📚 Year 11 WJEC Art: Formula & Theorem Quick Reference Guide | 11年级 WJEC 艺术：公式定理速查手册
In WJEC Year 11 Art, theoretical understanding can elevate your practical work from intuitive expression to informed design. This quick reference guide collects the essential formulas, ratios, and theorems that underpin composition, perspective, colour theory, and proportion. Whether you are analysing artworks or planning your own portfolio, these principles will help you make intentional, sophisticated choices. Keep this page handy for revision and studio work, and use the formulas to check and refine your visual decisions.
在 WJEC 11 年级艺术课程中，理论知识能将你的实践作品从直觉表达提升为有依据的设计。这份速查手册汇集了支撑构图、透视、色彩理论和人体比例的基本公式、比例及定理。无论你是在分析艺术作品还是规划自己的作品集，这些原理都能帮助你做出有意识且精妙的决策。请随时参考本页面进行复习和工作室创作，并用这些公式来检验和优化你的视觉决策。
1. The Golden Ratio in Art | 艺术中的黄金比例
The golden ratio, often denoted by the Greek letter φ (phi), approximately equals 1.618. In visual composition, dividing a line or rectangle according to this ratio is believed to create natural balance and aesthetic appeal. Many Renaissance masters, including Leonardo da Vinci, structured their works around golden rectangles and spirals. When analysing or creating an artwork, you can apply the golden ratio to the placement of a horizon line, a focal point, or the overall canvas proportions.
黄金比例通常用希腊字母 φ (phi) 表示，约等于 1.618。在视觉构图中，按照这一比例分割线条或矩形被认为能创造出自然的平衡与美感。许多文艺复兴大师，包括列奥纳多·达·芬奇，都围绕黄金矩形和黄金螺旋来构建作品。在分析或创作艺术作品时，你可以将黄金比例应用于地平线位置、视觉焦点或画布的整体比例。
a/b = (a+b)/a = φ ≈ 1.618
To construct a golden rectangle, start with a square and extend its side by multiplying by 1.618. The golden spiral can be drawn inside this rectangle by connecting quarter circles through the squares formed by the sequence of shrinking golden rectangles.
要构建黄金矩形，可从一个正方形开始，将其边长乘以 1.618 进行扩展。通过连接由一系列不断缩小的黄金矩形中正方形内的四分之一圆弧，即可在矩形内画出黄金螺旋。
2. The Rule of Thirds | 三分法则
The rule of thirds is a fundamental compositional guideline that divides the image area into nine equal parts using two equally spaced horizontal lines and two equally spaced vertical lines. Placing key elements at the four power points where the lines intersect tends to create a more dynamic and engaging composition than centering the subject. This rule is widely used in photography, painting, and film, and is often the first compositional formula taught to art students.
三分法则是一条基本的构图准则，用两条等距的水平线和两条等距的垂直线将画面分成九个相等的部分。将关键元素放置在四条线的四个交叉点（力度点）上，往往比将主体居中更能创造出富有动感和引人入胜的构图。这一法则广泛应用于摄影、绘画和电影中，通常是艺术学生最早学习的构图公式。
Intersections: (W/3, H/3), (2W/3, H/3), (W/3, 2H/3), (2W/3, 2H/3)
When sketching a landscape, try positioning the horizon along the upper or lower horizontal line rather than in the middle. Place a tree or figure near one of the vertical lines or at an intersection to strengthen visual tension. This formula remains effective even when you deliberately break it, because you first understand its logic.
在画风景速写时，试着将地平线放在靠上或靠下的水平线上，而不是正中。将树木或人物放置在靠近某条垂直线或交叉点上，以增强视觉张力。即使你有意打破这一法则，它也仍然有效，因为你首先理解了它的逻辑。
3. Linear Perspective Principles | 线性透视原理
Linear perspective creates the illusion of depth on a flat surface by ensuring that parallel lines appear to converge at one or more vanishing points on the horizon line. The basic formula relates the apparent size of an object to its distance from the viewer. This mathematical foundation allowed artists of the Renaissance to construct realistic spaces systematically.
