1. The Circle of Curvature: It's a Limit!  
   John Mathews  
   The AMATYC Review, Vol. 25, No. 1, Fall 2003, pp. 57-63.  
2. Discrete Curvature Based on Osculating Circle Estimation
   Coeurjolly, D.; Miguet, S.; Tougne, L.
   Lecture Notes in Computer Science, 2001, no. 2059, pp. 303-312, Ingenta.  
3. Automatic measurements of the radius of curvature of the cornea in slit lamp
   Ventura, L.; Marcio, A.; Messias, V.; Sousa, S.J.F.  
   Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings, v 2, 2000, p 864-867, Compendex.  
4. Circles of curvature for curves in space.
   Boehm, Wolfgang
   Dedicated to Paul de Faget de Casteljau. Comput. Aided Geom. Design 16 (1999), no. 7, 633--638, MathSciNet.  
5. Euclidean circles of curvature for geodesics of conformal metrics.
   Minda, David
   Computational methods and function theory 1997 (Nicosia), 397--403, Ser. Approx. Decompos., 11, World Sci. Publishing, River Edge, NJ, 1999, MathSciNet.  
6. The Bull and the Silo: An Application of Curvature (in Notes)  
   Michael E. Hoffman  
   The American Mathematical Monthly, Vol. 105, No. 1. (Jan., 1998), pp. 55-58, Jstor.  
7. Curvature and Torsion of Infinitely Repeating DNA Sequences: A Geometric Investigation  
   M. A. El Hassan; C. R. Calladine  
   Proceedings: Mathematical, Physical and Engineering Sciences, Vol. 453, No. 1957. (Feb. 8, 1997), pp. 365-386, Jstor.  
8. A Front Dynamics Approach to Curvature-Dependent Flow  
   D. W. Schwendeman  
   SIAM Journal on Applied Mathematics, Vol. 56, No. 6. (Dec., 1996), pp. 1523-1538, Jstor.  
9. Curvature and Frustration in Cellular Systems  
   Nicolas Rivier; Tomaso Aste  
   Philosophical Transactions: Mathematical, Physical and Engineering Sciences, Vol. 354, No. 1715, Curved Surfaces in Chemical Structure. (Sep. 16, 1996), pp. 2055-2069, Jstor.  
10. Convergence of a Crystalline Algorithm for the Motion of a Simple Closed Convex Curve by Weighted Curvature  
    Pedro Martins Girao  
    SIAM Journal on Numerical Analysis, Vol. 32, No. 3. (Jun., 1995), pp. 886-899, Jstor.  
11. Total radius of curvature.  
    Krawczyk, Jerzy
    Zesz. Nauk. Uniw. Opol. Mat.  29  (1995), 95--96, MathSciNet.  
12. On Length and Curvature (in Notes)  
    Hao Jiang; Jeffrey Nunemacher  
    Mathematics Magazine, Vol. 67, No. 5. (Dec., 1994), pp. 375-376, Jstor.  
13. Regular Simplices in Spaces of Constant Curvature (in Notes)  
    Horst Martini  
    The American Mathematical Monthly, Vol. 100, No. 2. (Feb., 1993), pp. 169-171, Jstor.  
14. A Regularized Equation for Anisotropic Motion-by-Curvature  
    Antonio Di Carlo; Morton E. Gurtin; Paolo Podio-Guidugli  
    SIAM Journal on Applied Mathematics, Vol. 52, No. 4. (Aug., 1992), pp. 1111-1119, Jstor.  
15. Algorithms for the approximation of corneal contour and radius of curvature.  
    Karpouzas, Ioanis
    Cybernetica  34  (1991),  no. 3, 147--171, MathSciNet.  
16. Curvature in the Eighties  
    Robert Osserman  
    The American Mathematical Monthly, Vol. 97, No. 8, Special Geometry Issue. (Oct., 1990), pp. 731-756, Jstor.  
17. Good approximation of circles by curvature-continuous Bézier curves.
    Dokken, Tor; Dæhlen, Morten; Lyche, Tom; Mørken, Knut
    Curves and surfaces in CAGD '89 (Oberwolfach, 1989). Comput. Aided Geom. Design 7 (1990), no. 1-4, 33--41, MathSciNet.  
18. Geodesic circles and total curvature.
    Maeda, Masao
    Yokohama Math. J. 36 (1989), no. 2, 91--103, MathSciNet.  
19. A new method using the circles of curvature for solving equations in R1.
    Park, Bong-kyu; Hitotumatu, Sin
    Publ. Res. Inst. Math. Sci. 24 (1988), no. 2, 249--252, MathSciNet.  
