Results 191 to 200 of about 36,928 (235)

Almost Equilateral Heronian Triangles

Mathematics Magazine, 2020
A Heronian triangle is one whose sides (a, b, c) and area K are integers. An almost equilateral Heronian triangle is a Heronian triangle whose sides are consecutive integers such as (3, 4, 5), with...
openaire   +1 more source

The dissection of equilateral triangles into equilateral triangles

Mathematical Proceedings of the Cambridge Philosophical Society, 1948
In a previous joint paper (‘The dissection of rectangles into squares’, by R. L. Brooks, C. A. B. Smith, A. H. Stone and W. T. Tutte, Duke Math. J. 7 (1940), 312–40), hereafter referred to as (A) for brevity, it was shown that it is possible to dissect a square into smaller unequal squares in an infinite number of ways.
openaire   +2 more sources

Analytic characterization of equilateral triangles

Annali di Matematica Pura ed Applicata (1923 -), 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Equilateral Triangles in ℤ4

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.
openaire   +1 more source

The Non-Equilateral Morley Triangles

The Mathematical Gazette, 1942
In 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
openaire   +1 more source

On Partitions of an Equilateral Triangle

Canadian Journal of Mathematics, 1967
Let T denote a closed unit equilateral triangle. For a fixed integer n, let dn denote the infimum of all those x for which it is possible to partition T into n subsets, each subset having a diameter not exceeding x. We recall that the diameter of a plane set A is given bywhere ρ (a, b) is the Euclidean distance between a and b.In this note we ...
openaire   +1 more source

The Eigenvalues of an Equilateral Triangle

SIAM Journal on Mathematical Analysis, 1980
Let D be an equilateral triangle of side 1. We consider solutions of $\Delta u + \lambda u = 0$ in D with either the boundary condition $u = 0$ or ${{\partial u} / {\partial n }} = 0$. Let $n(\lambda )$ be the number of distinct eigenvalues $ \leqq \lambda $, $N(\lambda )$ be the total number of eigenvalues $ \leqq \lambda $, including multiplicities ...
openaire   +1 more source

On mappings preserving equilateral triangles

Journal of Geometry, 2004
The 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
openaire   +2 more sources

Dissections into Equilateral Triangles

1981
I am delighted to have the opportunity to contribute to this Collection honouring Martin Gardner. I once wrote a paper for his column in Scientific American, about dissections of rectangles into squares [7]. Perhaps another article on dissections would be appropriate here.
openaire   +1 more source

Proof Without Words: Equilateral Triangle

Mathematics Magazine, 2001
(2001). Proof Without Words: Equilateral Triangle. Mathematics Magazine: Vol. 74, No. 4, pp. 313-313.
openaire   +1 more source