线性透视通过在平面上让平行线看似汇聚于地平线上的一个或多个消失点，从而营造深度错觉。其基本公式将物体的表观尺寸与观察者距离联系起来。这一数学基础使文艺复兴时期的艺术家能够系统性地构建逼真的空间。
Apparent height h' = h × (f / d)
Where h is the actual height, d is the distance from the viewer, and f is a constant related to the viewing angle or focal length. In one-point perspective, all receding parallel lines meet at a single vanishing point. In two-point perspective, vertical lines remain vertical while horizontal receding lines converge to two separate points. Remember to always establish your horizon line and vanishing points before detailing a scene.
其中 h 为实际高度，d 为距观察者的距离，f 是与视角或焦距相关的常数。在一点透视中，所有向后延伸的平行线都汇聚于一个消失点。在两点透视中，垂直线保持垂直，而水平向后延伸的线条分别汇聚于两个不同的点。记住，在细化场景之前，一定要先确定视平线和消失点。
4. Atmospheric Perspective Formula | 空气透视公式
Atmospheric perspective, also called aerial perspective, describes how the appearance of objects changes with distance due to the scattering of light by particles in the air. Distant objects appear lighter, less detailed, and shifted towards blue. This effect can be approximated by a contrast reduction formula, which is useful when painting landscapes or creating digital depth effects.
空气透视又称大气透视，描述了由于空气中微粒对光的散射，物体外观随距离变化的现象。远处的物体看起来更亮、细节更少且色调偏蓝。这种效果可以用一个对比度衰减公式来近似，这在绘制风景画或创造数字景深效果时非常有用。
Cd = C0 × e-σd
Cd represents the contrast at distance d, C0 is the initial contrast at zero distance, and σ (sigma) is the scattering coefficient of the atmosphere. A higher σ means hazier conditions. In practice, you can simulate atmospheric perspective by gradually mixing more white and a small amount of blue into objects as they recede, while reducing edge sharpness. This formula reminds you that the change is exponential, not linear.
Cd 表示距离 d 处的对比度，C0 是零距离时的初始对比度，σ (sigma) 为大气的散射系数。σ 值越大，表明雾气越重。在实践中，你可以通过随着物体后退逐渐混入更多白色和少量蓝色，同时降低边缘清晰度来模拟空气透视。这个公式提醒你，变化是指数级的，而非线性的。
5. Colour Theory: The Colour Wheel Formulas | 色彩理论：色轮公式
Colour theory organises hues into a circular wheel that reveals harmonious relationships. The traditional artist's colour wheel uses red, yellow, and blue as primary colours. Secondary colours are produced by mixing two primaries, and tertiary colours by mixing a primary with a neighbouring secondary. Understanding the angular positions on the colour wheel allows you to predict colour interactions with simple formulas.
色彩理论将色相组织成一个圆形色轮，揭示出和谐的色彩关系。传统的艺术家色轮以红、黄、蓝作为原色。间色由两种原色混合而成，复色由一种原色与邻近的间色混合而成。理解色轮上的角度位置，你就可以用简单的公式预测色彩之间的相互作用。
Secondary colours: Red + Yellow = Orange; Yellow + Blue = Green; Blue + Red = Violet
Tertiary colours: e.g. Red + Orange = Red-Orange, etc.
You can think of the colour wheel as a 360-degree circle. Hue angles are assigned continuously: 0° for red, 120° for yellow, 240° for blue, with mixtures in between. This numeric approach is especially useful in digital art and when planning colour schemes.
你可以将色轮视作一个 360 度的圆。可为其连续分配色相角度：0° 代表红色，120° 代表黄色，240° 代表蓝色，其他混合色处于其间。这种数字化方法在数字艺术和规划色彩方案时特别有用。
6. Complementary and Analogous Colour Schemes | 互补色与邻近色方案
Complementary colours are opposite each other on the colour wheel and create maximum contrast when placed side by side. Analogous colours sit next to each other and offer a tranquil, unified feel. WJEC examiners look for evidence of deliberate colour choices, and these formulas help you plan with precision.
