-244. Hallerberg, Arthur E., Georg Mohr and Euclidis Curiosi, Mathematics Teacher 53 (1960) 127-132 Heath, Sir Thomas L., A History of Greek Mathematics, Oxford, 1921. Heath, Sir Thomas L., The Thirteen Books of Euclid's Elements (3 vols.), Dover (reprint), 1956. Hess, Adrien L., Certain topics related to constructions with straightedge and compasses, Mathematics Magazine 29 (1956) 217-22l. Hilbert, David, Foundations of Geometry Tenth Edition (revised and en­ larged by Paul Bernays), Open Court, 1971. Hlavaty, Julius H., Mascheroni constructions, Mathematics Teacher 50 (1957) 482-487. Hobson, E. W., "Squaring the Circle" A History of the Problem, IN Squar­ ing the Circle and Other Monographs, Chelsea (reprint), 1969. Hogendijk, Jan P., Greek and Arabic constructions of the regular heptagon, Archive for History of Exact Sciences 30 (1984) 197-330. Hogendijk, Jan P., Arabic traces of lost works of Apollonius, Archive for History of Exact Sciences 35 (1986) 187-253. Honsberger, Ross, Mathematical Gems, Dolciani Mathematical Expositions Vol. 1, Mathematical Association of America, 1973. Honsberger, Ross, Ingenuity in Mathematics, New Mathematical Library Vol. 23, Mathematical Association of America, 1977. Honsberger, Ross, Mathematical Morsels, Dolciani Mathematical Exposi­ tions Vol. 3, Mathematical Association of America, 1978. Hudson, Hilda P., Ruler and Compasses IN Squaring the Circle and Other Monographs, Chelsea (reprint), 1969. Hull, Thomas, A note on "impossible" paper folding, American Mathemat­ ical Monthly 103 (1996) 240-24l. Huzita, H., The trisection of a given angle solved by the geometry of origami IN Proceedings of the First International Meeting of Oragami Science and Technology (Ferra, Italy, December 1989; Humiaki Huzita, ed.). Huzita, Humiaki, ed., Proceedings of the First International Meeting of Oragami Science and Technology (Ferra, Italy, December 1989), no date. Huzita, Humiaki, Drawing the regular heptagon and the regular nonagon
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