📚 Year 10 OCR Art: Formula & Theorem Quick Reference Handbook | Year 10 OCR 艺术：公式定理速查手册
This revision guide compiles the fundamental 'formulas' and 'theorems' that govern visual art and design in the OCR Year 10 curriculum. Whether you are analysing a masterpiece or building your own portfolio, these principles of proportion, colour, perspective, and composition act as your reliable toolkit. Learn them as if they were equations, and you will unlock a deeper understanding of how art communicates.
这份速查手册汇集了 OCR Year 10 艺术课程中支配视觉艺术与设计的基本“公式”和“定理”。无论你是在分析名作还是打造个人作品集，这些关于比例、色彩、透视和构图的原理都是你可靠的利器。像掌握方程式一样学会它们，你就能更深刻地理解艺术如何传递信息。
1. The Golden Ratio | 黄金比例
The Golden Ratio, denoted by the Greek letter φ (phi), is an irrational number approximately equal to 1.618. It emerges from the equation where a line is divided into two parts such that the ratio of the whole to the longer part equals the ratio of the longer part to the shorter part.
黄金比例用希腊字母 φ (phi) 表示，是一个约等于 1.618 的无理数。当一条线段被分成两部分，且整段与较长部分之比等于较长部分与较短部分之比时，就得到了这个比例。
a / b = (a + b) / a = φ ≈ 1.618
Artists have used golden rectangles (where the sides are in the ratio 1:φ) for centuries. From the Parthenon to Leonardo da Vinci's 'Mona Lisa', key elements are placed according to this 'divine proportion' to create a sense of natural balance.
艺术家们几个世纪以来一直使用黄金矩形（边长比为1:φ）。从帕特农神庙到达芬奇的《蒙娜丽莎》，关键元素都按照这一“神圣比例”布置，以营造自然的平衡感。
In practice, you can approximate the golden ratio by using a Fibonacci sequence or simply by placing focal points at about 0.382 or 0.618 of the width or height from the edge.
在实践中，你可以用斐波那契数列近似黄金比例，或者干脆将焦点放在距边缘约 0.382 或 0.618 宽度/高度的位置。
2. The Rule of Thirds | 三分构图法
The rule of thirds divides a canvas into nine equal rectangles by drawing two equally spaced horizontal lines and two equally spaced vertical lines. The intersections of these lines are called power points.
三分法通过两条等距水平线和两条等距垂直线将画面分成九个相等的矩形。这些线的交叉点称为力量点。
Grid lines at 1/3 and 2/3 of width & height → 4 power points
Placing the main subject on one of these power points or along a line creates a more dynamic and engaging composition than centring the subject. Landscapes often place the horizon on one of the horizontal lines.
将主体放在其中一个力量点上或沿线放置，比把主体居中更能产生动态且引人入胜的构图。风景画常常将地平线放在某条水平线上。
This rule is widely used in photography, painting, and even cinematography to guide the viewer's eye naturally through the scene.
这一法则广泛应用于摄影、绘画甚至电影艺术，以自然地引导观众的视线穿过画面。
3. Colour Wheel Fundamentals | 色轮基础
The colour wheel is a visual representation of colour theory. The primary colours (red, yellow, blue) cannot be mixed from other pigments. Secondary colours (orange, green, violet) are created by mixing two primaries. Tertiary colours result from mixing a primary with a neighbouring secondary.
色轮是色彩理论的视觉呈现。三原色（红、黄、蓝）无法通过其他颜料混合而成。间色（橙、绿、紫）由两种原色混合而成。复色由原色与相邻的间色混合产生。
| Category | Colours |
|---|---|
| Primary | Red, Yellow, Blue |
| Secondary | Orange (R+Y), Green (Y+B), Violet (B+R) |
| Tertiary | Red-Orange, Yellow-Orange, Yellow-Green, Blue-Green, Blue-Violet, Red-Violet |
Understanding the wheel helps you predict colour mixing results and select harmonious palettes. Adjacent colours create calm, analogous schemes; opposite colours generate vibrant contrast.
理解色轮有助于你预判调色结果并选择和谐的色彩组合。相邻的颜色产生宁静的近似色调；相对的颜色带来鲜明的对比。
4. Complementary & Analogous Colours | 互补色与邻近色
Complementary colours sit directly opposite each other on the colour wheel. Common pairs are red & green, blue & orange, yellow & violet. When placed side by side, they intensify each other and create maximum contrast.
互补色在色轮上正相对。常见的配对是红与绿、蓝与橙、黄与紫。当它们并置时，会相互增强，形成最强的对比。
Red + Green → high visual vibration
Analogous colours are groups of three to five colours that sit next to each other on the wheel, such as blue, blue-green, and green. They produce serene and cohesive designs, often found in nature.
邻近色是色轮上相邻的三到五种颜色，例如蓝、蓝绿和绿。它们产生宁静而统一的设计，在自然界中很常见。
Use complementary schemes to make elements pop; use analogous schemes for harmony. A split-complementary scheme uses one colour plus the two colours adjacent to its complement, offering contrast with less tension.
