(adsbygoogle = window.adsbygoogle || []).push({}); Let a0, . . . , an be points on the unit circle. Show that there is some other point p on the unit circle such that the product of the distances from p to ai for i=0,...,n at least 1. (Hint: Maximum Modulus Principle)

Maximum Modulus Principle: Let f be a nonconstant holomorphic function in the open connected subset G of C. Then absolute value of f does not attain a local maximum.

Man, I'm so stuck on this problem. I can't seem to figure out how the maximum modulus principle relates to the problem. Besides, the problem is asking me to find the lower bound for the product whereas the the maximum modulus principle states that there is no upper bound. I'm so confused.

Anything would help from you geniuses out there: A hint or advice.

Regards,

Steve

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Given n points on the unit circle

Loading...

Similar Threads for Given points unit | Date |
---|---|

Questions related to an unknown function given its values at some points | Oct 10, 2015 |

Parameterising a line given by two points | Jun 19, 2013 |

Calculus derivative of given function vanishes at some point between a and b | Oct 10, 2012 |

Value of second derivative at a given point? | Apr 30, 2012 |

Numerical integration, use given random distribution as integration points | Apr 5, 2012 |

**Physics Forums - The Fusion of Science and Community**