📚 Year 13 Edexcel Art: Formula & Theorem Quick Reference | Year 13 Edexcel 艺术：公式定理速查手册
This handbook distils the essential visual formulas, compositional theorems, and design principles that Year 13 Edexcel Art & Design students must internalise for both Component 1 (Personal Investigation) and Component 2 (Externally Set Assignment). From the golden ratio to colour harmony equations, each entry bridges intuitive creativity with analytical rigour, helping you annotate your portfolio and justify your decisions with precision.
本手册提炼了 Year 13 Edexcel 艺术与设计学生在个人调查研究（Component 1）和外部命题作业（Component 2）中必须内化的视觉公式、构图定理和设计原则。从黄金比例到色彩调和方程，每一条都将直觉创造力与分析性严谨相结合，帮助你精准地注释作品集并为自己的创作决策提供依据。
1. The Elements of Art: The Building Blocks | 艺术元素：基础构件
Every composition is built from seven fundamental elements. Line defines edges; shape is a two-dimensional enclosed area; form adds the third dimension; value controls lightness and darkness; texture describes surface quality; space creates depth; and colour communicates mood. Mastering these elements is the first formula for visual literacy.
每一件作品都由七大基本元素构成。线条界定边缘；形状是二维封闭区域；形体增添第三维度；明度控制明暗；质感描述表面特性；空间营造深度；色彩传递情绪。掌握这些元素是视觉素养的第一条公式。
- Line – straight, curved, thick, thin, implied | 线条——直线、曲线、粗、细、暗示线
- Shape – geometric, organic, positive, negative | 形状——几何形、有机形、正形、负形
- Form – sphere, cube, cone, cylinder (3D equivalents of shapes) | 形体——球体、立方体、锥体、圆柱体（形状的三维对应）
- Value – tints (add white), shades (add black), tones (add grey) | 明度——明调（加白）、暗调（加黑）、中间调（加灰）
- Texture – actual, simulated, abstract | 质感——真实质感、仿真的、抽象的
- Space – positive/negative, foreground/middleground/background, linear perspective | 空间——正负空间、前景/中景/背景、线透视
- Colour – hue, saturation, brightness | 色彩——色相、饱和度、亮度
2. Principles of Design: The Glue | 设计原则：粘合剂
If elements are the bricks, principles are the mortar. Balance distributes visual weight; contrast heightens difference; emphasis builds a focal point; movement guides the eye; pattern creates repetition; rhythm organises repetition into flow; and unity ensures everything belongs together. These principles operate as theorems controlling visual hierarchy.
如果元素是砖，原则就是灰浆。平衡分配视觉重量；对比强化差异；强调构建焦点；运动引导视线；图案制造重复；节奏将重复组织为流动；统一确保所有部分浑然一体。这些原则如同定理般控制着视觉层级。
| Principle | 原则 | Formula / Theorem | 公式 / 定理 | Visual Outcome | 视觉结果 |
|---|---|---|
| Balance | 平衡 | Symmetry = Axis + Mirrored Elements Asymmetry = Tension × Visual Weight Distribution |
Stability or dynamic tension |
| Contrast | 对比 | Δ(Hue, Value, Texture) ↑ → Visibility ↑ | Focal point emphasis |
| Rhythm | 节奏 | Regular → Progressive → Flowing | Eye movement across artwork |
| Proportion | 比例 | Golden Ratio Φ = 1.618, Rule of Thirds = 1/3 grid | Harmonious scaling |
3. The Golden Ratio and Fibonacci Spiral | 黄金比例与斐波那契螺旋
The golden ratio (Φ ≈ 1.618) appears when a line is divided so that the whole length divided by the long part equals the long part divided by the short part. In art, this creates a naturally balanced composition. The Fibonacci spiral, constructed from quarter-circles inside squares whose sides follow the Fibonacci sequence (1,1,2,3,5,8,13…), guides the viewer’s eye to the focal point effortlessly.
黄金比例（Φ ≈ 1.618）出现于一条线段被分割为两段，且整段长度除以长段等于长段除以短段时。在艺术中，这创造出天然平衡的构图。斐波那契螺旋由内接于边长符合斐波那契数列（1,1,2,3,5,8,13……）的正方形中的四分之一圆弧组成，能毫不费力地将观者的视线引向焦点。
Golden Ratio: a/b = (a+b)/a = 1.618…
黄金比例：a/b = (a+b)/a = 1.618…
Placing the subject at the spiral’s eye or along the dividing lines aligns the composition with centuries of aesthetic testing, from the Parthenon to Dalí’s Sacrament of the Last Supper.
