Plane Curve Bibliography

The following is a list of references from math journals i know about. This list is made in 1995.

• Cayley, Arthur, On the classification of cubic curves Trans. Camb. Phil. Soc. XI (1866) 81-128.
• Besant, W.H., Roulettes and Glissettes, London (1870).
• Salmon, George, Lessons in Higher Algebra, Dublin (1876).
• Proctor, R.A., The Geometry of Cycloids (1878).
• Salmon, George, Higher Plane Curves, Dublin (1879); reprinted by Chelsea Pub. Co. 1960.
• Salmon, George, and O.W. Fiedler, Analytische Geometrie der höheren ebenen Kurven, Leipzig (1882).
• Casey, J., A Treatise on the Analytic Geometry of the Point, Line, Circle, and Conic Section, London (1883).
• Schroeter, Heinrich, Theorie der ebenen Kurven, Leipzig (1888).
• Brocard, H., Le trifolium Mathesis (2) vol. 2 (1892), suppl. II.
• Frost, P., Curve Tracing, Macmillan (1892); reprinted by Chelsea Pub. Co.
• Basset, A.B., Elementary Treatise on Cubic and Quadric Curves (1901).
• Converse, H.A., On a system of hypocycloids Annals of Math. (2) 5 (1903-03) 105-139.
• Grace, J.H., and A. Young, Algebra of Invariants, Cambridge (1903).
• Texeira, F. Gomes, Traité des courbes spéciales remarqueables planes et gauches (1908-15).
• Wieleitner, H., Spezielle ebene Kurven, Leipzig (1908).
• Lefschetz, S., On the existence of loci with given singularities Trans. Amer. Math. Soc. 14 (1913) 23-41.
• Ganguli, Surendramohan, The Theory of Plane Curves, Univ. of Calcutta (1925).
• Hollcroft, T.R., Multiple points of algebraic curves AMS Bulletin 35 (1929) 841-849.
• Coolidge, J.L., Treatise on Algebraic Plane Curves, Oxford (1931); reprinted by Dover (1959).
• Hilton, Harold, Plane Algebraic Curves, Oxford (1932).
• Weaver, J.H., On the cubic of Tschirnhausen Nat. Math. Mag. 16 (1942) 371-374.
• Bilo, J., Remarkable cubic curves in metrically special homaloidal nets [Dutch] Simon Stevin 25 (1947) 59-82.
• Bosteels, G., The scyphoid, a rational quartic curve [Dutch] Nieuw. Tijdschr. Wiskunda 35 (1947) 121-125.
• Lilley, S., On the construction of algebraic curve branches of given composition J. London Math. Soc. 22 (1947) 67-74.
• Godeaux, Lucien, Géométrie Algébrique, Sciences et Lettres, Liége (1949).
• Semple, J.G., and L. Roth, Introduction to Algebraic Geometry, Oxford (1949).
• Edge, W.L., A plane quartic with eight undulations, Proc. Edinburgh Math. Soc. 2 (1950) 147-162.
• Edge, W.L., A plane quartic curve with twelve undulations Edinburgh Math. Notes 35 (1954) 10-13.
• Ganát, Ludêk, and Miroslav Fiedler, Rational curves with a maximum number of nodes [Czech] Casopis Pest. Mat. 79 (1954) 157-161.
• Primrose, E.J.F., Coincidence points of a curve, Tôhoku Math. J. 2 (1954) 35-37.
• Primrose, E.J.F., A property of quartic curves with two cusps and one node Edinburgh Math. Notes 39 (1954) 1-3.
• Northcott, D.G., A note on the genus formula for plane curves J. London Math. Soc. 30 (1955) 376-382.
• Primrose, E.J.F., Plane Algebraic Curves, New York (1955).
• Bernhart, Arthur, Curves of pursuit - II Scripta Math. 23 (1958) 49-65.

• Blum, Richard, On a pointwise construction of the lemniscate Canadian Math. Bull. 1 (1958) 1-4.
• Baker, Henry F., Principles of Geometry. Vol. 5: Analytic Principles of the Theory of Curves, New York (1960).
• Spain, Barry, Analytical Quadrics, New York (1960).
• Zwikker, C.; The Advanced Geometry of Plane Curves and their Applications; Dover Publications, N.Y.; 1963;
• Jeffrey, A., On the determination of the envelope of a family of epitrochoids with applications SIAM J. Applied Math. 14 (1966) 502-510.
• Curves and Special Curves Encyclopedia Britannica.
• C.B.Boyer; Historical Stages in the Definition of Curves; National Mathematics Magazine. XIX (1944-5) 294-310. (recommended by Robert C Yates in his preface.)
• George E. Martin; Transformation Geometry, An Introduction to Symmetry, Springer-Verlag, New York 1982.