20. Curvature, Circles, and Conformal Maps (in Notes)  
    Alan F. Beardon  
    The American Mathematical Monthly, Vol. 94, No. 1. (Jan., 1987), pp. 48-53, Jstor.  
21. Some Plane Curvature Approximations  
    R. C. Mjolsness; Blair Swartz  
    Mathematics of Computation, Vol. 49, No. 179. (Jul., 1987), pp. 215-230, Jstor.  
22. Parallel Translation of Curvature Along Geodesics  
    James J. Hebda  
    Transactions of the American Mathematical Society, Vol. 299, No. 2. (Feb., 1987), pp. 559-572, Jstor.  
23. Marginal Curvatures and Their Usefulness in the Analysis of Nonlinear Regression Models (in Theory and Methods)  
    G. P. Y. Clarke
    Journal of the American Statistical Association, Vol. 82, No. 399. (Sep., 1987), pp. 844-850, Jstor.  
24. Principal Lines on Surfaces Immersed With Constant Mean Curvature  
    C. Gutierrez; J. Sotomayor  
    Transactions of the American Mathematical Society, Vol. 293, No. 2. (Feb., 1986), pp. 751-766, Jstor.  
25. The Principal Curvatures of the Monkey Saddle (in Notes)  
    Thomas E. Cecil; Patrick J. Ryan  
    The American Mathematical Monthly, Vol. 93, No. 5. (May, 1986), pp. 380-382, Jstor.  
26. Curvatures for Parameter Subsets in Nonlinear Regression  
    R. Dennis Cook; Miriam L. Goldberg  
    The Annals of Statistics, Vol. 14, No. 4. (Dec., 1986), pp. 1399-1418, Jstor.  
27. Cut locus and parallel circles of a closed curve on a Riemannian plane admitting total curvature.  
    Shiohama, Katsuhiro
    Comment. Math. Helv.  60  (1985),  no. 1, 125--138, MathSciNet.  
28. Mean Curvature, The Laplacian, and Soap Bubbles  
    Robert C. Reilly  
    The American Mathematical Monthly, Vol. 89, No. 3. (Mar., 1982), pp. 180-188+197-198, Jstor.  
29. Probabilistic Version of a Curvature Formula (in Short Communications)  
    Vladimir Drobot  
    The Annals of Probability, Vol. 10, No. 3. (Aug., 1982), pp. 860-862, Jstor.  
30. The Length of a Curve in a Space of Curvature < K  
    B. V. Dekster  
    Proceedings of the American Mathematical Society, Vol. 79, No. 2. (Jun., 1980), pp. 271-278, Jstor.  
31. Formulae for the Curvatures of Circles in Chains  
    M. D. Fox  
    The American Mathematical Monthly, Vol. 87, No. 9. (Nov., 1980), pp. 708-715, Jstor.  
32. A Curvature Formula  
    Andrew M. Gleason  
    American Journal of Mathematics, Vol. 101, No. 1. (Feb., 1979), pp. 86-93, Jstor.  
33. A Geometric Inequality for Plane Curves with Restricted Curvature  
    G. D. Chakerian; H. H. Johnson; A. Vogt  
    Proceedings of the American Mathematical Society, Vol. 57, No. 1. (May, 1976), pp. 122-126, Jstor.  
34. The Curvature of Level Curves  
    Dorothy Browne Shaffer  
    Transactions of the American Mathematical Society, Vol. 158, No. 1. (Jul., 1971), pp. 143-150, Jstor.  
35. Critical Points and Curvature for Embedded Polyhedral Surfaces  
    T. F. Banchoff  
    The American Mathematical Monthly, Vol. 77, No. 5. (May, 1970), pp. 475-485, Jstor.  
36. Curvature and Arclength  
    H. G. Robertson  
    SIAM Journal on Applied Mathematics, Vol. 19, No. 4. (Dec., 1970), pp. 697-699, Jstor.  
37. Hyperspheres in Spaces of Constant Curvature (in Mathematical Notes)  
    C. M. Fulton  
    The American Mathematical Monthly, Vol. 76, No. 1. (Jan., 1969), pp. 43-44, Jstor.  
38. A Note on Curvatures Associated with a Vector Field (in Brief Versions)  
    R. N. Kaul  
    The American Mathematical Monthly, Vol. 75, No. 1. (Jan., 1968), pp. 49-50, Jstor.  
39. A Theorem on Spaces of Constant Curvature (in Mathematical Notes)  
    C. M. Fulton  
    The American Mathematical Monthly, Vol. 74, No. 5. (May, 1967), pp. 565-566, Jstor.  
