Ono's inequality

Ono's inequality

In mathematics, Ono's inequality is a theorem about triangles in the Euclidean plane. In its original form, as conjectured by T. Ono in 1914, the inequality is actually false; however, the statement is true for acute triangles, as shown by Balitrand in 1916.

Statement of the inequality

Consider an acute triangle in the Euclidean plane with side lengths a, b and c and area A. Then

27 (b^2 + c^2 - a^2)^2 (c^2 + a^2 - b^2)^2 (a^2 + b^2 - c^2)^2 \leq (4 A)^6.

This inequality fails for general triangles (which was Ono's original conjecture), as shown by the counterexample a = 3/4, b = 1/2, c = 1.

External links

References

  • Balitrand, F. (1916). "Problem 4417". Intermed. Math. 23: 86–87. 
  • Ono, T. (1914). "Problem 4417". Intermed. Math. 21: 146. 
  • Quijano, G. (1915). "Problem 4417". Intermed. Math. 22: 66. 

Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • List of inequalities — This page lists Wikipedia articles about named mathematical inequalities. Inequalities in pure mathematics =Analysis= * Askey–Gasper inequality * Bernoulli s inequality * Bernstein s inequality (mathematical analysis) * Bessel s inequality *… …   Wikipedia

  • List of triangle topics — This list of triangle topics includes things related to the geometric shape, either abstractly, as in idealizations studied by geometers, or in triangular arrays such as Pascal s triangle or triangular matrices, or concretely in physical space.… …   Wikipedia

  • Triangle — This article is about the basic geometric shape. For other uses, see Triangle (disambiguation). Isosceles and Acute Triangle redirect here. For the trapezoid, see Isosceles trapezoid. For The Welcome to Paradox episode, see List of Welcome to… …   Wikipedia

  • List of mathematics articles (O) — NOTOC O O minimal theory O Nan group O(n) Obelus Oberwolfach Prize Object of the mind Object theory Oblate spheroid Oblate spheroidal coordinates Oblique projection Oblique reflection Observability Observability Gramian Observable subgroup… …   Wikipedia

  • Riemann hypothesis — The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011 …   Wikipedia

  • List of mathematics articles (B) — NOTOC B B spline B* algebra B* search algorithm B,C,K,W system BA model Ba space Babuška Lax Milgram theorem Baby Monster group Baby step giant step Babylonian mathematics Babylonian numerals Bach tensor Bach s algorithm Bachmann–Howard ordinal… …   Wikipedia

  • POPULATION — THE JEWISH POPULATION Growth by Aliyah In 1882 the Jewish population of Ereẓ Israel numbered some 24,000, roughly 5% of the total, and about 0.3% of the world Jewish population. Since then there has been an almost continuous flow of aliyah, which …   Encyclopedia of Judaism

  • Degeneracy (graph theory) — In graph theory, a k degenerate graph is an undirected graph in which every subgraph has a vertex of degree at most k: that is, some vertex in the subgraph touches k or fewer of the subgraph s edges. The degeneracy of a graph is the smallest… …   Wikipedia

  • History of Bougainville — Bougainville is a province of Papua New Guinea. It was named after the French navigator Louis Antoine de Bougainville. Contents 1 Prehistory 2 European colonisation 3 Second World War …   Wikipedia

  • List of Guggenheim Fellowships awarded in 2003 — U.S. and Canadian Fellows= * Gerard Aching, Associate Professor of Spanish and Portuguese and Director of Graduate Studies, New York University: Black socialist thought and literature in the Caribbean, 1925 1945. * Diane Ackerman, Writer, Ithaca …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”