📚 AS Edexcel Art: Formula & Theorem Quick Reference Handbook | AS Edexcel 艺术：公式定理速查手册
In the world of art and design, creativity is often grounded in structured principles that behave like formulas. From colour mixing ratios and perspective vanishing points to the golden ratio and human proportions, these recurring 'rules' help artists make informed decisions. This quick reference handbook compiles essential formulas, theorems, and proportional systems relevant to the AS Edexcel Art & Design curriculum, offering a concise guide for studio work and critical analysis.
在艺术与设计的世界里，创造力往往建立在结构化的原则之上，这些原则就像公式一样。从色彩混合比例和透视消失点到黄金分割和人体比例，这些反复出现的“规则”帮助艺术家做出明智的选择。本速查手册汇编了与 AS Edexcel 艺术与设计课程相关的基本公式、定理和比例系统，为工作室实践和批判性分析提供简明指南。
1. The Colour Wheel & Subtractive Mixing Formulas | 色轮与减色混色公式
The traditional RYB (red-yellow-blue) colour wheel is the foundation of subtractive mixing used in painting and printing. Understanding primary, secondary, and tertiary colour formulas enables rapid palette decisions.
传统的 RYB（红-黄-蓝）色轮是绘画和印刷中减色混合的基础。理解原色、间色和复色的公式能帮助快速决定调色板。
Primary Colours: Red, Yellow, Blue — cannot be created by mixing.
原色：红、黄、蓝——无法通过混合获得。
Secondary Formulas: Red + Yellow = Orange; Yellow + Blue = Green; Blue + Red = Violet.
间色公式：红 + 黄 = 橙；黄 + 蓝 = 绿；蓝 + 红 = 紫。
Tertiary Formulas: Primary + adjacent secondary, e.g., Yellow + Orange = Yellow-Orange.
复色公式：原色 + 邻近间色，如黄 + 橙 = 黄橙。
| Desired Colour | Mix Ratio Guideline |
|---|---|
| Warm Orange | 2 parts Yellow : 1 part Red |
| Forest Green | 2 parts Blue : 1 part Yellow + touch of Red to dull |
Tip: To darken a colour without black, use its complement (e.g., add a little Violet to Yellow to mute).
提示：不用黑色调暗色彩，可用其互补色（例如，在黄色中加入少许紫色使其变暗）。
2. Additive Colour Mixing (Light) Formulas | 加色混色（光）公式
For digital artwork, photography, and screen-based media, the RGB additive model applies. The primary colours of light are Red, Green, and Blue.
对于数字艺术、摄影和屏幕媒体，适用 RGB 加色模型。光的三原色是红、绿、蓝。
Additive formulas: n + Blue = Cyan; Blue + Red = Magenta. All three combined at full intensity produce White.
加色公式：红 + 绿 = 黄；绿 + 蓝 = 青；蓝 + 红 = 品红。三色全强度叠加产生白色。
| RGB Value (0-255) | Perceived Colour |
|---|---|
| (255, 0, 0) | Pure Red |
| (255, 255, 0) | Yellow |
| (128, 0, 128) | Purple (Red+Blue mix reduced) |
Understanding additive mixing helps when adjusting screen colours or lighting in installation art.
理解加色混合有助于调整屏幕色彩或装置艺术中的灯光。
3. Complementary Colours & Contrast Ratios | 互补色与对比比例
Complementary pairs sit opposite on the colour wheel. Their high contrast creates visual vibration and emphasis. The approximate contrast ratio can be expressed as a perceptual formula: maximum contrast occurs when one colour is fully saturated and the other is its exact opposite hue.
互补色在色轮上位置相对。它们的高对比度产生视觉振动和强调。大致的对比比例可表达为感知公式：当一种颜色完全饱和而另一种是其严格对立色相时，对比度最大。
Red ↔ Green, Blue ↔ Orange, Yellow ↔ Violet.
红 ↔ 绿，蓝 ↔ 橙，黄 ↔ 紫。
For a balanced composition, use a split-complementary formula: choose one base colour and the two colours adjacent to its complement.
为了平衡构图，可以使用分裂互补公式：选择一个基础色和其互补色相邻的两个颜色。
Contrast ratio guideline: A small area of intense complementary accent can balance a larger muted area of the opposite hue (approximately 1:3 area ratio).
对比比例指导：小面积强烈的互补色点缀可以平衡大面积柔和的相对色相（大约面积比 1:3）。
4. Colour Harmony Rules (Analogous, Triadic) | 色彩调和法则（近似色、三色组）
Harmonious colour schemes follow geometric relationships on the wheel. These can be treated as formulas for selecting palettes.
和谐的色彩方案遵循色轮上的几何关系。这可以当作选择调色板的公式。
| Scheme | Formula/Selection Geometry | Example |
|---|---|---|
| Analogous | 3–5 adjacent colours on the wheel | Yellow, Yellow-Green, Green |
| Triadic | Three colours equally spaced (120° apart) | Red, Yellow, Blue |
| Tetradic (Rectangle) | Two complementary pairs forming a rectangle | Red, Green, Blue-Violet, Yellow-Orange |
These formulas guarantee a balanced visual result when using colour in painting, illustration, or design layouts.