40. Higher Curvatures of Curves in Euclidean Space, II  
    Herman Gluck  
    The American Mathematical Monthly, Vol. 74, No. 9. (Nov., 1967), pp. 1049-1056, Jstor.  
41. Constructions for Certain Circles of Curvature and Related Extreme Problems  
    Herta Taussig Freitag; Arthur H. Freitag  
    Mathematics Magazine, Vol. 40, No. 3. (May, 1967), pp. 145-150, Jstor.  
42. Plane Pursuit with Curvature Constraints  
    Ernest Cockayne  
    SIAM Journal on Applied Mathematics, Vol. 15, No. 6. (Nov., 1967), pp. 1511-1516, Jstor.  
43. Curvature by Normal Line Convergence  
    Jerome A. Seiner  
    Mathematics Magazine, Vol. 39, No. 3. (May, 1966), pp. 147-148, Jstor.  
44. Higher Curvatures of Curves in Euclidean Space  
    Herman Gluck  
    The American Mathematical Monthly, Vol. 73, No. 7. (Aug. - Sep., 1966), pp. 699-704, Jstor.  
45. On the Curvature of the Level Lines of a Harmonic Function  
    R. P. Jerrard; L. A. Rubel  
    Proceedings of the American Mathematical Society, Vol. 14, No. 1. (Feb., 1963), pp. 29-32, Jstor.  
46. The Circles of Curvature of the Curves of Steepest Descent of Green's Function  
    J. L. Walsh  
    The American Mathematical Monthly, Vol. 68, No. 4. (Apr., 1961), pp. 323-329, Jstor.  
47. Plane Motion with Curvature Limitations  
    Z. A. Melzak  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 9, No. 3. (Sep., 1961), pp. 422-432, Jstor.  
48. Curvatures of rn = cos nt (in Classroom Notes)  
    Robert C. Yates  
    The American Mathematical Monthly, Vol. 67, No. 3. (Mar., 1960), pp. 275-278, Jstor.  
49. Angle of Inclination and Curvature (in Teaching of Mathematics)  
    David Gans  
    Mathematics Magazine, Vol. 31, No. 1. (Sep. - Oct., 1957), pp. 31-32, Jstor.  
50. On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents  
    L. E. Dubins  
    American Journal of Mathematics, Vol. 79, No. 3. (Jul., 1957), pp. 497-516, Jstor.  
51. Centers of Curvatures of a Vector Field  
    T. K. Pan  
    Proceedings of the American Mathematical Society, Vol. 7, No. 2. (Apr., 1956), pp. 292-298, Jstor.  
52. On the Curvatures of a Surface  
    Aurel Wintner  
    American Journal of Mathematics, Vol. 78, No. 1. (Jan., 1956), pp. 117-136, Jstor.  
53. A Generalized Theorem of Center of Geodesic Curvature (in Mathematical Notes)  
    T. K. Pan  
    The American Mathematical Monthly, Vol. 62, No. 10. (Dec., 1955), pp. 717-718, Jstor.  
54. On the possiblity to determine the radius of curvature of intergalactic space and the rate of increase of this radius by astronomical observation.  
    Kooy, J. M. J.
    Simon Stevin  30,  (1955), MathSciNet.
55. On the Curvatures of a Surface  
    Philip Hartman; Aurel Wintner  
    American Journal of Mathematics, Vol. 75, No. 1. (Jan., 1953), pp. 127-141, Jstor.  
56. The Unsatisfactory Story of Curvature  
    J. L. Coolidge  
    The American Mathematical Monthly, Vol. 59, No. 6. (Jun. - Jul., 1952), pp. 375-379, Jstor.  
57. On the Total Curvature of Knots  
    J. W. Milnor  
    The Annals of Mathematics, 2nd Ser., Vol. 52, No. 2. (Sep., 1950), pp. 248-257, Jstor.  
58. Some Convexity Properties of Surfaces of Negative Curvature  
    E. F. Beckenbach  
    The American Mathematical Monthly, Vol. 55, No. 5. (May, 1948), pp. 285-301, Jstor.  
59. The Curvatures of the Polar Curves of a General Algebraic Curve  
    Edward Kasner; John De Cicco  
    The American Mathematical Monthly, Vol. 54, No. 5. (May, 1947), pp. 263-268, Jstor.  
60. Theorems on geodesic circles and the Gaussian curvature. (Spanish)
    Vázquez García, Roberto; Barros Sierra, Javier
    Bol. Soc. Mat. Mexicana 3, (1946). 45--56, MathSciNet.  
