Results 221 to 230 of about 6,790 (254)
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The Non-Equilateral Morley Triangles
The Mathematical Gazette, 1942In the Gazette , No. 248 (February, 1938), pp. 50-57, Mr. W J Dobbs gave a very interesting and complete descriptive account of the 18 equilateral “Morley” triangles of a given triangle. The article is especially memorable for its diagrams (1-8) and the present reader is asked to have them at
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The Heat Equation in the Interior of an Equilateral Triangle
Studies in Applied Mathematics, 2010Summary: We present the solution of the classical problem of the heat equation formulated in the interior of an equilateral triangle with Dirichlet boundary conditions. This solution is expressed as an integral in the complex Fourier space, i.e., the complex \(k_1\) and \(k_2\) planes, involving appropriate integral transforms of the Dirichlet boundary
Kalimeris, K., Fokas, A. S.
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Exit Times from Equilateral Triangles
Applied Mathematics and Optimization, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alabert, Aureli +2 more
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Vietnam Journal of Mathematics, 2014
We characterize all three point sets in ℝ4 with integer coordinates, the pairs of which are the same Euclidean distance apart. In three dimensions, the problem is characterized in terms of solutions of the Diophantine equation a 2 + b 2 + c 2 = 3d 2.
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We characterize all three point sets in ℝ4 with integer coordinates, the pairs of which are the same Euclidean distance apart. In three dimensions, the problem is characterized in terms of solutions of the Diophantine equation a 2 + b 2 + c 2 = 3d 2.
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On mappings preserving equilateral triangles
Journal of Geometry, 2004The authors show that if a non-constant self-map \(\varphi\) of a finite-dimensional Euclidean space of dimension \(\geq 2\) preserves isosceles triangles (or if it is measurable and preserves equilateral triangles), then it is a similarity. If the dimension is \(\geq 3\) and \(\varphi\) is not constant and preserves equilateral triangles, then it is a
Sikorska, Justyna, Szostok, Tomasz
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On the largest outscribed equilateral triangle
The Mathematical Gazette, 2014An outscribed triangle of a triangle 4ABC is a triangle 4DEF such that each side of 4DEF contains a vertex of 4ABC. In this article we study the equilateral outscribed triangles of an arbitrary triangle and determine the area of the largest such triangles. We prove that the largest outscribed equilateral triangle of 4ABC can be constructed by ruler and
Fengming Dong +2 more
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A sacred geometry of the equilateral triangle
International Journal of Mathematical Education in Science and Technology, 2008In this article, we investigate the construction of spirals on an equilateral triangle and prove that these spirals are geometric. In further analysing these spirals we show that both the male (straight line segments) and female (curves) forms of the spiral exhibit exactly the same growth ratios and that these growth ratios are constant independent of ...
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A Characterization of the Equilateral Triangles and Some Consequences
The Mathematical Intelligencer, 2014Equilateral triangles are characterised as having three sides of equal length. The author generalises this characterisation to what he calls Conway's Little Theorem: Equilateral triangles are characterised by the assertion that each ratio of two sides and each ratio of two angles are rational.
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Equilateral Triangles and Triangles
The American Mathematical Monthly, 2002Richard Jerrard, John E. Wetzel
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Some Remarks on Equilateral Triangles and Squares
The Mathematical Gazette, 1953Let a 1 , a 2 , a 3 denote the sides α 1 , α2, α 3 the angles and
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