这些公式确保在绘画、插画或设计布局中使用色彩时获得平衡的视觉效果。
5. Golden Ratio in Composition | 构图中的黄金比例
The golden ratio, often denoted by the Greek letter phi (Φ), is approximately 1 : 1.618. It appears in nature and classical art, and is used to place focal points and define harmonious proportions.
黄金比例通常用希腊字母 phi (Φ) 表示，大约为 1 : 1.618。它出现在自然界和古典艺术中，用于安排焦点和确定和谐的比例。
Φ = (1 + √5) / 2 ≈ 1.618
Golden Rectangle formula: A rectangle where the ratio of the longer side (A) to the shorter side (B) equals Φ. Cut a square from it, and the remaining rectangle also has the same ratio.
黄金矩形公式：一个矩形，其长边 (A) 与短边 (B) 的比例等于 Φ。切去一个正方形后，剩下的矩形仍具有相同比例。
In composition, the golden spiral can be drawn through successive golden rectangles, and the eye naturally follows this curve to the focal point. Many artists use the golden section line as a guide for placing the horizon or main subject.
在构图中，可以通过连续的黄金矩形绘制黄金螺旋，眼睛会自然沿着曲线到达焦点。许多艺术家使用黄金分割线作为放置地平线或主要题材的引导。
6. Rule of Thirds Grid Formula | 三分法网格公式
The rule of thirds divides the image frame into nine equal sections using two equally spaced horizontal lines and two vertical lines. The intersections are 'power points' ideal for placing key elements.
三分法将画面分为九个相等的部分，使用两条等距的水平线和两条垂直线。交点就是适合放置关键元素的“力量点”。
Formula: For a canvas of width W and height H, the lines are at W/3, 2W/3 horizontally and H/3, 2H/3 vertically.
公式：对于宽 W、高 H 的画布，水平线位于 W/3 和 2W/3 处，垂直线位于 H/3 和 2H/3 处。
Place the horizon along one of the horizontal lines (usually lower third for sky emphasis).
沿其中一条水平线放置地平线（通常强调天空时放在下三分之一处）。
Position a portrait's eyes or main subject at an intersection.
将人像的眼睛或主要对象放在某一交点上。
This easy-to-remember compositional formula instantly improves visual balance and interest.
这个易记的构图公式能立即改善视觉平衡和趣味性。
7. Linear Perspective Formulas (Vanishing Points) | 线性透视公式（消失点）
Linear perspective creates the illusion of depth on a flat surface. The key formulas relate to vanishing points (VP) and the horizon line (eye level).
线性透视在平面上创造深度错觉。关键公式涉及消失点 (VP) 和视平线（眼高）。
One-Point Perspective: All receding parallel lines converge to a single VP on the horizon. The depth of an object can be scaled using the diagonal method: the diagonal of a rectangle extended to the horizon locates the next equally sized unit.
一点透视：所有后退的平行线汇聚于地平线上的一个消失点。物体的深度可用对角线法缩放：矩形的对角线延伸至地平线，可定位下一个等大单元。
Two-Point Perspective: Vertical edges remain vertical. Horizontal edges of a cube recede to two separate VPs, both on the horizon line. The distance between the two VPs influences the distortion — closer VPs create a wider-angle effect.
两点透视：垂直边保持垂直。立方体的水平边分别后退到地平线上的两个消失点。两点间距影响变形——消失点越近，广角效应越强。
Spacing formula in perspective: To divide a receding plane into equal parts (e.g., fence posts), draw a horizontal line from the nearest end, mark equal segments, connect the farthest mark to the opposite far corner, and the intersections give the divisions.
透视中的等分公式：要等分一个后退平面（如栅栏柱），从最近端画一条水平线，标出等份，将最远标记与对面的远角相连，交点即为等分位置。
8. Atmospheric Perspective Depth Formula | 空气透视深度公式
Atmospheric (aerial) perspective relies on how the atmosphere scatters light. The formula for depicting depth is based on four shifts in values, colours, and edges with distance.
空气（大气）透视依赖于大气如何散射光线。表现深度的公式基于随着距离增加而发生的四种数值、颜色和边缘变化。
| Attribute | Close Objects | Distant Objects |
|---|---|---|
| Value (Tone) | Wider range, darker darks | Narrower, lighter (closer to sky tone) |
| Colour Saturation | High, warm and intense | Reduced, cooler/bluer veil |
| Edge Sharpness | Sharp, defined | Soft, blurred |
| Texture/Detail | Visible | Simplified, lost |
Formula summary: As depth increases, shift hue slightly towards blue/ violet, reduce contrast, and soften edges. This mimics Rayleigh scattering and gives a convincing sense of space.
公式总结：随着深度增加，将色相稍微偏蓝/紫，降低对比度，柔化边缘。这模拟了瑞利散射，给出可信的空间感。
9. Human Figure Proportions (Canon) | 人体比例准则（头身）
Artists have long used proportional canons to draw the human figure. The '8-heads tall' idealised canon is a standard formula for figure drawing.
