TeXipedia

vartriangle

Represents an open triangle symbol commonly used in mathematical notation for various operators and relations.

Overview

Serves as a versatile mathematical symbol frequently employed in abstract algebra, topology, and analysis to denote specific operations or changes.

  • Often used to indicate differences or variations in mathematical expressions
  • Appears in operator theory and functional analysis contexts
  • Common in proofs and theoretical mathematics where distinct triangle notation is needed
  • Provides a visually distinct alternative to the solid triangle symbol

Examples

Representing change in a physical quantity, such as change in temperature.

ΔT=25 KT\Delta T = 25\text{ K} \approx \vartriangle T
\Delta T = 25\text{ K} \approx \vartriangle T

Geometric expression showing the area of a triangle with base b and height h.

A=12bhA_{\vartriangle} = \frac{1}{2}bh
A_{\vartriangle} = \frac{1}{2}bh

Mathematical relation using triangle symbol as an operator.

f(x)g(x)=f(x)+g(x)2f(x) \vartriangle g(x) = \frac{f(x) + g(x)}{2}
f(x) \vartriangle g(x) = \frac{f(x) + g(x)}{2}