References

Below is a list of the main references for this course.


C. Adler. An isoperimetric problem with an inequality. Amer. Math. Monthly 52, (1945). 59--69.

R. V. Ambartzumian. Factorization calculus and geometric probability. Cambridge University Press, Cambridge: 1990.

P. Bateman and P. Erdös. Geometrical extrema suggested by a lemma of Besicovitch. Amer. Math. Monthly 58, (1951). 306--314.

T. Botts. Convex sets. Amer. Math. Monthly 49, (1942). 527--535.

G. D. Chakerian and M. S. Klamkin. Inequalities for sums of distances. Amer. Math. Monthly 80 (1973). 1009--1017.

C. Davis. The short-cut problem. Amer. Math. Monthly 55, (1948). 147--150.

Ren De-lim. Topics in integral geometry. World Scientific, Singapore: 1994.

D. Dekker. Convex regions in projective N-space. Amer. Math. Monthly 62, (1955). 430--431.

D. W. DeTemple and J. M. Robertson. Constructing Buffon curves from their distributions. Amer. Math. Monthly 87 (1980), no. 10. 779--784.

S. R. Dunbar. The average distance between points in geometric figures. College Math. J. 28 (1997), no. 3. 187--197.

B. Eisenberg and R. Sullivan. Crofton's differential equation. Amer. Math. Monthly 107 (2000), no. 2. 129--139.

K. J. Falconer. Applications of a result on spherical integration to the theory of convex sets. Amer. Math. Monthly 90 (1983), no. 10. 690--693.

T. L. Fejes. New proof of a minimum property of the regular n-gon. Amer. Math. Monthly 54, (1947). 589.

M. Fraser. The grazing goat in n dimensions. College Math. J. 15 (1984), no. 2. 126--134.

M. Goldberg. Circular-arc rotors in regular polygons. Amer. Math. Monthly 55, (1948). 393--402.

M. Goldberg. Trammel rotors in regular polygons. Amer. Math. Monthly 64 (1957). 71--78.

H. Hadwiger. Nonseparable convex systems. Amer. Math. Monthly 54, (1947). 583--585.

R. Howard and P. Sisson. Capturing the origin with random points: generalizations of a Putnam problem. College Math. J. 27 (1996), no. 3. 186--192.

P. J. Kelly. A property of Minkowskian circles. Amer. Math. Monthly 57, (1950). 677--678.

P. J. Kelly. Curves with a kind of constant width. Amer. Math. Monthly 64 (1957). 333--336.

D. A. Klain and Gian-Carlo Rota. Introduction to geometric probability. Cambridge University Press, Cambridge: 1997.

V. L. Klee, Jr. A characterization of convex sets. Amer. Math. Monthly 56, (1949). 247--249.

V. L. Klee. A note on extreme points. Amer. Math. Monthly 62, (1955). 30--32.

P. W. Kuchel and R. J. Vaughan. Average lengths of chords in a square. Math. Mag. 54 (1981), no. 5. 261--269.

V. Linis. Ovals with equichordal points. Amer. Math. Monthly 64 (1957). 420--422.

National Council of Teachers of Mathematics. Geometric probability. NCTM, Reston, VA: 1988.

W. V. Parker and J. E. Pryor. Polygons of greatest area inscribed in an ellipse. Amer. Math. Monthly 51, (1944). 205--209.

N. Peyerimhoff. Areas and intersections in convex domains. Amer. Math. Monthly 104 (1997), no. 8. 697--704.

G. Pólya. An elementary analogue to the Gauss-Bonnet theorem. Amer. Math. Monthly 61, (1954). 601--603.

R. Redheffer. A curious formula for distance. Amer. Math. Monthly 64 (1957). 195--196.

L. A. Santalo. Introduction to integral geometry. Librairie Scientifique Hermann et Cie, Paris: 1953.

L. A. Santalo. Integral geometry and geometric probability. Prentice-Hall, Inc. New Jersey: 1966.

E. R. Scheinerman and H. S. Wilf. The rectilinear crossing number of a complete graph and Sylvester's "four point problem" of geometric probability. Amer. Math. Monthly 101 (1994), no. 10. 939--943.

I. J. Schoenberg. On a theorem of Kirzbraun and Valentine. Amer. Math. Monthly 60, (1953). 620--622.

B. Segre and K. Mahler. On the densest packing of circles. Amer. Math. Monthly 51, (1944). 261--270.

H. Solomon. Geometric Probability. Society for Industrial and Applied Mathematics, Philadelphia, PA: 1978.

G. Steensholt. Note on an elementary property of triangles. Amer. Math. Monthly 63 (1956). 571--572.

B. M. Stewart. A maximum problem. Amer. Math. Monthly 49, (1942). 454--456.

B. M. Stewart. The two-area covering problem. Amer. Math. Monthly 58, (1951). 394--403.

F. A. Valentine. A characteristic property of the circle in the Minkowski plane. Amer. Math. Monthly 58, (1951). 484--487.

L. J. Wallen. All the way with Wirtinger: a short proof of Bonnesen's inequality. Amer. Math. Monthly 94 (1987), no. 5. 440--442.

J. Whittaker. Random triangles. Amer. Math. Monthly 97 (1990), no. 3. 228--230.

L. L. Whyte. Unique arrangements of points on a sphere. Amer. Math. Monthly 59, (1952). 606--611.

L. Zalcman. Offbeat integral geometry. Amer. Math. Monthly 87 (1980), no. 3. 161--175.