用互补色调使元素突出；用邻近色调追求和谐。分裂互补色调使用一种颜色加上其补色两侧的两种颜色，既形成对比又减少了紧张感。
5. Linear Perspective | 线性透视
Linear perspective is a mathematical system for creating the illusion of three-dimensional space on a flat surface. It relies on a horizon line (eye level) and one or more vanishing points where receding parallel lines appear to converge.
线性透视是一种在平面上创造三维空间错觉的数学系统。它依赖于一条水平线（视平线）和一个或多个消失点，后退的平行线在那里似乎汇聚。
In 1-point perspective: All receding lines meet at a single VP on the HL.
In one-point perspective, the viewer's face is parallel to the front of the object. A famous example is Da Vinci's 'The Last Supper', where the vanishing point is behind Christ's head, drawing focus to the central figure.
在一点透视中，观者的脸正对物体的正面。一个著名的例子是达芬奇的《最后的晚餐》，消失点位于基督头部后方，将注意力引向中心人物。
Two-point perspective uses two vanishing points on the horizon, ideal for showing objects at an angle, like a building viewed from a corner. Three-point perspective adds a vertical vanishing point for dramatic 'bird's-eye' or 'worm's-eye' views.
两点透视在水平线上使用两个消失点，适合表现成角度的物体，比如从拐角看一座建筑。三点透视增加一个垂直消失点，用于夸张的“鸟瞰”或“虫视”效果。
6. The Gestalt Principles | 格式塔原理
Gestalt psychology describes how humans perceive visual elements as unified wholes. Key principles include proximity, similarity, continuity, closure, and figure-ground. These 'laws' help designers control how viewers group and interpret forms.
格式塔心理学描述了人类如何将视觉元素感知为统一的整体。关键原理包括接近性、相似性、连续性、闭合性和图形-背景。这些“定律”帮助设计师控制观众如何分组和解读形式。
Proximity: objects placed close together are seen as a unit. Similarity: items sharing colour, shape or size are grouped. Continuity: the eye follows the smoothest path. Closure: we mentally fill gaps to see complete shapes.
接近性：靠得很近的物体被视为一个单元。相似性：共享颜色、形状或大小的物品被归为一组。连续性：视线沿最平滑的路径移动。闭合性：我们脑补空缺以看到完整的形状。
Apply these to your collage, typography, or poster design. For example, overlapping letters (closure) can still be read, and consistent colour (similarity) can unite disparate elements.
把这些原理应用在你的拼贴、排版或海报设计中。例如，重叠的字母（闭合性）依然能被识别，一致的颜色（相似性）可以将不同的元素联合起来。
7. The Value Formula | 明暗值公式
In art, value describes the lightness or darkness of a colour. A value scale typically ranges from 0 (pure black) to 10 (pure white), with 5 being a middle grey. The contrast between values creates form, depth, and mood.
在艺术中，明暗值指颜色的明暗程度。明度标尺通常从0（纯黑）到10（纯白），5为中间灰。明暗值之间的对比创造了形体、深度和氛围。
Highlights ≈ Value 9–10 | Midtones ≈ 5 | Core Shadow ≈ 2–3
A simple sphere shading formula: lightest area faces the light source (highlight); the darkest area is the core shadow away from the light; reflected light lifts the shadow edge slightly. Understanding value is the key to realistic rendering.
一个简单的球体着色公式：面对光源的区域最亮（高光）；最暗的区域是背光的核心阴影；反光会稍微提亮阴影边缘。理解明暗值是实现逼真渲染的关键。
When mixing paints, add white to increase value (tint) or black to decrease (shade). To lower value without dulling colour, use a complementary colour instead of black.
调色时，加白色提亮（浅色调），加黑色变暗（深色调）。想要降低亮度而又不使颜色变灰，就用补色来代替黑色。
8. Balance and Symmetry | 平衡与对称
Visual balance is the distribution of visual weight within a composition. Symmetrical balance mirrors elements on either side of a central axis, creating a formal, calm appearance. It is commonly used in religious art and heraldic designs.
视觉平衡是构图中视觉重量的分布。对称平衡以中轴线为镜面反射两侧元素，产生正式、平静的外观。它常用于宗教艺术和纹章设计。
Asymmetrical balance achieves equilibrium through dissimilar objects that have equal visual weight. For instance, a large light shape can be balanced by a smaller dark shape. This feels more dynamic and modern.
不对称平衡通过视觉重量相等的不同物体达到均衡。例如，一个大的浅色形状可以被一个小的深色形状平衡。这感觉更动态、更现代。
Radial balance radiates from a central point, like the petals of a flower or the vault of a cathedral ceiling. The 'formula' for balance can be tested by imagining a pivot point at the centre of your composition.
