Murray S. Klamkin
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American mathematician
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Mathematics
Why Is Murray S. Klamkin Influential?
(Suggest an Edit or Addition)According to Wikipedia, Murray Seymour Klamkin was an American mathematician, known as prolific proposer and editor of professionally-challenging mathematical problems. Life Klamkin was born on March 5, 1921, in Brooklyn, New York. He received a bachelor's degree from the Cooper Union in 1942 and, after four years of service in the United States Army, earned a master's degree from the Polytechnic Institute of Brooklyn in 1947, where he taught from 1948 until 1957.
Murray S. Klamkin's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Extensions of the birthday surprise (1967) (79)
- ON THE TRANSFORMATION OF A CLASS OF BOUNDARY VALUE PROBLEMS INTO INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS (1962) (70)
- Elementary Approximations to the Area of N-Dimensional Ellipsoids (1971) (66)
- Cyclic Pursuit or “the Three Bugs Problem” (1971) (43)
- Transformation of boundary value problems into initial value problems (1970) (36)
- Mathematical Modelling: Classroom Notes in Applied Mathematics (1987) (31)
- Minimal Covers for Closed Curves (1973) (26)
- Corrections to Ëlementary Approximations to the Area of N-Dimensional Ellipsoids" (1976) (26)
- The Circumradius-Inradius Inequality for a Simplex (1979) (21)
- The Excluded Volume of Polymer Chains (1952) (21)
- An Ellipse Inequality (1977) (21)
- The Philosophy and Applications of Transform Theory (1961) (19)
- Triangulations and Pick's Theorem (1976) (18)
- Inequality for a Simplex (1985) (17)
- Conjectured Isoptic Characterization of a Circle (1988) (17)
- On the teaching of mathematics so as to be useful (1968) (17)
- Inequalities for Sums of Distances (1973) (16)
- Problems in applied mathematics : selections from SIAM review (1990) (15)
- Extensions of the Weierstrass Product Inequalities II (1970) (15)
- Vector Proofs in Solid Geometry (1970) (15)
- Simultaneous Generalizations of the Theorems of Ceva and Menelaus (1992) (14)
- Problem of the Month (2002) (14)
- Geometric Inequalities Via the Polar Moment of Inertia (1975) (14)
- USA Mathematical Olympiads 1972-1986 (1988) (12)
- Polyominoes on the Infinite Checkerboard (1980) (12)
- On some multiple integrals (1976) (11)
- The Industrial Mathematician Views his Profession: A Report of the Committee on Corporate Members (1974) (10)
- A Physical Characterization of a Sphere (1964) (10)
- Unsolved Problems in Intuitive Mathematics, Vol. II, Unsolved Problems in Geometry (H. T. Croft, K. J. Falconer, and R. K Guy) (1992) (10)
- The Asymmetric Propeller (1973) (9)
- Ptolemy's inequality, chordal metric, multiplicative metric. (1982) (9)
- An Extension of the Butterfly Problem (1965) (9)
- Elementary Problems: E3301-E3306 (1989) (9)
- Diffraction by fcc Crystals with Intrinsic and Extrinsic Faults (1969) (9)
- EXTENSIONS OF DIRICHLET'S MULTIPLE INTEGRAL* (1971) (8)
- On best quadratic triangle inequalities (1973) (8)
- The kissing number of the square (1995) (8)
- A Conjectured Heat Flow Problem (1994) (8)
- Inequalities and Identities for Sums and Integrals (1976) (7)
- On the ideal role of an industrial mathematician and its educational implications (1971) (7)
