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COUNTING HERON TRIANGLES WITH CONSTRAINTS
[chapter]

*
Integers
*

We also provide a

doi:10.1515/9783110298161.24
fatcat:lcvsxika4vgytiszpc3ge4ob44
*count*for the number of*Heron**triangles**with*a fixed height (there exists only one such when the height is prime). ... In this paper, we give some estimates for the number of*Heron**triangles**with*two of their sides fixed. ... We also*count**Heron**triangles**with*a fixed height and provide an estimate of the number of*Heron**triangles**with*a fixed prime height. ...##
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Classifying Diophantine parallelepipeds
[article]

2018
*
arXiv
*
pre-print

It is proposed to name these classes: acute (triclinic), obtuse (triclinic), 1-ortho (biclinic), 2-ortho (monoclinic), and rectangular, according to the

arXiv:1812.01107v1
fatcat:jilw2jglfjawhaqiqmbadq6rk4
*count*of rights angles which may exist. ... A computer search of 1,981,336,681 tetrahedrons*with*6 rational face diagonals uncovers interesting examples of pipeds, including the perfect parallelepiped of Sawyer-Reiter (and 5 others), and the rectangular ... In fact*triangles**with*this property have been given a special name: '*Heron**triangles*'. ...##
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Causal dynamical triangulations in the spincube model of quantum gravity

2016
*
Physical Review D
*

By relating the edge-lengths to the integer areas of

doi:10.1103/physrevd.94.024058
fatcat:rzk33ytzgzdxfdkdhm65gpplhq
*triangles*, the simplicity*constraint*imposes very strong restrictions between them, ultimately leading to a requirement that all 4-simplices in the ... We study the implications of the simplicity*constraint*in the spincube model of quantum gravity. ... Here A H (l) is the*Heron*formula for the area of the*triangle*∆*with*edge-lengths l, A H (l 1 , l 2 , l 3 ) = s(s − l 1 )(s − l 2 )(s − l 3 ) , (6) where s ≡ (l 1 + l 2 + l 3 )/2, while γ is a dimensionless ...##
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How does the sun shine?

1996
*
Physics Letters B
*

Assuming that MSW neutrino oscillations occur and ignoring all solar physics except for the

doi:10.1016/0370-2693(96)00187-6
fatcat:ppoxyja2bnhh7laf5hcnt6km5q
*constraint*that nuclear fusion produces the solar luminosity, we show that new solar neutrino experiments are ... solutions [16, 17] are indicated by dark*triangles*. ... These solutions are inconsistent*with*the standard solar model, but they are consistent*with*the luminosity*constraint*, i. e., the fusion energy release to the star associated*with*the neutrino production ...##
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The Smallest Shape Spaces. III. Triangles in 2- and 3-d
[article]

2018
*
arXiv
*
pre-print

We finally make insightful comparison of

arXiv:1711.10115v2
fatcat:37wal4e2evbfracarc3ij7rpae
*triangles*in 2-d*with*a) Part II's 4 points on the line. b)*Triangles*in 3-d, which are particularly significant as the smallest model exhibiting stratification ... Medians, and regular*triangles*bounding between tall and flat*triangles*, also play prominent roles. ... Reza Tavakol, Malcolm MacCallum, Enrique Alvarez and Jeremy Butterfield for support*with*my career. ...##
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How does the Sun shine?

1989
*
Nature
*

Assuming that MSW neutrino oscillations occur and ignoring all solar physics except for the

doi:10.1038/340265a0
fatcat:5btv6gmibra3dka42eiq3b7tuy
*constraint*that nuclear fusion produces the solar luminosity, we show that new solar neutrino experiments are ... solutions [16, 17] are indicated by dark*triangles*. ... These solutions are inconsistent*with*the standard solar model, but they are consistent*with*the luminosity*constraint*, i. e., the fusion energy release to the star associated*with*the neutrino production ...##
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Bifurcations of relative equilibria in the 4- and 5-body problem

1988
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Ergodic Theory and Dynamical Systems
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We show that families of isosceles

doi:10.1017/s0143385700009433
fatcat:z5poxho6xzae5dza766lp5ne4a
*triangle*relative equilibria bifurcate from the equilateral*triangle*family as m passes through the degenerate value. ... The equilateral*triangle*family of relative equilibria of the 4-body problem consists of three particles of mass 1 at the vertices of an equilateral*triangle*and the fourth particle of arbitrary mass m ... This is the three-dimensional generalization of*Heron*of Alexandria's formula for the area of a*triangle*given its three sides. ...##
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'Meaning in a Bororo jaguar skin'

2001
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Revista do Museu de Arqueologia e Etnologia
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In both stories, Adugo appears

doi:10.11606/issn.2448-1750.revmae.2001.109421
fatcat:jr6kferivbdj3o5or5dyraqmwi
*with*other vertebrates in sequences that involve*counting*and numerical logic. ... The fives to the left are*counted*cumulatively, i.e. through all the numbers up to and including five, to give twice 15 (1+2+3+4+5), in what may be called 'sigma'*count*, in line*with*the Greek letter which ...##
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The Area of a Polygon with an Inscribed Circle
[article]