互补色在色轮上相互对立，并置时可产生最大的对比度。邻近色则彼此相邻，能带来宁静、统一的感受。WJEC 考官注重刻意的色彩选择，而这些公式能帮助你精确规划。
Complementary hue: Hcomplement = (Horiginal + 180°) mod 360°
Analogous range: Horiginal ± 30° (or ±60° for extended schemes)
For a split-complementary scheme, use one base colour and the two colours adjacent to its complement. A triadic scheme uses three colours equally spaced by 120°. These formulas guarantee harmony, but always test them in your sketchbook, as the context and saturation levels will affect the final perception.
对于分裂互补色方案，使用一种基色及其互补色两侧的两种颜色。三色方案则使用彼此间隔 120° 的三种颜色。这些公式能确保和谐，但一定要在速写本上进行测试，因为背景和饱和度水平会影响最终感知。
7. Proportion: The Eight-Head Figure Canon | 人体比例：八头身法则
Artists have devised canons of proportion to idealise the human figure. The eight-head canon divides the total height of a standing figure into eight equal parts, with the head itself counting as one unit. This system provides a memorable formula for checking proportions when drawing from life or imagination, and it appears in classical Greek sculpture and Renaissance art.
艺术家们设计了人体比例准则来理想化人物形象。八头身法则将站立人物的总身高分为八个等份，头部本身算作一个单位。这个系统提供了一个易于记忆的公式，用于在写生或凭想象作画时检查比例，它出现在古希腊雕塑和文艺复兴艺术中。
Body height = Head height × 8
Key landmarks measured from the top: chin at 1 unit, nipples at 2 units, navel at 3 units, pubic bone at 4 units, fingertips around 5 units, knees at 6 units, lower calves at 7 units, and soles at 8 units. For a more naturalistic figure, some artists use a 7.5-head canon, but the eight-head version remains an excellent starting point for stylised or heroic figures.
从头顶开始测量的关键标志点：下巴位于 1 头身，乳头位于 2 头身，肚脐位于 3 头身，耻骨位于 4 头身，指尖约在 5 头身，膝盖位于 6 头身，小腿下部位于 7 头身，脚底为 8 头身。对于更自然的人物，一些艺术家使用 7.5 头身标准，但八头身版本依然是绘制风格化或英雄式人物的绝佳起点。
8. Fibonacci Sequence in Composition | 构图中的斐波那契数列
The Fibonacci sequence is a series of numbers where each term is the sum of the two preceding ones. This progression is closely linked to the golden ratio and appears in natural forms such as shells, flowers, and pinecones. In art, the Fibonacci spiral and related grids guide the viewer's eye through the composition in a pleasing, organic flow.
斐波那契数列是一系列数字，其中每一项都是前两项之和。这一递进关系与黄金比例紧密相连，并出现在贝壳、花朵和松果等自然形态中。在艺术中，斐波那契螺旋及相关的网格能引导观众的视线在画面中形成愉悦且有机的流动。
Fn = Fn-1 + Fn-2, with F1 = 1, F2 = 1
Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...
You can overlay a Fibonacci spiral on your canvas by drawing quarter circles inside squares whose side lengths follow the sequence. Placing the focal point inside the smallest box naturally draws attention. This technique is an extension of the golden ratio and is especially powerful when you want to create a sense of growth, movement, or organic energy in your artwork.
你可以通过在一系列边长遵循该数列的正方形内绘制四分之一圆，将斐波那契螺旋叠加在画布上。将视觉焦点放在最小的方框内，能自然地吸引注意力。这一技法是黄金比例的延伸，当你想在作品中营造生长、运动或有机能量的感觉时，它尤为有效。
9. The Gestalt Principles | 格式塔原理
Gestalt psychology provides a set of principles explaining how humans naturally organise visual elements into groups. These are not mathematical formulas, but perceptual theorems that you can apply to control the viewer's reading of your work. The main principles include similarity, proximity, continuity, closure, and figure-ground relationship. In the context of WJEC Art, applying Gestalt principles demonstrates sophisticated compositional awareness.
