In geometry, the angle of repose, also known as the critical angle of repose, is the smallest angle created as a granular substance slides down the horizontal surface of an inclined plane and settles. According to Math Forum, the angle of repose may be studied using a pile of table salt on a flat surface.
What Is the Angle of Repose?
"The Angle of Repose" is the title of a novel written by Wallace Stegner and published in 1971. The book won the Pulitzer Prize for Fiction in 1972. One of the ideas the book is based on refers to an actual "angle of repose." This is a term that is used in both geometry and engineering.

Geometry Definition
How It Works

When granular particlessuch as salt, soil, sand or grainsare poured on a horizontal surface, they form a pile that resembles a cone. Measure the internal angle between the top of the pile and the flat surface below and you get the angle of repose; you can then use it to figure out the pile's stability, according to a Seattle Press Online article by Roger Faris entitled "Find Your Safe Angle of Repose."

Engineering Use

Engineers use the angle of repose to study how stable piles of soil or mine tailings discarded from mining operations are as they settle, according to the Seattle Press Online article.
Other Uses

Engineers also use the angle of repose to study stability in hill slopes, according to a JSTOR article by Ian Statham on the angle of repose, published under the auspices of Chelsea College in London. The angle of repose can also be used to study and help prevent landslides and avalanches, according to the Seattle Press Online article.
In Nature

Antlion larvae naturally exploit the principle of the angle of repose by nesting at the bottom of inverted cones tunneled in sand. As ants walk by, the sloping wall and loose sand collapse under them and they roll to the bottom, where antlion predators wait for them.