- Corrections to “Elementary Approximations to the area of N-Dimensional Ellipsoids”: (This Monthly, 78 (1971) 280–283) (1976) (7)
- A spherical characterization of the normal distribution (1976) (7)
- On Cooking a Roast (1961) (7)
- Five hundred mathematical challenges (1995) (7)
- Problems for Solution: 4713-4717 (1956) (6)
- Cyclic Pursuit or "The Three Bugs Problems" (1971) (6)
- Advanced Problems: 6439-6441 (1983) (6)
- Simultaneous Triangle Inequalities (1987) (6)
- On the Coefficients of a Partial Fraction Decomposition (1979) (5)
- Euler's Ratio-Sum Theorem and Generalizations (2006) (5)
- Note on a Result of Niven on Impossible Tessellations (1980) (5)
- Nonlinear Differential Equations Equivalent to Solvable Nonlinear Equations (1976) (5)
- Problems for Solution: 4428-4432 (1951) (5)
- Mathematical modelling: die cutting for a fresnel lens (1980) (5)
- On Two Classes of Extremum Problems without Calculus (1992) (5)
- A Boundary Value Problem (1964) (5)
- On the Reducibility of Some Linear Differential Operators (1959) (4)
- On some inverse problems in potential theory (1968) (4)
- A Reverse Card Shuffle (1976) (4)
- Flying in a Wind Field, II (1969) (4)
- Elementary Problems: E2546-E2551 (1975) (3)
- On an Elementary Derivation of Cramer's Rule (1953) (3)
- CLASSROOM NOTES IN APPLIED MATHEMATICS (1983) (3)
- Elementary Problems: E3237-E3242 (1987) (3)
- Existence of Four Concurrent Normals to a Smooth Closed Curve (1970) (3)
- International Mathematical Olympiads 1978-1985 and Forty Supplementary Problems (1986) (3)
- 3249. On the roots of a certain determinantal equation (1970) (3)
- On the Uniqueness of the Distribution Function for the Buffon Needle Problem (1953) (3)
- On the Volume of a Class of Truncated Prisms and Some Related Centroid Problems (1968) (3)
- Extrema of Polynomials (1977) (3)
- On soluble nth order linear differential equations (1981) (3)
- Triangle inequalities from the triangle inequality. (1979) (3)
- Elementary Problems: E2932, E2956-E2961 (1982) (3)
- Mathematical modelling: A student optimal control problem and extensions (1985) (3)
- A Probability of More Heads (1971) (3)
- On the Number of Distinct Zeros of Polynomials (1959) (3)
- Ceva's and Menelaus' Theorems and Their Converses via Centroids (1996) (3)
- On some inverse problems in dynamics (1968) (3)
- On an nth Order Differential Equation (1967) (3)
- A Minimum Value (1984) (3)
- Some Combinatorial Problems of Arithmetic (1969) (3)
- A Property of Harmonic Functions (1962) (3)
- On the Butterfly Property (1969) (2)
- Advanced Problems: 5460-5469 (1967) (2)
- Problems for Solution: E1271-E1275 (1957) (2)
- An Inverse Potential Problem (1988) (2)
- Rigid and Very Rigid Tetrahedra: 10717 (2000) (2)
- An Experience in Problem Solving (1981) (2)
- A Three-Point Characterization of Central Symmetry (2004) (2)
- N-Dimensional Volume (1959) (2)
- On a Generlization of the Geometric Series (1957) (2)
- On Proving Trigonometric Identities (1983) (2)
- On Some Symmetric Sets of Unit Vectors (1991) (2)
- An Optimal Strategy (1974) (2)
- International Mathematical Olympiads, 1978–1985: Glossary (1986) (2)
- Expectations for Sums of Powers (1959) (2)
- VERTICAL MOTION WITH AIR RESISTANCE (1984) (2)
- Orthocenters upon Orthocenters: 10453 (1998) (2)
