The arc length of the lemniscate

Author:
Peter Borwein

Journal:
Proc. Amer. Math. Soc. **123** (1995), 797-799

MSC:
Primary 31A15; Secondary 26D05

DOI:
https://doi.org/10.1090/S0002-9939-1995-1223265-3

MathSciNet review:
1223265

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the length of the set

**[1]**George A. Baker Jr.,*Essentials of Padé approximants*, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR**0454459****[2]**P. Erdős, F. Herzog, and G. Piranian,*Metric properties of polynomials*, J. Analyse Math.**6**(1958), 125–148. MR**0101311**, https://doi.org/10.1007/BF02790232**[3]**P. Erdős,*Extremal problems on polynomials*, Approximation theory, II (Proc. Internat. Sympos., Univ. Texas, Austin, Tex., 1976) Academic Press, New York, 1976, pp. 347–355. MR**0477003****[4]**Ch. Pommerenke,*On some metric properties of polynomials with real zeros*, Michigan Math. J.**6**(1959), 377–380. MR**0109876****[5]**Ch. Pommerenke,*On some problems by Erdős, Herzog and Piranian*, Michigan Math. J.**6**(1959), 221–225. MR**0109875****[6]**Ch. Pommerenke,*On some metric properties of polynomials with real zeros. II*, Michigan Math. J**8**(1961), 49–54. MR**0120350****[7]**Ch. Pommerenke,*On metric properties of complex polynomials*, Michigan Math. J.**8**(1961), 97–115. MR**0151580****[8]**Luis A. Santaló,*Integral geometry and geometric probability*, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. With a foreword by Mark Kac; Encyclopedia of Mathematics and its Applications, Vol. 1. MR**0433364****[9]**Elias Wegert and Lloyd N. Trefethen,*From the Buffon needle problem to the Kreiss matrix theorem*, Amer. Math. Monthly**101**(1994), no. 2, 132–139. MR**1259826**, https://doi.org/10.2307/2324361

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1223265-3

Keywords:
Capacity,
arclength,
Erdös,
lemniscate,
polynomial

Article copyright:
© Copyright 1995
American Mathematical Society