The Best Constant in a Geometric Inequality Relating Medians, Inradius and Circumradius in a Triangle

نویسندگان

  • SHI-CHANG SHI
  • YU-DONG WU
  • Y.-D. WU
چکیده

In this paper, the authors give a refinement of the inequality associated with the medians, inradius and circumradius in a triangle by making use of certain analytical techniques for systems of nonlinear algebraic equations.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Quantum steering ellipsoids, extremal physical states and monogamy

Any two-qubit state can be faithfully represented by a steering ellipsoid inside the Bloch sphere, but not every ellipsoid inside the Bloch sphere corresponds to a two-qubit state. We give necessary and sufficient conditions for when the geometric data describe a physical state and investigate maximal volume ellipsoids lying on the physical-unphysical boundary. We derive monogamy relations for ...

متن کامل

IMO/KKK/Geometric Inequality/1 Geometric Inequalities

Notation and Basic Facts a, b, and c are the sides of ∆ABC opposite to A, B, and C respectively. [ABC] = area of ∆ABC s = semi-perimeter =) c b a (2 1 + + r = inradius R = circumradius Sine Rule: R 2 C sin c B sin b A sin a = = = Cosine Rule: a 2 = b 2 + c 2 − 2bc cos A [ABC] = B sin ac 2 1 A sin bc 2 1 C sin ab 2 1 = = = R 4 abc =) c s)(b s)(a s (s − − − (Heron's Formula) = 2 cr 2 br 2 ar + + ...

متن کامل

Symmetric Homogeneous Triangle Inequalities

A brief scan through the problem columns of various mathematical journals shows a continual outpouring of proposed problems involving what can be roughly described as “triangle inequalities”. A few examples will suffice to indicate the flavor of these perennial favorites: Let the sides of a triangle be a, b, c and let the angles be A, B, C. Let r and R be the inradius and circumradius, respecti...

متن کامل

ON INEQUALITY Rp < R OF THE PEDAL TRIANGLE

In this paper we give a simple proof of the pedal triangle inequality Rp < R , where R is the circumradius of a triangle and Rp is the circumradius of the pedal triangle of an interior point with respect to this triangle. We also establish a stronger result and a refinement of inequality Rp < R . Some related interesting conjectures checked by the computer are put forward. Mathematics subject c...

متن کامل

Condition number and eccentricity of a closed convex cone

We discuss some extremality issues concerning the circumradius, the inradius, and the condition number of a closed convex cone in Rn. The condition number refers to the ratio between the circumradius and the inradius. We also study the eccentricity of a closed convex cone, which is a coefficient that measures to which extent the circumcenter differs from the incenter.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013