- Two Non-Negative Quadratic Forms. (1973) (2)
- An Expected Value (1971) (2)
- The ballot problem (1959) (2)
- An Infinite Permutation (1963) (2)
- Problems Dedicated to Emory P. Starke: S9-S10 (1979) (2)
- An anomalous heat conduction problem (1989) (2)
- Problems: 10487-10493 (1995) (2)
- Minimum Triangles Inscribed in a Convex Curve (1973) (2)
- Problems for Solution: E1121-E1125 (1954) (1)
- Elementary Problems: E3337-E3342 (1989) (1)
- Calculus: Basic Concepts for High Schools (L. V. Tarasov) (1984) (1)
- Problems for Solution: 4528,4543-4547 (1953) (1)
- Elementary Problems: E2215-E2220 (1970) (1)
- On Some Problems in Gravitational Attraction (1968) (1)
- A Parking Problem (1960) (1)
- Determination of the temperature dependence of material properties in image furnaces (1960) (1)
- Extensions of an elementary geometric inequality (1983) (1)
- On the Diagonals of a Polygon (1971) (1)
- Generalizations of a Complex Number Identity (1989) (1)
- Generalization of Clairaut's Differential Equation and the Analogous Difference Equation (1953) (1)
- Elementary Problems: E2980-E2985 (1983) (1)
- Perfect Squares of the Form (m 2 - 1)a 2 n + t (1969) (1)
- Elementary Problems: E2426-E2431 (1973) (1)
- Problems for Solution: 5025-5030 (1962) (1)
- A Moving Boundary Filtration Problem or “The Cigarette Problem” (1957) (1)
- Symmetry in Probability Distributions (1988) (1)
- On a Graphical Solution of the First Order Linear Differential Equation (1954) (1)
- Problems for Solution: E1346-1350 (1959) (1)
- International Mathematical Olympiads, 1978–1985: Appendix A (1986) (1)
- Flight in an Irrotational Wind Field. II(M. S. Klamkin) (1962) (1)
- A Quartic (1970) (1)
- An Isoperimetric Inequality (1983) (1)
- Advanced Problems: 5734-5739 (1970) (1)
- Circle Through Three Given Points (1971) (1)
- An asymptotic problem in renewal theory (1972) (1)
- Using the Walls to Find the Center: 10386 (1999) (1)
- 8. Numerical Analysis (1987) (1)
- Problems for Solution: 4869-4874 (1959) (1)
- Problems from Murray Klamkin: The Canadian Collection (2009) (1)
- A Generalization of the Pythagorean Theorem Seen as a Problem of Equivalent Resistances (1986) (1)
- The product of the distances of a point inside a regular polytope to its vertices (2007) (1)
- Vorticity Interaction (Sin-I Cheng) (1961) (1)
- A Volume Inequality for a Pair of Associated Simplexes (1978) (1)
- Problems for Solution: 4941-4946 (1961) (1)
- Extensions of Some Geometric Inequalities (1976) (1)
- Extended Reducibility of Some Differential Operators (1967) (1)
- A Triangle Inequality (M. S. Klamkin) (1980) (0)
- Elementary Problems: E1965-E1974 (1967) (0)
- Ordered Affine Geometry: 10560 (1998) (0)
- Problems and Solutions (2000) (0)
- A Note on an nth Order Linear Differential Equation (1958) (0)
- 21. Functional Equations (1990) (0)
- 7. Ordinary Differential Equations (1990) (0)
- Problems for Solution E1441-E1445 (1960) (0)
- Problems for Solution: 5013-5018 (1962) (0)
- Problems for Solution: 4748-4752 (1957) (0)
- Problems for Solution: 4572,4583-4587 (1954) (0)
- Problem corner (1983) (0)
- Mathematics: Problem Solving through Recreational Mathematics. By Bonnie Averbach and Orin Chein (1983) (0)
- NOT COMPLETELY CONTROLLABLE (1987) (0)
- 10. Optimization (Including Linear; Nonlinear, Dynamic, and Geometric Programming, Control Theory, Games and Other Miscellaneous Topics) (1987) (0)
