area of triangle

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1: 4.42 Solution of Triangles

§4.42 Solution of Triangles

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§4.42(i) Planar Right Triangles

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§4.42(ii) Planar Triangles

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Figure 4.42.2: Planar triangle. Magnify

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§4.42(iii) Spherical Triangles

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2: Sidebar 9.SB2: Interference Patterns in Caustics

… ►The bright sharp-edged triangle is a caustic, that is a line of focused light. …

3: 34.10 Zeros

… ►In a $\mathit{3}j$ symbol, if the three angular momenta $j_1,j_2,j_3$ do not satisfy the triangle conditions (34.2.1), or if the projective quantum numbers do not satisfy (34.2.3), then the $\mathit{3}j$ symbol is zero. Similarly the $\mathit{6}j$ symbol (34.4.1) vanishes when the triangle conditions are not satisfied by any of the four $\mathit{3}j$ symbols in the summation. …However, the $\mathit{3}j$ and $\mathit{6}j$ symbols may vanish for certain combinations of the angular momenta and projective quantum numbers even when the triangle conditions are fulfilled. …

4: Frank Garvan

… ►His research is in the areas of $q$-series and modular forms, and he enjoys using MAPLE in his research. …He is managing editor of the Ramanujan Journal, a journal devoted to areas of mathematics influenced by Ramanujan. …

5: 18.37 Classical OP’s in Two or More Variables

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§18.37(ii) OP’s on the Triangle

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Definition in Terms of Jacobi Polynomials

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18.37.7 $$P_{m,n}^{\alpha ,\beta ,\gamma }(x,y)=P_{m-n}^{(\alpha ,\beta +\gamma +2n+1)}\left(2x-1\right)x^n{P}_n^{(\beta ,\gamma )}\left(2x^{-1}y-1\right),$$ $m\ge n\ge 0$, $\alpha ,\beta ,\gamma >-1$.

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Defines:

$P_{m,n}^{\alpha ,\beta ,\gamma }(x,y)$: triangle polynomial

Symbols:

$P_n^{(\alpha ,\beta )}\left(x\right)$: Jacobi polynomial, $y$: real variable, $m$: nonnegative integer, $n$: nonnegative integer and $x$: real variable

Referenced by:

§18.37(ii)

Permalink:

http://dlmf.nist.gov/18.37.E7

Encodings:

pMML, png, TeX

See also:

Annotations for §18.37(ii), §18.37(ii), §18.37 and Ch.18

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18.37.8 $m\ne j$ and/or $n\ne \mathrm{\ell }$.

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Symbols:

$dx$: differential of $x$ , $P_{m,n}^{\alpha ,\beta ,\gamma }(x,y)$: triangle polynomial, $y$: real variable, $\mathrm{\ell }$: nonnegative integer, $m$: nonnegative integer, $n$: nonnegative integer and $x$: real variable

Permalink:

http://dlmf.nist.gov/18.37.E8

Encodings:

pMML, png, TeX

See also:

Annotations for §18.37(ii), §18.37(ii), §18.37 and Ch.18

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6: Simon Ruijsenaars

… ►His main research interests cover integrable systems, special functions, analytic difference equations, classical and quantum mechanics, and the relations between these areas. …

7: 26.19 Mathematical Applications

… ►Other areas of combinatorial analysis include graph theory, coding theory, and combinatorial designs. …

8: Brian Antonishek

… ►His research areas include human robot interaction, medical data anlysis, and 3D web interactions using VRML and X3D.

9: T. Mark Dunster

… ►He has received a number of National Science Foundation grants, and has published numerous papers in the areas of uniform asymptotic solutions of differential equations, convergent WKB methods, special functions, quantum mechanics, and scattering theory. …

10: Christopher J. Howls

… ►Howls has published numerous papers in the areas of asymptotics and its applications. …