grade, gradian, gradient

In trigonometry [三角学], the gradian [百分度], also known as the gon (from Ancient Greek: γωνία, romanized: gōnía, lit. ‘angle’), grad, or grade, is a unit of measurement of an angle, defined as one hundredth of the right angle. In other words, there are 100 gradians in 90 degrees. Measuring angles in gradians is said to employ the centesimal [百分的] system of angular measurement. The unit originated in connection with the French Revolution in France as the grade, along with the metric system, hence it is occasionally referred to as a metric degree.

• -gon  (用以构成名词) figure with a specified number of angles 有若干角的图形 octagon, polygon, etc.
•  1利弗=1法郎 1法郎=20苏=100生丁 1苏=5生丁
• 1英镑=20先令 1先令=12便士 1几尼=21先令=1.05英镑

In the Centesimal System, an angle is measured in grades, minutes and seconds. In this system, a right angle is divided into equal parts and each such part is called a Grade (1g). Again, a grade is divided into equal parts and each such part is called a Centesimal Minute (1′). And a minute is further subdivided into equal parts, each of which is called a Centesimal Second (1″).

The following systems of units are used in the measurement of angles:

• Sexagesimal System (or English System)
• Centesimal System (or French System)
• Circular System. In this System, an angle is measured in radians [弧度]
• 密位
• Imperial Russia used a different approach, dividing a circle into equilateral [等+边] ]triangles (60° per triangle, 6 triangles in a circle) and hence 600 units to a circle.

Gradient in vector calculus is a vector field representing the maximum rate of increase of a scalar field or a multivariate function and the direction of this maximal rate. Gradient may also refer to:

• Gradient descent, a first-order iterative optimization algorithm for finding the minimum of a function
• Stochastic gradient descent, iterative method for optimizing a differentiable objective function. A variable is random. A process is stochastic. Apart from this difference, the two words are synonyms. What’s the difference between stochastic and random?
• Gradient theorem, theorem that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve 梯度定理，通过梯度场的线积分可以由计算曲线端点处的原始标量场来计算
• Slope, a number that describes both the direction and the steepness of a line

The grade (also called slope, incline, gradient, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper degree of “tilt”. Often slope is calculated as a ratio of “rise” to “run”, or as a fraction (“rise over run”) in which run is the horizontal distance (not the distance along the slope) and rise is the vertical distance.

六级/考研单词: comb, revolve, farther, imperial, triangle, integrity, evaluate, curve, incline, physics, construct, horizon, nil, steep, tilt, seldom, fraction, vertical

如果“梯度”改叫“坡度”，想快速下山就走眼前最陡的坡……