- Problems for Solution: 4816-4821 (1958) (0)
- Advanced Problems: 6293-6295 (1980) (0)
- 10. Integral Equations (1990) (0)
- NOT COMPLETELY CONTROLLABLE (1987) (0)
- Five Hundred Mathematical Challenges: Solutions (1995) (0)
- A Possible Characterization of Uniformly Accelerated Motion (1994) (0)
- Problems for Solution: 4670-4671,4679-4682 (1956) (0)
- Problems for Solution: 4578-4582 (1954) (0)
- Problem Section (2001) (0)
- PROBLEMS Variational Problem for Overlapping Laser Pulses (2013) (0)
- Problems for Solution: 4768-4772 (1958) (0)
- Problem corner (1988) (0)
- Problems for Solution: 4593-4597 (1954) (0)
- The Equation of a Sphere (1969) (0)
- Intersecting Curves on a Surface (1968) (0)
- Letters to the editor (2002) (0)
- Problem section (2000) (0)
- On Extreme Length Flight Paths (1976) (0)
- Elementary Problems: E2599-E2604 (1976) (0)
- Problems and Solutions (2000) (0)
- A Steady-State Temperature (Alan L. Tritter) (1964) (0)
- A Center of Gravity Perturbation (1960) (0)
- An n-th Order Linear Differential Equation (1976) (0)
- Problems for Solution: 4453-4457 (1951) (0)
- Problems for Solution: 4508-4512 (1952) (0)
- Problem Corner (1992) (0)
- Problem Section (2001) (0)
- Elementary Problems: E2208,E2228-E2234 (1970) (0)
- Problems for Solution: 4663-4667 (1955) (0)
- 12. Numerical Approximations and Asymptotic Expansions (1990) (0)
- Five Hundred Mathematical Challenges: Problems (1995) (0)
- Elementary Problems: E2391-E2396 (1973) (0)
- Problems for Solution: 4558-4562 (1953) (0)
- Elementary Problems: E2962-E2967 (1982) (0)
- Problems: 10389-10395 (1994) (0)
- Elementary Problems: E1822,E2570-E2574 (1976) (0)
- Problems for Solution: 4877, 4887-4892 (1960) (0)
- Problem corner (1984) (0)
- Problems for Solution: 4563-4567 (1953) (0)
- Problems for Solution: E1431-E1435 (1960) (0)
- Problems for Solution: E1291-E1295 (1957) (0)
- Problems for Solution: 4822-4827 (1959) (0)
- Elementary Problems: E2534-E2539 (1975) (0)
- 6. Graph Theory and Applications (1987) (0)
- SOLUTIONS A Conjectured Heat Flow Problem Problem (0)
- International Mathematical Olympiads, 1978–1985: Olympiad Problems (1986) (0)
- An Inverse Potential Problem (M. S. Klamkin) (1989) (0)
- Problems for Solution: 4673-4677 (1956) (0)
- International Mathematical Olympiads, 1978–1985: Editors' Note (1986) (0)
- Elementary Problems: E3177-E3182 (1986) (0)
- Extension of Routh’s Theorem to Spherical Triangles (1985) (0)
- Another Sphere From Off-Center: 10488 (1998) (0)
- A Single Inequality Condition for the Existence of Many r-gons (1990) (0)
- Problem corner (1981) (0)
- On Some Soluble Nth Order Differential Equations (1970) (0)
- Discrete and System Models (William F. Lucas, Fred S. Roberts and Robert M. Thrall, eds.) (1984) (0)
- Problems for Solution: 4983-4988 (1961) (0)
- An Optimum Multistage Rocket Design (M. S. Klamkin) (1988) (0)
- 7. Applied Geometry (1987) (0)
- Solutions of Supplementary Problems (2011) (0)
- On Vector Sums and Products (1954) (0)
- How Does One Cut A Triangle? By Alexander Soifer (1991) (0)
- Problems for Solution: E1196-E1200 (1956) (0)
- Problem corner (1983) (0)
- Problem corner (1981) (0)
- An Identity for Complex Numbers (1980) (0)
- An Application of the Gauss Multiplication Theorem (1957) (0)
