# gradient

[grey-dee-uh nt]

- the degree of inclination, or the rate of ascent or descent, in a highway, railroad, etc.
- an inclined surface; grade; ramp.
- Physics.
- the rate of change with respect to distance of a variable quantity, as temperature or pressure, in the direction of maximum change.
- a curve representing such a rate of change.

- Mathematics. a differential operator that, operating upon a function of several variables, results in a vector the coordinates of which are the partial derivatives of the function. Abbreviation: grad. Symbol: ∇

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- rising or descending by regular degrees of inclination.
- progressing by walking; stepping with the feet as animals do.
- of a type suitable for walking or running, as the feet of certain birds; gressorial.

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## Origin of gradient^{}

1635–45; < Latin gradient- (stem of gradiēns), present participle of gradī to walk, go, equivalent to grad- walk + -i- thematic vowel + -ent- -ent

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

## Related Words

acclivityangleinclinedeclivitygradetiltriseleanslantrampcanthillleaningpitchbankinclination## Examples from the Web for gradient

### Historical Examples

#### It may have been the gradient of the hills, but somehow her gait had lost something of its buoyancy.

The Law-BreakersRidgwell Cullum

#### The 'ways' sloped at a gradient of one foot in twelve, and had iron surfaces.

Chatterbox, 1906Various

#### We march to our crises by a gradient, every step of which is a moral decision.

My Daily Meditation for the Circling YearJohn Henry Jowett

#### Their gradient is commonly greater than that of the present rivers.

The Elements of GeologyWilliam Harmon Norton

#### The gradient steepened, the snow was hard, and the axe was invoked.

Hours of Exercise in the AlpsJohn Tyndall

## gradient

- Also called (esp US): grade a part of a railway, road, etc, that slopes upwards or downwards; inclination
- Also called (esp US and Canadian): grade a measure of such a slope, esp the ratio of the vertical distance between two points on the slope to the horizontal distance between them
- physics a measure of the change of some physical quantity, such as temperature or electric potential, over a specified distance
- maths
- (of a curve) the slope of the tangent at any point on a curve with respect to the horizontal axis
- (of a function, f (x, y, z)) the vector whose components along the axes are the partial derivatives of the function with respect to each variable, and whose direction is that in which the derivative of the function has its maximum value. Usually written: grad f, ∇ f or ∇ fCompare curl (def. 11), divergence (def. 4)

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- sloping uniformly

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## Word Origin

C19: from Latin gradiēns stepping, from gradī to go

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## Word Origin and History for gradient

Online Etymology Dictionary, © 2010 Douglas Harper

## gradient

(grā′dē-ənt)- The rate at which a physical quantity, such as temperature or pressure, changes relative to change in a given variable, especially distance.
- A series of progressively increasing or decreasing differences in the growth rate, metabolism, or physiological activity of a cell, an organ, or an organism.

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The American Heritage® Stedman's Medical Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.

## gradient

[grā′dē-ənt]

- The degree to which something inclines; a slope. A mountain road with a gradient of ten percent rises one foot for every ten feet of horizontal length.
- The rate at which a physical quantity, such as temperature or pressure changes over a distance.
- A operator on scalar fields yielding a vector function, where the value of the vector evaluated at any point indicates the direction and degree of change of the field at that point.

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The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.