Andrica–iwata’s Inequality in Hyperbolic Triangle

نویسندگان

  • CĂTĂLIN BARBU
  • LAURIAN-IOAN PIŞCORAN
چکیده

[1] D. ANDRICA, O inegalitate ı̂n triunghi şi aplicaţiile acesteia, Gazeta Matematică, Seria B, Bucureşti, 1 (1986), 2–4. [2] L. BALOG, Gazeta Matematică, Seria B, Bucureşti, 9 (1989), p. 334. [3] H. S. M. COXETER, Non-Euclidean geometry, M.A.A., 1998. [4] S. IWATA, Encyclopedia of Geometry (Japanese), Tokyo, 1971, Vol. 5, p. 345. [5] D. S. MITRINOVIĆ, J. E. PEČARIĆ, V. VOLENEC, Recent Advances in Geometric Inequalities, Kluwer Academic Publishers, 1989, p. 198. [6] C. I. ŢIU, Aplicaţii ı̂n trigonometrie, Ed. Academiei, 1992, p. 183. [7] W. STOTHERS, Geometry Pages, http://www.maths.gla.ac.uk/.

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

A Geometric Proof of Blundon’s Inequalities

A geometric approach of Blundon’s inequality is presented. Theorem 2.1 gives the formula for cos ̂ ION in terms of the symmetric invariants s , R , r of a triangle, implying Blundon’s inequality (Theorem 2.2). A dual formula for cos ̂ IaONa is given in Theorem 3.1 and this implies the dual Blundon’s inequality (Theorem 3.2). As applications, some inequalities involving the exradii of the triangle...

متن کامل

A Stronger Triangle Inequality for Neutral Geometry

Bailey and Bannister [College Math. Journal, 28 (1997) 182–186] proved that a stronger triangle inequality holds in the Euclidean plane for all triangles having largest angle less than arctan( 7 ) ≈ 74◦. We use hyperbolic trigonometry to show that a stronger triangle inequality holds in the hyperbolic plane for all triangles having largest angle less than or equal to 65.87◦ .

متن کامل

Non-Euclidean Versions of Some Classical Triangle Inequalities

In this paper we recall with short proofs of some classical triangle inequalities, and prove corresponding non-Euclidean, i.e., spherical and hyperbolic versions of these inequalities. Among them are the well known Euler’s inequality, Rouché’s inequality (also called “the fundamental triangle inequality”), Finsler–Hadwiger’s inequality, isoperimetric inequality and others.

متن کامل

A Strong Triangle Inequality in Hyperbolic Geometry

For a triangle in the hyperbolic plane, let α, β, γ denote the angles opposite the sides a, b, c, respectively. Also, let h be the height of the altitude to side c. Under the assumption that α, β, γ can be chosen uniformly in the interval (0, π) and it is given that α + β + γ < π, we show that the strong triangle inequality a + b > c + h holds approximately 79% of the time. To accomplish this, ...

متن کامل

On the metric triangle inequality

A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T$_{1}$-separated and generally, non-Hausdorff.

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 2012