- Elementary Problems: E2235-E2241 (1970) (0)
- 2. Electrical Resistance (1990) (0)
- On the Convergence of the p-Series (1953) (0)
- Problems for Solution: E1236-E1240 (1956) (0)
- Problem Corner (1982) (0)
- Problems for Solution: 4548-4552 (1953) (0)
- IN A PULL-UP FROM A DIVE* (1988) (0)
- Avoiding Lattice Points: 10538 (1998) (0)
- Problem 17, May 2001 (2004) (0)
- Problems for Solution: E1241-E1245 (1956) (0)
- Review: Z. A. Melzak, Companion to concrete mathematics (1978) (0)
- Elementary Problems: E1073,E1445,E2510-E2515 (1975) (0)
- A Dice Problem (1980) (0)
- Problems for Solution: 4623-4627 (1955) (0)
- Problems for Solution: 4778-4782 (1958) (0)
- Elementary Problems: E2196-E2201 (1969) (0)
- Advanced Problems: 5701-5706 (1969) (0)
- Optimization problems in gravitational attraction (1972) (0)
- Problem corner (1993) (0)
- Non-Symmetric Cyclic Pursuit on a Sphere (1995) (0)
- Problems and Solutions (2000) (0)
- Problems for Solution: E1426-E1430 (1960) (0)
- Solutions of Olympiad Problems (2011) (0)
- 11. Matrices and Determinants (1990) (0)
- Problems: 10452-10458 (1995) (0)
- 9. Mathematical Economics (1987) (0)
- Problems for Solutions: E1046-E1050 (1953) (0)
- 4. Electrical Networks (1987) (0)
- Geodesics on Surfaces of Revolution (1968) (0)
- Problems and Solutions: Elementary Problems: E2480-E2485 (1974) (0)
- Conductors of Unit Resistance (1970) (0)
- Evaluation of Surface and Volume Integrals Over a Sphere (1964) (0)
- Problems for Solution: 4743-4747 (1957) (0)
- The Smallest Escape Asteroid (1959) (0)
- Problems and Solutions (2000) (0)
- Problems and Solutions (2000) (0)
- 11. Stochastic Models (1987) (0)
- A Physical Application of a Rearrangement Inequality (1970) (0)
- Problem corner (1983) (0)
- 9. Definite Integrals (1990) (0)
- Problems for Solution: E1366-E1370 (1959) (0)
- On A Graphical Solution of Linear Differential Equations (1957) (0)
- Inequality for a Simplex (M. S. Klamkin) (1986) (0)
- Problems for Solution: E1533-E1540 (1962) (0)
- Extreme Gravitational Attraction (1992) (0)
- Problem corner (1993) (0)
- 13. Population Models (1987) (0)
- Elementary Problems: E3307-E3312 (1989) (0)
- A Vector Norm Inequality (1975) (0)
- Problems for Solution: 4783-4787 (1958) (0)
- Problem section (2000) (0)
- Advanced Problems: 5970-5975 (1974) (0)
- Triangle: An Orthocentric Study (2003) (0)
- Problems for Solution: 4828-4833 (1959) (0)
- The Scottish book: Mathematics from the Scottish cafe: Edited by R. Daniel Mauldin. Boston (Birkhauser). 1981. xiii + 268 pp. $24.95 (1984) (0)
- Problem corner (1999) (0)
- Problems for Solution: 4588-4592 (1954) (0)
- Problems for Solution: E1056-E1060 (1953) (0)
- A Duality Relation in Differential Equations and Some Associated Functional Equations (1966) (0)
- Problems for Solution: 4788-4792 (1958) (0)
- A Geometric Determination of the Nature of the Roots of the Cubic, Biquadratic, and Quintic Equations (1954) (0)
- Problems for Solution: 4513-4517 (1952) (0)
- Problems: 10274-10281 (1993) (0)
- Elementary Problems: E2495,E2516-E2521 (1975) (0)
- Problems for Solution: 4935-4940 (1960) (0)
- Counting the Solutions: 10540 (2001) (0)
- 2. Heat Transfer and Diffusion (1987) (0)
- Problems and Solutions (1997) (0)
- Elementary Problems: E2202-E2207 (1969) (0)
- Elementary Problems: E3183-E3188 (1987) (0)