格式塔心理学提供了一套原理，解释人类如何自然地将视觉元素组织成组。这些不是数学公式，而是你可以用来控制观众理解作品的感知定理。主要原理包括相似性、接近性、连续性、闭合性以及图底关系。在 WJEC 艺术考试语境中，应用格式塔原理能体现出精妙的构图意识。
Similarity means that elements sharing visual characteristics (shape, colour, size) are seen as related. Proximity groups elements that are close together. Continuity suggests that the eye follows smooth paths rather than abrupt changes. Closure allows the brain to complete incomplete shapes. The figure-ground relationship explains how we separate an object from its background. To use these as formulas, constantly ask yourself: Are my grouped elements visually similar and close enough? Does the implied line continue? Can I use closure to engage the viewer's imagination?
相似性意味着共享视觉特征（形状、颜色、大小）的元素会被视为相关。接近性将靠得很近的元素归为一组。连续性表明眼睛会沿着平滑路径而非突然变化移动。闭合性让大脑能补全不完整的形状。图底关系则解释了我们如何将物体从其背景中分离出来。要把这些当作公式来用，你需要不断自问：我分组的元素在视觉上是否足够相似且靠近？暗示的线条是否延续？我能否利用闭合性来激发观者的想象？
10. Symmetry and Balance Equations | 对称与平衡方程
Balance is a fundamental principle of design, and it can be approached as an equation of visual weights. In a symmetrical composition, both sides of the central axis are mirror images. In asymmetrical balance, different elements are arranged so that their perceived visual weight is equal. You can think of this as a simple balancing act where the sum of weights on the left side must equal the right, taking into account size, colour intensity, and placement.
平衡是一种基本的设计原则，可以将其视作一个视觉重量的方程式。在对称构图中，中轴线两侧互为镜像。在不对称平衡中，不同的元素被安排得使其感知到的视觉重量相等。你可以将其视为一种简单的平衡行为，左侧的总视觉重量必须等于右侧的总视觉重量，同时考虑尺寸、色彩强度和位置等因素。
Σ Weightleft = Σ Weightright
Each element's weight can be roughly estimated by multiplying its relative area by a factor for tonal contrast and a factor for colour saturation. For instance, a small dark shape near the edge can balance a large light shape near the centre. Use this equation when your composition feels unsettling and you need to diagnose the problem. Sketch a quick thumbnail and assign approximate weights to see where the imbalance lies.
每个元素的重量可以通过将其相对面积乘以一个色调对比系数和一个色彩饱和度系数来大致估算。例如，靠近边缘的一个小深色形状可以平衡靠近中心的一个大浅色形状。当你的构图感觉不安定、需要诊断问题时，可以使用这个等式。画一个简略小稿并分配大致的重量值，看看不平衡之处在哪里。
11. Exam Quick Tips: Applying Formulas Under Time Pressure | 考试快速技巧：在时间压力下应用公式
During your WJEC preparatory period and the timed exam, you won't have room for lengthy calculations. Instead, internalise these formulas as visual checkpoints. Before starting a final piece, quickly sketch a thumbnail and run through key formulas: Does it follow the rule of thirds or golden ratio? Are my vanishing points consistent? Have I planned a deliberate colour harmony using the wheel? Is the figure's proportion believable according to the eight-head canon? Practise these checks now so they become instinctive later.
在 WJEC 准备阶段和限时考试期间，你没有多余时间进行冗长的计算。相反，你要将这些公式内化为视觉检查点。在开始最终作品之前，快速画一个缩略图并过一遍关键公式：它是否遵循三分法则或黄金比例？我的消失点是否一致？我是否利用色轮规划了刻意的色彩和谐？根据八头身法则，人物的比例是否可信？现在就开始练习这些检查，以便日后成为本能。
Create a small revision card with the central formulas: φ = 1.618, h' take the first two minutes to verify that your composition is structurally sound using these rules. This disciplined approach impresses examiners, because it shows that your creative decisions are grounded in solid theoretical understanding.
制作一张小复习卡片，写上核心公式：φ = 1.618, h' = h × (f/d)，互补色角度 = H + 180°，以及八头身分割法。背面配上简单图标注明格式塔原理。考试时，用前两分钟时间运用这些规则验证作品结构是否扎实。这种严谨的方法会给考官留下深刻印象，因为它表明你的创作决策建立在扎实的理论理解之上。
Published by TutorHao | Art Revision Series | aleveler.com
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