放射状平衡从一个中心点向外辐射，如花瓣或大教堂穹顶。检查平衡的“公式”是想象构图中心有一个支点，看视觉重量是否均衡分布。
9. Proportion and Scale | 比例与尺度
Proportion refers to the size relationship between parts of a whole, and scale relates the size of an object compared to a standard or to human dimensions. Classical art often idealised human proportions using a canon, such as the Vitruvian canon.
比例指整体各部分之间的大小关系，而尺度则是物体尺寸与标准或人体尺寸的对比。古典艺术常用一种典范来理想化人体比例，比如维特鲁威典范。
Idealised head-to-body ratio ≈ 1:7.5 or 1:8
Leonardo's 'Vitruvian Man' illustrates that the human figure fits perfectly into a circle and square. The face can be divided into thirds: hairline to brow, brow to base of nose, nose to chin. These proportional rules help ensure accurate figure drawing.
达芬奇的《维特鲁威人》说明人体完美地内接于圆形和方形。面部可以分为三等份：发际线到眉毛，眉毛到鼻底，鼻底到下巴。这些比例法则有助于准确的人体绘画。
Exaggerating proportion is a powerful tool in caricature and surrealism. Changing scale can make everyday objects monumental or miniscule, altering the viewer's sense of importance and perspective.
在漫画和超现实主义中，夸张的比例是强大的工具。改变尺度可以让日常物体变得巨大或微小，从而改变观者的重要感和视角。
10. The Fibonacci Sequence in Art | 斐波那契数列在艺术中的应用
The Fibonacci sequence starts 0, 1, 1, 2, 3, 5, 8, 13, 21... where each term is the sum of the two preceding ones. The ratio between consecutive terms approaches the golden ratio as the sequence progresses.
斐波那契数列以0, 1, 1, 2, 3, 5, 8, 13, 21...起始，每一项是前两项之和。随着数列推进，相邻项的比值趋近于黄金比例。
Fₙ = Fₙ₋₁ + Fₙ₋₂
This sequence appears in natural forms, such as sunflower seed spirals, pinecone scales, and nautilus shells. Many historical artworks incorporate Fibonacci numbers, whether through deliberate application or intuitive design.
此数列出现在自然形态中，如向日葵种子螺旋、松果鳞片和鹦鹉螺壳。许多历史上的艺术品都融入了斐波那契数，无论是刻意运用还是直觉设计。
You can use Fibonacci numbers to build a grid or to determine the placement of elements in a composition. A common layout uses 8:13 rectangles, close to the golden ratio, to structure panels and frames.
你可以用斐波那契数来构建网格或决定构图元素的放置。常见的版式采用8:13的矩形，接近黄金比例，来组织画格和画框。
11. Grids and Layout | 网格与版式
A layout grid is an invisible structure that organises text and visual elements into columns, rows, and modules. It brings logical consistency and readability to publications, posters, and digital interfaces. The 'formula' often starts with a clear page margin and a set number of columns.
版式网格是一种将文本与视觉元素组织为栏、行和模块的隐形结构。它为出版物、海报和数字界面带来逻辑的一致性和可读性。这个“公式”常始于明确的页面边距和固定的栏数。
For example, a 12-column grid is highly flexible: you can split content into two halves (6+6), three equal parts (4+4+4), or asymmetrically (8+4). Consistent gutter widths maintain separation and rhythm.
例如，12栏网格灵活性极强：你可以把内容分成两半（6+6）、三等份（4+4+4）或不对称（8+4）。一致的栏间距保持分隔和节奏。
The Swiss/International Style makes heavy use of mathematical grids. In your work, always align key horizontal and vertical elements to the grid, but allow intentional breaking for emphasis.
瑞士国际主义风格大量使用数学网格。在你的作品中，始终将关键水平和垂直元素对齐到网格，但为了强调可以有目的地打破网格。
12. Dynamic Symmetry | 动态对称
Dynamic symmetry is a compositional system based on root rectangles, such as the √2, √3, and √5 rectangles. These provide a framework for arranging elements along diagonal lines that generate further harmonic subdivisions.
动态对称是一种基于根号矩形的构图体系，如√2、√3和√5矩形。它们提供了一个框架，使元素沿对角线排列并生成进一步的和谐细分。
√2 rectangle: 1 : √2 ≈ 1 : 1.414
This approach was favoured by artists like Georges Seurat and is used in classical architecture and in modern logo design. By creating reciprocal diagonals and perpendiculars, the composition gains a subtle, rhythmic flow.
乔治·修拉等艺术家偏爱这种方法，古典建筑和现代标志设计也会用到。通过创建互反对角线和垂直线，构图获得一种微妙的韵律流动。
Studying dynamic symmetry helps you move beyond static centring, enabling you to create complex, energetic layouts that still feel perfectly balanced.
学习动态对称帮助你超越呆板的居中构图，创造出复杂、充满活力的版式，同时又让人感到完美的平衡。
Published by TutorHao | Art & Design Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图