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In geometry, the Conway triangle notation, named after John Horton Conway, allows trigonometric functions of a triangle to be managed algebraically. Given a reference triangle whose sides are a, b and c and whose corresponding internal angles are A, B, and C then the Conway triangle notation is simply represented as follows:
where S = 2 × area of reference triangle and
in particular
Furthermore the convention uses a shorthand notation for S ϑ S φ = S ϑ φ {\displaystyle S_{\vartheta }S_{\varphi }=S_{\vartheta \varphi }\,} and S ϑ S φ S ψ = S ϑ φ ψ . {\displaystyle S_{\vartheta }S_{\varphi }S_{\psi }=S_{\vartheta \varphi \psi }\,.}