将主体置于螺旋的中心点或沿分割线布局，使构图与数百年来的审美检验一致，从帕特农神庙到达利《最后的晚餐的圣礼》。
4. Rule of Thirds and Composition Grids | 三分法与构图网格
The rule of thirds divides the frame into nine equal rectangles using two horizontal and two vertical lines. Placing key elements along these lines or at their intersections creates more energy than centring the subject. This format is the most widely taught compositional theorem in photography and painting.
三分法使用两条水平线和两条垂直线将画面分成九个相等的矩形。将关键元素沿这些线条或它们的交叉点放置，能比居中构图产生更强的活力。这一法则是在摄影和绘画中最广泛教授的构图定理。
- Intersection points – four power points for focal areas | 交叉点——四个用于焦点的能量点
- Horizon placement – on lower third for vast sky, on upper third for foreground emphasis | 地平线放置——置于下三分之一处以表现广阔天空，置于上三分之一处以强调前景
- Leading room – leave space in the direction a subject faces or moves | 引导空间——在主体面向或移动的方向留出空间
Combine the rule of thirds with a golden rectangle overlay for heightened compositional integrity. The difference: 1/3 ≈ 0.333 vs Φ 0.618 divisions; both coexist in dynamic asymmetry.
将三分法与黄金矩形叠加使用，以增强构图的整体性。区别在于：1/3 ≈ 0.333 对比黄金分割 0.618；两者都存在于动态不对称中。
5. Color Theory: The Color Wheel Formulas | 色彩理论：色轮公式
Colour theory begins with the 12-part colour wheel: three primary colours (red, yellow, blue), three secondaries (orange, green, violet), and six tertiaries (red-orange, yellow-orange, yellow-green, blue-green, blue-violet, red-violet). This wheel provides the basis for every colour mixing formula.
色彩理论始于十二色色轮：三种原色（红、黄、蓝），三种间色（橙、绿、紫）和六种复色（红橙、黄橙、黄绿、蓝绿、蓝紫、红紫）。这个色轮是所有调色公式的基础。
| Mixing Formula | 调色公式 | Equation | 方程 |
|---|---|
| Secondary | 间色 | R + Y = Orange; Y + B = Green; B + R = Violet |
| Tertiary | 复色 | Primary + adjacent Secondary (1:1 ratio) |
| Tint | 明调 | Hue + White |
| Shade | 暗调 | Hue + Black |
| Tone | 中间调 | Hue + Grey (or complement + white) |
| Neutralisation | 中和 | Mix complementary pairs → brown/neutral grey |
Temperature is another key variable: warm colours (reds, oranges, yellows) advance, cool colours (blues, greens, violets) recede—a theorem essential for creating depth without linear perspective.
色温是另一关键变量：暖色（红、橙、黄）前进，冷色（蓝、绿、紫）后退——这是无需线透视即可创造景深的重要定理。
6. Color Harmony Formulas (Analogous, Complementary, Triadic) | 色彩和谐公式（邻近色、互补色、三色组合）
Select colours that sit in proven geometric relationships on the wheel. This eliminates guesswork and produces intentional emotional responses. Edexcel personal study demands explicit demonstration of such knowledge.
选择在色轮上处于被证实的几何关系中的色彩。这能消除猜测并产生有意识的情感反应。Edexcel 个人调研明确要求展示这类知识。
- Complementary – opposite colours (e.g. Red + Green). Maximum contrast; use dominant/subordinate balance to avoid vibration. | 互补色——相对的色彩（如红与绿）。最大对比；使用主次配比以避免颤动。
- Analogous – 3–5 adjacent colours (e.g. Yellow, Yellow-Green, Green). Serene, cohesive; vary value and saturation to avoid monotony. | 邻近色——3 至 5 种相邻色（如黄、黄绿、绿）。宁静、统一；变化明度与饱和度以避免单调。
- Triadic – three colours equally spaced (e.g. Red, Yellow, Blue). Vibrant, balanced; let one dominate and use the others as accents. | 三色组合——三种均匀分布的色彩（如红、黄、蓝）。活泼、均衡；让其中一种主导，其他点缀。
- Split-Complementary – a base colour plus the two colours adjacent to its complement. High contrast with less tension. | 分裂互补色——一个基色加上其互补色两侧的两个颜色。高对比而紧张感较低。
- Tetradic (Double Complementary) – two complementary pairs, forming a rectangle. Rich, complex; requires careful temperature and value control. | 四色组合（双互补）——两对互补色，构成矩形。丰富、复杂；需要谨慎控制色温和明度。
The formula for harmony: visual balance of hue, saturation, and value across the chosen scheme.
