Essential Formulas & Theorems for Edexcel Art | Edexcel 艺术公式定理速查手册

📚 Essential Formulas & Theorems for Edexcel Art | Edexcel 艺术公式定理速查手册

Art may seem a free-flowing subject, but behind every masterwork lies a set of fundamental rules, formulas, and theorems that guide composition, proportion, colour mixing, and perspective. This quick-reference handbook gathers the essential mathematical and scientific principles that every Year 11 Edexcel Art student should know – from the Golden Ratio to the colour wheel equations, from vanishing points to the rule of thirds. Use these formulas to strengthen your sketchbook annotations, improve your practical work, and ace your examination analysis.

艺术看起来是一门自由流淌的学科，但在每一件杰作背后，都有一套指导构图、比例、色彩调和与透视的基本规则、公式和定理。这本速查手册汇集了每位 Year 11 Edexcel 艺术学生都应该掌握的关键数学与科学原理——从黄金分割比到色轮公式，从消失点到三分法。运用这些公式来充实你的速写本注释、提升你的实践作品，并在考试分析中脱颖而出。

1. The Golden Ratio (Φ) | 黄金分割比 (Φ)

The Golden Ratio, approximately 1.618, is found when a line is divided into two parts so that the whole length divided by the longer part is equal to the longer part divided by the shorter part. This proportion appears in nature, classical architecture, and famous artworks like Leonardo da Vinci’s ‘Vitruvian Man’. In composition, placing the focal point at a golden ratio division of the canvas enhances visual harmony.

黄金分割比约等于 1.618，当一条线段被分成两部分，使得全长与较长部分之比等于较长部分与较短部分之比时，就得到了这一比例。这个比例出现在自然界、古典建筑以及列奥纳多·达·芬奇的《维特鲁威人》等著名艺术作品中。在构图中，将焦点放置在画布的黄金分割点上能够增强视觉和谐感。

If a > b then (a + b) ÷ a = a ÷ b = Φ ≈ 1.618

2. Rule of Thirds | 三分法则

Divide the image area into nine equal parts by two equally spaced horizontal lines and two equally spaced vertical lines. The four intersections of these lines are points of visual strength. Placing key elements along these lines or at the intersections creates balance and interest, and is far more dynamic than centring the subject.

用两条等距的水平线和两条等距的垂直线将画面区域分成九个相等的部分。这些线条的四个交点是视觉上的强点。将关键元素沿这些线条或交点放置能够创造平衡与趣味，比将主体居中要生动得多。

Frame width ÷ 3 = distance of vertical lines; Frame height ÷ 3 = distance of horizontal lines

3. One-Point Perspective | 一点透视

One-point perspective involves a single vanishing point on the horizon line. All lines parallel to the viewer’s line of sight converge at this point. The formula for depth is that objects further away appear smaller. To draw a perfect grid in perspective, every receding horizontal line must go to the vanishing point, while verticals stay vertical and width lines remain parallel to the horizon.

一点透视包括地平线上的一个消失点。所有与观众视线平行的线条都汇聚于这一点。深度的公式是：物体越远，显得越小。要在透视中绘制完美的网格，每条后退的横线必须走向消失点，竖线保持垂直，宽度线则与地平线平行。

Vanishing Point (VP) on Horizon Line (HL). All depth lines → VP

4. Two-Point Perspective | 两点透视

Two-point perspective uses two vanishing points on the horizon line, typically off the canvas edges. Vertical lines remain vertical; all other lines recede to either the left or right vanishing point. The angle between any two receding lines determines the perceived corner of an object. This system is essential for drawing buildings, furniture, and any form not parallel to the viewer.

两点透视使用地平线上的两个消失点，通常位于画布边缘之外。垂直线保持垂直；所有其他线条分别消失于左消失点或右消失点。任意两条后退线之间的角度决定了物体感知到的转角。这一体系对于绘制建筑、家具和任何不与观众平行的形体至关重要。

Vertical edges = straight lines. Left planes → VP1; Right planes → VP2

5. Atmospheric Perspective Formula | 大气透视公式

Atmospheric perspective states that objects in the distance lose contrast, become cooler in colour temperature, and lighten in value due to particles in the air. The approximate formula: for every 1 km of distance, contrast reduces by approximately 10% and blue light scatters more, shifting hues towards blue-grey. Artists use this to create depth by mixing distant colours with a small amount of white and blue.

大气透视指出，由于空气中的微粒，远处的物体对比度降低、色温变冷、明度变亮。近似公式为：每增加 1 公里距离，对比度大约降低 10%，蓝光散射更多，使色调向蓝灰色偏移。艺术家通过将远处颜色与少量白色和蓝色混合来创造深度感。

Distance ↑ → Contrast ↓, Hue → Blue-Grey, Value → Light

6. Colour Wheel & Mixing Ratios | 色轮与调色比

The traditional colour wheel has 12 hues: three primaries (red, yellow, blue), three secondaries (orange, green, purple) made by mixing equal parts of two primaries, and six tertiaries mixed from a primary and a secondary. To mix a specific colour, note the formula: a hue plus its complement (opposite on the wheel) creates brown or grey. The ratio can be varied for warm or cool neutrals.

