Agoraphobia 发表于 2025-3-21 20:02:55

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chuckle 发表于 2025-3-21 21:39:34

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背叛者 发表于 2025-3-22 02:47:40

Geometry and Trigonometrye following property of the equilateral triangles, which was noticed by the Romanian mathematician D. Pompeiu in 1936. Pompeiu’s theorem is a simple fact, part of classical plane geometry. Surprisingly, it was discovered neither by Euler in the eighteenth century nor by Steinitz in the nineteenth.

弓箭 发表于 2025-3-22 07:45:34

Algebra and AnalysisIn this section we will consider some applications of the simplest inequality in algebra:.,where equality holds if and only if . = 0.

NEX 发表于 2025-3-22 10:13:23

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混合物 发表于 2025-3-22 16:30:43

Geometry and Trigonometry1. The idea is to look at what happen in a neighborhood of a vertex. Let . be a triangle that is not equilateral and suppose that . < .. Let .. Choose . inside . such that . and .. This is possible because of the continuity of the distance function.

整理 发表于 2025-3-22 20:49:38

Algebra and Analysis1. If the inequalities.hold simultaneously, then by adding them we obtain .(.+.+.+) > 1.

燕麦 发表于 2025-3-23 01:14:01

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上釉彩 发表于 2025-3-23 01:24:54

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树木心 发表于 2025-3-23 07:44:51

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查看完整版本: Titlebook: Mathematical Olympiad Challenges; Titu Andreescu,Răzvan Gelca Textbook 20001st edition Birkhäuser Boston 2000 algebra.geometry.number theo