61. Notes on Curvature of Curves and Surfaces  
    H. J. Hamilton  
    The American Mathematical Monthly, Vol. 47, No. 9. (Nov., 1940), pp. 613-620, Jstor.  
62. We Discover the Meaning of Curvature (in The Teacher's Department)  
    Edwin G. Olds  
    National Mathematics Magazine, Vol. 14, No. 8. (May, 1940), pp. 469-471, Jstor.  
63. On the Circles of Curvature of the Images of Circles under a Conformal Map  
    J. L. Walsh  
    The American Mathematical Monthly, Vol. 46, No. 8. (Oct., 1939), pp. 472-485, Jstor.  
64. Solution of Numerical Equations by Use of the Circle of Curvature  
    Richard J. Wells  
    National Mathematics Magazine, Vol. 13, No. 2. (Nov., 1938), pp. 67-72, Jstor.  
65. Repeating Designs in Surfaces of Negative Curvature (in Questions, Discussions, and Notes)  
    C. A. Richmond  
    The American Mathematical Monthly, Vol. 44, No. 1. (Jan., 1937), pp. 33-35, Jstor.  
66. Curvature Trajectories  
    George Comenetz  
    American Journal of Mathematics, Vol. 58, No. 1. (Jan., 1936), pp. 225-235, Jstor.  
67. The Description of a Surface of Constant Curvature  
    Robert C. Yates  
    The American Mathematical Monthly, Vol. 38, No. 10. (Dec., 1931), pp. 573-574, Jstor.  
68. Optics in Space of Constant Non-Vanishing Curvature  
    James Pierpont  
    American Journal of Mathematics, Vol. 49, No. 3. (Jul., 1927), pp. 343-354, Jstor.  
69. The Curve Whose Curvature is Everywhere the Same as that of its Pedal  
    A. R. Williams  
    The American Mathematical Monthly, Vol. 32, No. 3. (Mar., 1925), pp. 121-125, Jstor.  
70. The Effect of Change of Scale on Curvature  
    James K. Whittemore  
    The American Mathematical Monthly, Vol. 30, No. 1. (Jan., 1923), pp. 22-26, Jstor.  
71. A One-to-One Representation of Geodesics on a Surface of Negative Curvature  
    Harold Marston Morse  
    American Journal of Mathematics, Vol. 43, No. 1. (Jan., 1921), pp. 33-51, Jstor.  
72. Discussions: The Existence of Cusps on the Evolute at Points of Maximum and Minimum Curvature on the Base Curve (in Questions and Discussions)  
    G. H. Light  
    The American Mathematical Monthly, Vol. 26, No. 4. (Apr., 1919), pp. 151-154, Jstor.  
73. Conjugate Systems of Curves on a Surface Both of Whose Laplace Transforms are Lines of Curvature   
    J. M. Stetson  
    The Annals of Mathematics, 2nd Ser., Vol. 19, No. 2. (Dec., 1917), pp. 106-126, Jstor.  
74. Determination of the Radius of Curvature of the Cycloid without the Aid of the Calculus  
    Frederic R. Honey  
    The American Mathematical Monthly, Vol. 12, No. 5. (May, 1905), pp. 103-104, Jstor.  
75. Lines of Curvature on Minimum Developables  
    Frederick S. Woods  
    The Annals of Mathematics, 2nd Ser., Vol. 5, No. 1. (Oct., 1903), pp. 46-50, Jstor.  
76. Note on Center of Curvature (in Solutions of Problems; Calculus)  
    George R. Dean  
    The American Mathematical Monthly, Vol. 8, No. 2. (Feb., 1901), pp. 45-46, Jstor.  
77. Note on Radius of Curvature (in Solutions of Problems; Calculus)  
    George R. Dean  
    The American Mathematical Monthly, Vol. 8, No. 1. (Jan., 1901), pp. 17-18, Jstor.  
78. On the Chord Common to a Parabola and the Circle of Curvature at any Point  
    R. H. Graves  
    The Annals of Mathematics, Vol. 3, No. 2. (Apr., 1887), p. 50, Jstor.  
79. On the Singularities of Curves of Double Curvature  
    Henry B. Fine  
    American Journal of Mathematics, Vol. 8, No. 2. (Feb., 1886), pp. 156-177, Jstor.  
80. On Curvature and Orthogonal Surfaces  
    A. Cayley  
    Philosophical Transactions of the Royal Society of London, Vol. 163. (1873), pp. 229-251, Jstor.  

(c) John H. Mathews 2004