Conic Sections

• B. Bridge, Treatise on the Construction, Properties, and Analogies of the Three Conic Sections (from the 2nd London edition), jointly published by Durrie and Peck, New Haven and Collins, Keese, and Co., New York, 1839.
• Martin Gardner; Penrose Tiles to Trapdoor Ciphers; W.H.Freeman and Co.; 1989. Chapter 15.
• David Hilbert and S. Cohn-Vossen; Geometry and the Imagination; Chelsea; 1952; Chapter 1.
• H.S.M. Coxeter; The Real Projective Plane; Springer-Verlag; 1993; Chapter 6-7.
• Lee. Whitt; The standup conic presents: the parabola and applications; UMAP Journal (The Jounal of Undergraduate Math and its applications) 3 (1982); p.285-313.
• Lee. Whitt; The standup conic presents: the ellipse and applications; UMAP Journal 4 (1983); p.157-183.
• Lee. Whitt; The standup conic presents: the hyperbola and applications; UMAP Journal 5 (1984); p.9-21.

These are great articles on conic sections. Not mathematical. It describe a multitude of applications of conic sections, many of which are not well-known. Most interesting read.

Mathematics Magazine (Published by Mathematical Association of America)

• v.50. 1977. p.87-89. Rotary engine geometry By David H. Nash. (Possible keyword: trochoid, cycloid, hypotrochoid, hypocycloid, epicycloid)
• v.60, No.3. June 1987. p.131-140. Curves of Constant Width from a Linear Viewpoint By J. Chris Fisher. [Lots reference. I have the article.]
• v.60, No.3. June 1987. p.167-168. Reflections on the Ellipse By William C. Schulz; Charles G. Moore. [A proof on the reflection property of ellipse. I have the article. Have not read it yet.]
• v.65, No.3. June 1992. p.147. Reflection Properties of Curves and Surfaces By Daniel Drucker. [Proof that conic sections and surface of revolutions of such are the only curve and surfaces with reflection property. 20 references.]

The Mathematical Gazette (The Journal of the Mathematical Association)

• v.13 1926. p.232-235The asymptotes of plane curves By H.G.Green
• v.13 1926. p.97-103Asymptotes By T.P.Nunn
• v.15 1930. p.486-487The polar equations of a curve By C.Fox
• v.15 1930. 22The involute of the astroid By H.V.Mallison
• v.15 1930. 436The curve of pursuit By E.H.Neville
• v.18 1934. p.258-266The tracing of cubic curves By E.H.Neville
• v.21 1937. 418Note on the three-cusped hypocycloid By D.Arang
• v.23 1939. 92On the three-cusped hypocycloid By R.Goormaghtigh
• v.25 1941. p.165-167Repeating curves By J.H.Caldwell
• v.25 1941. p.12-15The cissoid of Diocles By J.P.McCarthy
• v.26 1942. 214The inflexions of a plane cubic By T.W.Chaundy
• v.27 1943. p.4-12On some general ovals of Cassinian type By H.G.Green
• v.27 1943. p.194-197Real quadrics and the circle at infinity By H.G.Green
• v.29 1945. p.66-67On the three-cusped hypocycloid By J.Hadamard
• v.29 1945. p.219-220The limacon and the cardioid By J.P.McCarthy
• v.30 1946. p.145-146On the three-cusped hypocycloid By R.Goormaghtigh
• v.36 1952. p.51-53The Cartesian oval By R.C.Lyness
• v.36 1952. p.207-208On a special type of plane trinodal quartic curve By H.Simpson
• v.37 1953. p.256-260The curve of pursuit By C.C.Puckette
• v.40, No.331. Feb. 1956. p.1-4Curves of Pursuit. By R.H.Macmillan [Very much application on military of fighter plane persuing a bomber.]
• v.40, No.331. Feb. 1956. p.11The Power of a Point for a Curve. By E.H.Neville. Too mathematical, on algebraic curves.
• v.41, No.336. May 1957. p.102-105The Cissoid of Diocles. By J.P.McCarthy (copy made)
• v.41, No.338. Dec.1957. p.254-257Negative Pedal of the Ellipse with Respect to a Focus. By E.H.Lockwood (copy made)
• v.43, No.343. Feb. 1959. p.34. Pursuit Curves and Mathematical Art. By I.J.Good. [A very short (two paragraphes) note on how some doodle using the idea of envelope of lines could be drawn to form a beautiful wallpaper design. No mathematics discussed. (copy made)]