艺术家长期使用比例准则来绘制人体。“8 头身”的理想化准则是人体素描的标准公式。
Classical Greek canon: ure height = 7.5 to 8 heads. The midpoint of the body is at the pubic bone, not the waist.
古典希腊准则：身高 = 7.5 到 8 个头长。身体中点在耻骨，而非腰部。
Key divisions: s, 8th to feet. Arm length: upper arm = 1.5 heads, forearm = 1.25 heads, hand = 0.75 head.
关键划分：第2个头到乳头，第3个到肚脐，第4个到腹股沟，第6个到膝盖，第8个到脚底。臂长：上臂 = 1.5 头，前臂 = 1.25 头，手 = 0.75 头。
Face proportions: Eyes are at the horizontal midline of the head. The face divides into thirds: hairline to brow, brow to nose base, nose base to chin.
面部比例：眼睛位于头部水平中线。面部分为三等分：发际线到眉，眉到鼻底，鼻底到下巴。
These formulas provide a reliable starting point before observing individual differences.
在观察个体差异之前，这些公式提供了一个可靠的起点。
10. Shading & Value Scale Formula | 明暗与色阶公式
A standard value scale simplifies shading and form rendering. The formula for a ten-step scale from pure white (value 0) to pure black (value 10) creates a reference for consistent tones.
标准的色阶简化了明暗和形体的表现。从纯白（明度 0）到纯黑（明度 10）的十级色阶公式为一致的调子提供了参考。
| Step | Perceived Tone | Typical Use |
|---|---|---|
| 0 | White (highlight) | Specular highlights |
| 1-3 | Light greys | Lit planes facing light |
| 4-6 | Mid-tones | Local colour area |
| 7-9 | Dark greys | Shadow, core shadow |
| 10 | Black | Deepest occlusion shadow |
Chiaroscuro formula: Contrast of light and dark to model volume. To calculate a shadow tone, mix the local colour with a small amount of its complement and darken, then apply glazing.
明暗对照公式：利用明暗对比塑造体积感。要计算阴影色调，可将物体固有色与少量补色混合并加深，再使用罩染。
Exaggerating edge transfer (hard edge for cast shadow, soft edge for form shadow) further defines form.
夸张边缘过渡（投射阴影硬边缘，形体阴影软边缘）能进一步塑造形体。
11. Gestalt Principles of Visual Perception | 视觉感知的格式塔定理
Gestalt psychology provides theorems about how the human mind organises visual elements. These principles act as compositional formulas in design and art.
格式塔心理学提供了关于人类思维如何组织视觉元素的定理。这些原则在设计艺术中充当构图公式。
Law of Proximity: Objects close together are perceived as a group. Formula: Reduce distance to unify.
接近律：接近的物体被视为一组。公式：缩短距离以统一。
Law of Similarity: Elements sharing similar shape, colour, or size are grouped. Formula: Repeat a visual property to create rhythm.
相似律：形状、颜色或大小相似的元素被归为一组。公式：重复某种视觉属性以创造节奏。
Law of Closure: The mind completes incomplete forms. Formula: Use suggestive rather than fully delineated shapes to engage the viewer.
闭合律：大脑会补全不完整的形状。公式：使用暗示性而非完全描绘的形状来吸引观众。
Figure-Ground Relationship: Separation of foreground from background. Formula: Manipulate contrast, size, and overlap to define the figure.
图形-背景关系：区分前景与背景。公式：操纵对比、大小和重叠来界定图形。
These 'theorems' explain why certain arrangements feel balanced or dynamic, and are essential for visual analysis.
这些“定理”解释了为何某些安排感觉平衡或有动感，对视觉分析至关重要。
12. Fibonacci Sequence in Art | 艺术中的斐波那契数列
The Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13, 21… essive Fibonacci numbers approximates Φ increasingly well (e.g., 8/5 = 1.6, 13/8 = 1.625).
斐波那契数列 (0, 1, 1, 2, 3, 5, 8, 13, 21…) 与黄金比例密切相关。相邻斐波那契数之间的比值越来越接近 Φ（例如 8/5 = 1.6，13/8 = 1.625）。
Artists can use Fibonacci numbers to determine the size of compositional elements or to construct spirals. For instance, a Fibonacci grid places focal points at intersections of lines based on these numbers rather than simple thirds.
艺术家可以使用斐波那契数来决定构图元素的尺寸或构建螺旋。例如，斐波那契网格根据这些数字放置线条的交点，而不是简单的三分法。
Practical formula: Use a series of squares with side lengths equal to Fibonacci numbers (1,1,2,3,5,8) arranged to form a golden spiral. This creates a visually satisfying flow in a painting or a logo design.
实用公式：使用一系列边长等于斐波那契数 (1,1,2,3,5,8) 的正方形排列成黄金螺旋。这在绘画或标志设计中创造视觉上令人满意的流动感。
The connection between Fibonacci and natural forms (sunflowers, shells) also provides a powerful conceptual link for artists studying organic patterns.
斐波那契与自然形式（向日葵、贝壳）的联系也为研究有机图案的艺术家提供了有力的概念链接。
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