- Advanced Problems: 6310-6315 (1980) (0)
- Problems for Solution: E1301-E1305 (1958) (0)
- Problems for Solution: 5101-5110 (1963) (0)
- 5. Communication and Coding (1987) (0)
- Problem Solver's Toolkit: No. 3 (2012) (0)
- Elementary Problems: E3319-E3324 (1989) (0)
- Problems for Solution: E1361-E1365 (1959) (0)
- Problem corner (1988) (0)
- Letters to (and from) the Editor (2000) (0)
- 18. Simultaneous Equations (1990) (0)
- Point of Minimum Temperature (1991) (0)
- A Characterization of Uniformly Accelerated Motion (1995) (0)
- 3. Traffic Flow (1987) (0)
- Elementary Problems: E2208-E2214 (1970) (0)
- Problems for Solution: E1151-E1155 (1955) (0)
- A Triangle Inequality (1979) (0)
- Characterizations of Parabolic Motion (1988) (0)
- Inequalities for Inscribed and Circumscribed Polygons (1980) (0)
- “ Quickie ” Inequalities (2003) (0)
- Problems Dedicated to Emory P. Starke: S11-S13 (1979) (0)
- Problems for Solution: E1581-E1590 (1963) (0)
- Problems and Solutions (2000) (0)
- Five Hundred Mathematical Challenges: The Tool Chest (1995) (0)
- Problem corner (1981) (0)
- Problems Dedicated to Emory P. Starke: S6-S8 (1979) (0)
- Flight in an Irrotational Wind Field. II (1961) (0)
- Advanced Problems: 5952,5994-5999 (1974) (0)
- Problem section (2001) (0)
- Problems for Solution: E1141-E1145 (1954) (0)
- Problems for Solution: E1126-E1130 (1954) (0)
- Advanced Problems: 5754,5777-5782 (1971) (0)
- On the Vector Triple Product (1954) (0)
- Duality in Spherical Triangles (1973) (0)
- Moving Axes and the Principle of the Complementary Function (1974) (0)
- Solution to problem 75-20 : Limit of an integral (2010) (0)
- Problems for Solution: E1176-E1180 (1955) (0)
- Problems for Solution: 4851-4856 (1959) (0)
- Cyclic Pursuit with Lead Angle (1990) (0)
- Determinant of a Partitioned Matrix (1980) (0)
- Problems for Solution: 4845-4850 (1959) (0)
- Fundamentals of Linear Algebra and Analytical Geometry (Ya. S. Bugrov and S. M. Nokolsky) (1984) (0)
- Problems for Solution: 4881-4886 (1960) (0)
- 14. Medical Models (1987) (0)
- Polynomials (E. J. Barbeau) (1990) (0)
- An algebraic theorem related to the theory of relativity (1982) (0)
- An Optimum Multistage Rocket Design (1987) (0)
- A Two Point Triangle Inequality (1977) (0)
- On Barbier's Solution of the Buffon Needle Problem (1955) (0)
- A Note on a Geometric Inequality (2001) (0)
- An Integral Inequality (1990) (0)
- Elementary Problems: E2221-E2227 (1970) (0)
- Advanced Problems: 5753-5758 (1970) (0)
- Problem corner (1999) (0)
- A Polynomial Diophantine Equation (1973) (0)
- A Problem Seminar (Donald J. Newman) (1984) (0)
- Five Hundred Mathematical Challenges: PREFACE (1995) (0)
- Advanced Problems: 5736,5746-5752 (1970) (0)
- Problem corner (1981) (0)
- Three Particles Moving on a Circle (1989) (0)
- On a Probability of Overlap (1964) (0)
- One-Dimensional Steady-State Ablation (Tom Munson) (1963) (0)
- Problems and Solutions (2000) (0)
- On a Chainomatic Analytical Balance (1955) (0)
- On a Graphical Solution of a Class of Differential Equations (1954) (0)
- IN A ROTATING MANOMETER (1990) (0)
- 8. Partial Differential Equations (1990) (0)
- 6. Special Functions (1990) (0)
- IN A ROTATING MANOMETER (1990) (0)
- Problems for Solution: E952,E961-E965 (1951) (0)
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