传统色轮有 12 个色相：三原色（红、黄、蓝），三间色（橙、绿、紫）由两种原色等量混合而成，六种复色由原色与间色混合而成。要调和特定颜色，请记住这一公式：色相加上它的补色（色轮上相对的色彩）产生棕色或灰色。通过改变比例可以得到偏暖或偏冷的中性色。

Red + Yellow = Orange; Blue + Yellow = Green; Red + Blue = Purple. Hue + Complement = Neutral (Brown/Grey)

7. Complementary Colour Contrast | 补色对比公式

When placed side by side, complementary colours (opposites on the colour wheel) intensify each other. The maximum contrast formula is pure complementary pair with high chroma. This creates visual vibration and draws the eye. In pointillism, tiny dots of complementary colours placed close together mix optically in the viewer’s eye to produce a vibrant neutral.

当补色（色轮上相对的色彩）并排放置时，会相互增强。最大对比度的公式是使用高彩度的纯补色组合。这会产生视觉振动并吸引视线。在点彩画法中，将补色的微小点紧密排列，会在观者眼中进行光学混合，产生充满活力的中性色调。

Complementary Pair: Red ↔ Green, Blue ↔ Orange, Yellow ↔ Purple. Proximity → Intensified Hue

8. Value Scale & Tonal Gradation | 明度尺与色调层次

Value is the lightness or darkness of a colour. A standard 9-step value scale moves from pure white (value 1) to pure black (value 9). To model form realistically, apply the formula: highlight = lightest value, midtone = local colour, core shadow = darker midtone, reflected light = slightly lighter than core shadow, cast shadow = darkest. The transition from light to dark should follow a smooth gradation – often described as a ‘10% change per step’ in controlled shading.

明度指色彩的明暗程度。标准的 9 级明度尺从纯白（明度 1）过渡到纯黑（明度 9）。要真实塑造形体，请运用这一公式：高光 = 最浅明度，中间调 = 固有色，明暗交界线 = 较暗的中间调，反光 = 比明暗交界线稍亮，投影 = 最暗。从亮到暗的过渡应遵循平滑的渐变——在控制性明暗处理中，常被描述为“每级变化 10%”。

Value scale: 1 (White) → 5 (Mid-grey) → 9 (Black). Smooth shading: Δvalue ≈ 10% per step

9. Proportions of the Human Figure | 人体比例公式

The classical canon of proportions, derived from Vitruvius and used by Leonardo, states that the ideal human height is 7.5 to 8 head lengths. The body can be divided into measurable units: the distance from the top of the head to the chin = 1 unit; chin to nipple line = 1 unit; nipple line to navel = 1 unit; navel to crotch = 1 unit; crotch to mid-thigh = 1 unit; mid-thigh to knee = 1 unit; knee to mid-calf = 1 unit; mid-calf to sole = 1 unit. Shoulder width equals 2 head widths.

源自维特鲁威并经达·芬奇运用的古典比例法则指出，理想的人体身高为 7.5 到 8 个头长。身体可划分为若干可量测的单位：头顶至下颌 = 1 单位；下颌至乳头连线 = 1 单位；乳头连线至肚脐 = 1 单位；肚脐至裆部 = 1 单位；裆部至大腿中部 = 1 单位；大腿中部至膝盖 = 1 单位；膝盖至小腿中部 = 1 单位；小腿中部至脚底 = 1 单位。肩宽等于 2 个头宽。

Body height ≈ 7.5 – 8 heads. Arm span ≈ height. Shoulder width ≈ 2 heads

10. Triangle of Composition | 构图三角形

Many Renaissance and Baroque masterpieces are built on a triangular or pyramidal structure. The base of the triangle provides stability, while the apex directs the eye upwards. To construct a strong composition, arrange the main figures or objects so their contours form a rough triangle. This formula works because the human eye naturally follows diagonal lines and settles at intersections.

许多文艺复兴和巴洛克时期的杰作都构建在一个三角形或金字塔形结构之上。三角形的底边提供稳定感，顶点则将视线引向上方。要构建强有力的构图，需将主要人物或物体安排得使其轮廓形成一个粗略的三角形。这一公式之所以有效，是因为人眼会自然跟随对角线并在交点处停留。

Compositional triangle: Base = stability, Apex = focal point. Diagonals guide eye movement

11. The 60-30-10 Colour Rule | 60-30-10 色彩法则

In interior design and painting, the 60-30-10 rule creates colour balance: 60% of the area is a dominant colour, 30% a secondary colour, and 10% an accent colour. Applied to a canvas, this formula ensures that one hue does not overwhelm the composition and that visual interest is scattered proportionally. Use your colour wheel to select a harmonious palette that fits this distribution.

在室内设计和绘画中，60-30-10 法则创造色彩平衡：60% 的区域为主色彩，30% 为辅助色彩，10% 为强调色彩。将这一公式应用于画布，可确保没有单一色相压倒构图，并且视觉兴趣点按比例分散分布。运用你的色轮选择一个符合这一分布的和谐调色板。

Dominant colour 60%, Secondary colour 30%, Accent 10%. Keeps palette balanced

12. Reflection & Shadow Angles | 反射与阴影角度公式

The law of reflection states that the angle of incidence equals the angle of reflection relative to the surface normal. For drawing highlights on shiny objects, this means the brightest spot appears where the light source reflects directly into the viewer’s eye. For cast shadows, the shadow direction is opposite the light source, and its length can be calculated by extending a line from the light source past the object’s top to the ground plane.

反射定律指出，入射角等于相对于表面法线的反射角。在绘制闪亮物体的高光时，这意味着最亮的点出现在光源直接反射到观者眼睛的位置。对于投影，阴影方向与光源相反，其长度可以通过从光源经过物体顶部延伸到地平面的直线来计算。

Angle of incidence θᵢ = Angle of reflection θᵣ. Shadow length ∝ object height ÷ tan(light elevation)

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