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657
On Integer Right Triangles With Equal Area
"... Introduction Right triangles with integer side lengths are one of the earliest traces of human interest in mathematics. Already in ancient Egypt the right triangle with legs a = 3 and b = 4, and with hypothenuse c = 5, was known. As it is well known, and easily checked by the reader, the formulas ..."
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Introduction Right triangles with integer side lengths are one of the earliest traces of human interest in mathematics. Already in ancient Egypt the right triangle with legs a = 3 and b = 4, and with hypothenuse c = 5, was known. As it is well known, and easily checked by the reader, the formulas
ANOTHER INSTANCE OF THE GOLDEN RIGHT TRIANGLE
, 1992
"... The golden ratio r = (l + v5)/2, the positive root of x 2 =x + l, makes an unexpected appearance in [1], where a certain right triangle turns out to be a "Golden Right Triangle " (GRT), one having sides proportional to (1, r 1/2, r). The author wonders about the existence of other sets of ..."
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The golden ratio r = (l + v5)/2, the positive root of x 2 =x + l, makes an unexpected appearance in [1], where a certain right triangle turns out to be a "Golden Right Triangle " (GRT), one having sides proportional to (1, r 1/2, r). The author wonders about the existence of other sets
Periodic billiard orbits in right triangles II
"... Periodic billiard orbits are dense in the phase space of all but countably many right triangles. A stronger pointwise density result is also proven. ..."
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Cited by 3 (1 self)
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Periodic billiard orbits are dense in the phase space of all but countably many right triangles. A stronger pointwise density result is also proven.
Monochromatic equilateral right triangles on the integer grid
"... For any coloring of the N × N grid using less than log log n colors, one can always find a monochromatic equilateral right triangle, a triangle with vertex coordinates (x, y), (x + d, y), and (x, y + d). ..."
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Cited by 13 (0 self)
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For any coloring of the N × N grid using less than log log n colors, one can always find a monochromatic equilateral right triangle, a triangle with vertex coordinates (x, y), (x + d, y), and (x, y + d).
Generic spectral properties of right triangle billiards
, 2001
"... Abstract. This article presents a new method to calculate eigenvalues of right triangle billiards. Its efficiency is comparable to the boundary integral method and more recently developed variants. Its simplicity and explicitness however allow new insight into the statistical properties of the spect ..."
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Cited by 1 (0 self)
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Abstract. This article presents a new method to calculate eigenvalues of right triangle billiards. Its efficiency is comparable to the boundary integral method and more recently developed variants. Its simplicity and explicitness however allow new insight into the statistical properties
The Golden Section in the Inscribed Square of an Isosceles Right Triangle
"... Abstract. We prove the occurrence of the golden section with the inscribed square of an isosceles right triangle on its hypotenuse and its circumcircle. Given a right isosceles triangle ABC and its circumcircle, inscribed a square DEFG with a side FG along the hypotenuse AB. If the side DE is extend ..."
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Abstract. We prove the occurrence of the golden section with the inscribed square of an isosceles right triangle on its hypotenuse and its circumcircle. Given a right isosceles triangle ABC and its circumcircle, inscribed a square DEFG with a side FG along the hypotenuse AB. If the side DE
Alabama Journal of Mathematics 37 (2013) Relating the Area and Perimeter of Right Triangles
"... For a natural number n, we find the number of right triangles that have an area equal to n times perimeter. We begin by showing that the number of primitive right triangles for which twice the area is n times the perimeter is 2k where k is the number of distinct odd primes in the canonical factoriza ..."
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For a natural number n, we find the number of right triangles that have an area equal to n times perimeter. We begin by showing that the number of primitive right triangles for which twice the area is n times the perimeter is 2k where k is the number of distinct odd primes in the canonical
CENTRAL SYMMETRIES OF PERIODIC BILLIARD ORBITS IN RIGHT TRIANGLES
, 2002
"... Abstract. We show that the midpoint of each periodic perpendicular beam hits the rightangle vertex of the triangle. The beam returns to itself after half its period with the opposite orientation, i.e. a Möbeius band. 1. ..."
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Abstract. We show that the midpoint of each periodic perpendicular beam hits the rightangle vertex of the triangle. The beam returns to itself after half its period with the opposite orientation, i.e. a Möbeius band. 1.
Hansen’s Right Triangle Theorem, Its Converse and a Generalization
 FORUM GEOM
, 2006
"... We generalize D. W. Hansen’s theorem relating the inradius and exradii of a right triangle and its sides to an arbitrary triangle. Specifically, given a triangle, we find two quadruples of segments with equal sums and equal sums of squares. A strong converse of Hansen’s theorem is also established. ..."
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Cited by 4 (0 self)
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We generalize D. W. Hansen’s theorem relating the inradius and exradii of a right triangle and its sides to an arbitrary triangle. Specifically, given a triangle, we find two quadruples of segments with equal sums and equal sums of squares. A strong converse of Hansen’s theorem is also established.
Results 1  10
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657