和谐公式：所选方案中色相、饱和度和明度的视觉平衡。
7. Perspective: One-Point and Two-Point Vanishing Formulas | 透视：一点和两点消失点公式
Linear perspective creates the illusion of depth on a flat surface. The fundamental theorem: parallel lines appear to converge at a vanishing point (VP) on the horizon line (eye level). For one-point perspective, all receding lines orthogonal to the picture plane converge to a single VP.
线透视在平面上创造出深度错觉。基本定理：平行线看似消失于地平线（视平线）上的消失点（VP）。对于一点透视，所有与画面正交的后退线汇聚于单一消失点。
One-Point: VP = intersection of receding orthogonals
一点透视：VP = 后退正交线的交点
Two-point perspective uses two VPs on the horizon. The station point (viewer’s position) and the cone of vision determine distortion. A standard formula: keep VPs far apart and objects within a 60° cone of vision to avoid unnatural stretching.
两点透视使用地平线上的两个消失点。视点（观者位置）和视锥决定了变形程度。标准公式：让消失点间距足够大，并将物体保持在 60° 视锥内，以避免不自然的拉伸。
| Perspective Type | 透视类型 | Vanishing Points | 消失点 | Key Formula | 关键公式 |
|---|---|---|
| One-point | 一点 | 1 VP on horizon | All depth lines → VP |
| Two-point | 两点 | 2 VPs on horizon | Vertical edges remain vertical; depth edges → VPs |
| Three-point | 三点 | 2 VPs on horizon + 1 above or below | Dramatic bird’s-eye or worm’s-eye views |
| Atmospheric | 空气透视 | N/A | Contrast & detail ↓ with distance, colour shifts to cool |
8. The Proportions of the Human Figure | 人体比例公式
Classical figure drawing relies on measurable proportional canons. The average adult figure is about 7.5–8 heads tall. Key landmarks: the pubis marks the halfway point; the arms, when extended, equal the total height; the face is divided into equal thirds (hairline to brow, brow to nose base, nose base to chin).
古典人物素描依赖于可测量的比例法则。成人平均身高约为 7.5 至 8 个头长。关键地标：耻骨是身高的中点；双臂伸展时的长度等于全身高度；面部被均分为三部分（发际线到眉弓、眉弓到鼻底、鼻底到下巴）。
Head-to-Body Ratio: Total Height ≈ 7.5–8 × Head Length
头身比：总高度 ≈ 7.5–8 × 头长
- Vitruvian proportions (da Vinci): arm span = height, hand = 1/10 height, foot = 1/6 height | 维特鲁威比例（达·芬奇）：臂展 = 身高，手长 = 1/10 身高，足长 = 1/6 身高
- Facial thirds: hairline–eyebrow = eyebrow–nose base = nose base–chin | 面部三庭：发际线–眉弓 = 眉弓–鼻底 = 鼻底–下巴
- Eye spacing: face width ≈ 5 eye-widths; eyes one eye-width apart | 眼间距：面宽 ≈ 5 个眼宽；两眼相距一个眼宽
- Child proportions: head larger relative to body (4–5 heads at age 3), eyes lower on skull | 儿童比例：头相对于身体更大（3 岁时约 4–5 个头长），眼睛在颅骨上位置较低
9. The Rule of Odds and Visual Balance | 奇数法则与视觉平衡
An odd number of subjects (3, 5, 7) in a composition typically creates more visual interest than an even number. The eye tends to pair even-numbered items, leading to static symmetry, whereas odd groupings frame a central subject and encourage the eye to move around the periphery. This principle works alongside the rule of thirds and negative space distribution.
构图中奇数的主体数量（3、5、7）通常比偶数更富有视觉趣味。眼睛倾向于将偶数物品配对，导致静态对称；而奇数组能框住中心主体并鼓励视线在周边移动。这一原则与三分法和负空间分布协同作用。
Visual weight balancing formula: light area × distance from centre can counterbalance a heavy area closer to centre. Experiment by placing a small, dark shape far from the centre and a large, light shape nearer the centre to achieve asymmetric equilibrium.