American Mathematical Monthly

• v.8 1901. p.241. Certain hyperbolic curves of the nth order By A.C.Smith
• v.13 1906 p.221-226. On a certain class of curves given by transcendental equations By R.D.Carmichael
• v.14 1907. p.52. On a certain quartic curve which may degenerate into an ellipse By R.D.Carmichael
• v.15 1908. p.7. On a certain class of quartic curves By R.D.Carmichael
• v.24. 1917. p.213-220. On the construction of certain curves given in polar coordinates By R.E.Moritz
• v.25. 1918. p.223-225. Relating to Generalizations of the Witch and the Cissoid By Frederick H. Hodge. (copy made)
• v.25. 1918. p.189-193. The Logarithmic Spiral. [copy made. I have not read it.]
• v.25. 1918. p.276-282. Euler Integrals and Euler Spiral-Sometimes called Fresnel Integrals and the Clothoïde or Cornu's Spiral. [copy made. I have not read it.]
• v.26. 1919. p.21-32. Concerning a new method of tracing cardioids By William F. Rigge
• v.26 1919. p.151-154. The existence of cusps on the evolute at points of maximum and minimum curvature on the base curve By G.H.Light
• v.26. 1919. p.332-340. Cuspidal Rossettes By William F. Rigge
• v.27. 1920. p.151-157. Envelope Rosettes By William F. Rigge
• v.27 1920. p.398-401The danger area curve By A.S.Merrill
• v.28 1921. p.54-61A curve of pursuit By F.V.Morley
• v.29. 1922. p.6-8. Cuspidal Envelope Rosettes By William F. Rigge
• v.31 1924. p.71-77The three bar curve By F.V.Morley
• v.31 1924. p.222-227The cochlioid By R.Woods
• v.33 1926. p.273-274La courbe du diable By B.H.Brown
• v.34 1927. p.426-429A simple way to discuss points of inflection on plane cubic curves By A.O.Campbell
• v.34 1927. p.262-263The devil's curve again By A.J.Kempner
• v.39 1932. p.409-412Cycloidal curves By S.Bilinsky
• v.40 1933. p.596-598An unusual spiral By L.S.Johnston
• v.44 1937. p.167-168The quadratrix and the associated cochleoid By L.S.Johnston
• v.46 1939. p.85-86The deltoid regarded as the envelope of Simson lines By J.H.Butchart
• v.47 1940. p.11-18The triangle; its deltoids and foliates By B.C.Patterson
• v.52 1945. p.384-387Some properties of the limacon and cardioid By J.H.Butchart
• v.55 1948. p.7-14An anallagmatic cubic By C.E.Noble
• v.56 1949. p.165Note on quartic curves By H.T.R.Aude
• v.61. 1954. p.381. Doodles. By G.B. Robinson
• v.64. No.5. 1957. p.333. Curves with a Kind of Constant Width. By Paul J. Kelly. [Mathematical treatment related to pedal curves. Makes a interesting read.]
• v.64. No.5. May 1957. p.359-361. The Names of the Curve Agnesi By T.F.Mulcrone, S.J. (copy made)
• v.64 1957. p.362-364On degenerate conics By J.W.Lasley, Jr. (copy made)
• v.75. No.1. Jan. 1968. The Problem of Apollonius. By H.S.M.Coxeter
• v.75. No.4. April. 1968. Classroom Notes: The Optical Property of the Conics. By Harley Flanders. [A half page article that proves optical property of conics by vectors.]
• v.87. No.4. April.1980. p.295. Classroom notes: On the Reflective Property of Ellipses[A non-calculus proof and a argument using force/energy concepts.]
• v.102. No.9. November 1995. p.771. My Favorite Elliptic Curve: A Tale of Two Types of Triangles By Richard K. Guy.
• v.102. No.9. November 1995. p.782. Stalking the Wild Ellipse By Keith M. Kendig
• v.102. No.9. November 1995. p.831. The Evolution of Elliptic Curves By John Stillwell

The College Mathematics Journal

• v.23. 1992. p.20-35. Trochoids, Roses, and Thorns--Beyond the Spirograph. By Leon M. Hall [12 references. Copy made. Have not read yet.]
• v.24. No.5. November 1993. p.422-430. Two Trisectrices for the Price of One Rolling Circle By Jack Eidswick [Copy Made. Have not read yet. Key words: trisectrix of Maclaurin]

Scripta Mathematica

• v.23. Memorial Issue, 1957. Nos.1-4.p.49 Curves of Pursuit II. By Arthur Bernhart. [A mathematical treatment, but I think accesible to undergraduate.]
• v.23. Memorial Issue, 1957. Nos.1-4.p.49 Miscellaneous Notes: Conic Sections in Perspective. By Ali R. Amir-Moéz. (copy made)

Ann. Math.

• v.30 1928. p.52-60 Canonical forms of plane cubic curves By R.S.Burington
• v.31 1930 p.629-632 Matrix conditions for multiple points of a ternary cubic By L.P.Copeland