2012
*
arXiv
*
pre-print

Heron's formula states that the area K of a

arXiv:1203.3438v1
fatcat:2tysi2g4uzck3pbsitdkikyjhq
*triangle**with*sides a, b, and c is given by K=√(s(s-a) (s-b) (s-c)) where s is the semiperimeter (a+b+c)/2. ... In this paper we derive formulas giving the areas of any n-gon,*with*odd n, in terms of the ordered list of side lengths, if the n-gon is circumscribed about a circle (instead of being inscribed in a circle ... He starts*with*any right*triangle*, makes a mirror image copy of the*triangle*about the hypotenuse, joins the two*triangles*to form a quadrilateral*with*an inscribed circle. ...##
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Streaming Temporal Graphs: Subgraph Matching

2019
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2019 IEEE International Conference on Big Data (Big Data)
*

Apache Flink has an advantage when

doi:10.1109/bigdata47090.2019.9006429
dblp:conf/bigdataconf/GoodmanG19
fatcat:bij7zwsodbaqdhb26gla6ceppq
*triangles*are rare,*with*max aggregate throughput for Flink at 32 nodes greater than the max achievable rate of SAM. ... We find that SAM is able to scale to 128 nodes or 2560 cores, while Apache Flink has max throughput*with*32 nodes and degrades thereafter. ... In this example, we have defined a*triangle*. The second part of the query defines the temporal*constraints*. ...##
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Self-duality of the 6j-symbol and Fisher zeros for the Tetrahedron
[article]

2019
*
arXiv
*
pre-print

formula for the asymptotics for the 6j-symbol at large spins in terms of the tetrahedron geometry, we obtain a geometric formula for the zeros of the (inhomogeneous) Ising partition function in terms of

arXiv:1905.00348v1
fatcat:iyawo46u35hdbgkitmadi54mmm
*triangle*... 3 − l 2 5 − l 2 6 ) + (l 2 2 − l 2 3 )(l 2 6 − l 2 5 ) 16 A 123 A 156 . (88) Here A ijk is the area of the*triangle**with*edges (ijk) given in terms of the edge lengths by the*Heron*formula, as in (37 ... This is exactly the equation (70) This*constraint*reflects that we are working*with*seven cycle variables L C instead of the six edge variables Y e , so the L C have to satisfy one*constraint*. ...##
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Constructing 7-clusters
[article]

2013
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arXiv
*
pre-print

On the way, we exhaustively determined all Heronian

arXiv:1312.2318v1
fatcat:lhwyvzgtfne4rcxwcnc2ic5gxa
*triangles**with*largest edge length up to 6· 10^6. ... We determine the smallest existent 7-cluster*with*respect to its diameter. ... Let*count*(x) denote the number of primitive Heronian*triangles**with*diameter between (x − 1) · 10 000 + 1 and x · 10 000. ...##
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Translanguaging in Translation: Evidence from Japanese Mimetics

2017
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International Journal of Linguistics & Communication
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To explore the possibility of translanguaging in translation, a corpus of seven English translations of a Japanese novel, GingaTetsudō no Yoru, was quantitatively and qualitatively studied

doi:10.15640/ijlc.v5n1a2
fatcat:d2sagaei2naarl6ik5xs5w7mly
*with*a focus ... See Abdulla (2001) and Dahlgren (2005) for the significance of keeping reiterative device in translation.22*Herons*are medium to large sized birds*with*long legs and necks. ...*Herons*...an ..falling downward like snowflakes. many*heron*, squawking "gyagya" gently landed, falling like snow. ...##
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Identifying important habitats for waterbird conservation at a Greek Regional Nature Park

2020
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Avian Research
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help assess the importance of habitats and improve management strategies to benefit waterbirds, especially in areas

doi:10.1186/s40657-020-00224-7
fatcat:fdxseros75dhpbyysrupghvad4
*with*similar Mediterranean-type habitats and climate. ... Mud*with*rocky substrate was used by nine species and selected by eight species. Medium (2–4 m) and deep (4–6 m) open water habitats were used by seven species and selected by four species. ... The inlet holds nationally important wintering populations of four waterbird species (comparisons*with*country-wide mid-winter*counts*in Liordos 2011): the Common Shelduck (Tadorna tadorna; 55 individuals ...##
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Mathematics teaching development as a human practice: identifying and drawing the threads

2012
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ZDM: Mathematics Education
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They could

doi:10.1007/s11858-012-0437-7
fatcat:yzhqhuxqevgdtju3dabqfnprsy
*count*it, talk about it, work*with*it and manipulate it. ... They*counted*sides in the perimeter and*counted*again. It seemed to add up to 13. ...
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