视觉重量平衡公式：光亮区域 × 到中心的距离可以平衡靠中心较近的沉重区域。尝试把一个暗色小形放在远离中心的位置，而将一个浅色大形靠近中心，以实现不对称的平衡。
10. Gestalt Principles in Art | 艺术中的格式塔原理
Gestalt psychology describes how humans naturally organise visual elements into groups. The six core principles serve as perceptual theorems: similarity (items that look alike are grouped), proximity (items close together are grouped), continuity (the eye follows smooth paths), closure (incomplete shapes are mentally completed), figure/ground (separating the subject from the background), and symmetry/order (we perceive symmetrical forms as a unified whole).
格式塔心理学描述了人类如何自然地将视觉元素组织成组。六项核心原则如同感知定理：相似性（相似物品被归为一组）、接近性（靠近的物品被分组）、连续性（视线追随平滑路径）、闭合性（不完整的形状心理解读出完整）、图底关系（将主体与背景分离）以及对称/秩序（我们把对称形式感知为统一整体）。
Apply these to strengthen your composition’s instant readability. For example, use closure to imply an edge without literally drawing it, or proximity to create a relationship between two separate figures.
运用这些原则来增强构图的即时可读性。例如，使用闭合性去暗示一条边界而不用实际画出它，或使用接近性在两个分离的形象间建立关系。
11. Typography and Layout Formulas | 排版与布局公式
When integrating text into artwork or designing an artist’s book, typographic hierarchy directs the viewer’s reading order. The modular scale formula determines harmonious font sizes: next size = base size × ratio (often 1.25, 1.333, or 1.5). Leading (line spacing) should be around 120–150% of the font size; measure (line length) is ideal at 45–75 characters per line.
当在作品或艺术家书设计中融入文字时，字体层级引导观者的阅读顺序。模数比例公式决定和谐的字体大小：下一字号 = 基础字号 × 比例（常为 1.25、1.333 或 1.5）。行距（行间距）应为字号的 120–150%；行长（行的长度）理想为每行 45–75 个字符。
| Layout Formula | 布局公式 | Application | 应用 |
|---|---|
| Grid Systems | 网格系统 | Divide page into columns (e.g. 3, 5, 8) for structured alignment |
| Gutenberg Diagram | 古腾堡图表 | Eye scans top-left to bottom-right; place key info along this axis |
| Z-pattern Layout | Z 型布局 | For minimal text; sight line moves like a Z across the page |
| Golden Ratio Layout | 黄金比例布局 | Content area ratio of 1.618; sidebar width = (page width / 1.618) × 0.618 |
12. Quick Reference: Key Mathematical Ratios in Art | 速查：艺术中的关键数学比率
Memorise these ratios; they recur in exam board exemplar annotations. Understanding them allows you to deconstruct historic masterpieces and embed intentional geometry into your own work.
记住这些比率；它们反复出现在考试局范例评注中。理解它们能让你解构历史杰作，并将有意图的几何学嵌入你自己的创作中。
- Φ (Golden Ratio) ≈ 1.618 : 1 | 黄金比例 ≈ 1.618 : 1
- Silver Ratio ≈ 2.414 : 1 (used in Japanese architecture, A-series paper √2:1) | 白银比 ≈ 2.414 : 1（用于日本建筑，A 系列纸 √2:1）
- Rule of Thirds : 1/3 and 2/3 divisions | 三分法：1/3 与 2/3 划分
- Aspect Ratios: 3:2 (35mm film), 4:3 (traditional monitor), 16:9 (widescreen) | 宽高比：3:2（35mm 胶片）、4:3（传统显示器）、16:9（宽屏）
- Body Proportions: Adult head = 1/8 total height; adolescent = 1/6–1/7 | 人体比例：成人头长 = 1/8 身高；青少年 = 1/6–1/7
- Colour Luminance: Yellow is naturally the lightest pure hue; violet the darkest. Use this brightness hierarchy to control spatial advance/recede effects. | 色彩亮度：黄色是自然最亮的纯色相；紫色最暗。运用此亮度层级来控制空间前进/后退效果。
Integrate these numeric touchstones into your sketchbook reflection and essay writing. Citing that you employed a silver-ratio rectangle to frame a still-life demonstrates analytical depth that raises marks in AO1 (Develop) and AO3 (Record).
将这些数字基准融入你的速写本反思和论文写作中。引用你使用白银比例矩形来框定静物，这展示出的分析深度能够提升在 AO1（发展）和 AO3（记录）评估目标上的得分。
Published by TutorHao | Art Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导