TeXipedia

bigtriangleup

Represents a large upward-pointing triangle operator commonly used in mathematical notation for expressing differences or changes.

Overview

Serves as a prominent mathematical operator indicating significant changes, differences, or transformations in various contexts.

  • Frequently used in calculus and analysis to denote finite differences or increments
  • Appears in physics equations to represent changes in physical quantities
  • Common in theoretical mathematics for expressing symmetric differences or special operators
  • Distinguished from the smaller \triangle by its larger size, making it more suitable for operator notation

Examples

Representing the Laplace operator in three dimensions.

△f=∂2f∂x2+∂2f∂y2+∂2f∂z2\bigtriangleup f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2} 
\bigtriangleup f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2}

Showing the difference operator in discrete mathematics.

△xn=xn+1−xn\bigtriangleup x_n = x_{n+1} - x_n 
\bigtriangleup x_n = x_{n+1} - x_n

Indicating a change in a physical quantity.

△E=E2−E1\bigtriangleup E = E_2 - E_1 
\bigtriangleup E = E_2 - E_1