📚 Year 10 Eduqas Art: Formula and Theorem Quick Reference Handbook | Year 10 Eduqas 艺术：公式定理速查手册
In Art and Design, ‘formulas’ and ‘theorems’ are not abstract calculations but the proven visual principles that underpin strong compositions, accurate proportions and harmonious colour schemes. This quick reference handbook gathers the essential rules, ratios and patterns that will help you analyse masterworks and strengthen your own creative practice for the Eduqas GCSE course. Keep it close by when sketching, designing or evaluating artwork, and use it to make intentional, informed decisions.
在艺术与设计中，“公式”与“定理”并非抽象的计算，而是经过验证的视觉原则，支撑着有力的构图、精确的比例与和谐的色彩方案。这本速查手册汇集了基本规则、比例与模式，将帮助你在 Eduqas GCSE 课程中分析名家作品并提升自己的创作实践。绘制草图、设计方案或评价作品时请随时参考，用它做出有意识、有依据的选择。
1. The Golden Ratio | 黄金比例
The Golden Ratio, often denoted by the Greek letter φ (phi), is an irrational number approximately equal to 1.618. It expresses a relationship where the ratio of the whole to the larger part is the same as the ratio of the larger part to the smaller part: a+b : a = a : b. This proportion appears repeatedly in nature, from nautilus shells to sunflower seed heads, and has been used intentionally in art and architecture for centuries.
黄金比例通常用希腊字母 φ（phi）表示，约等于 1.618。它表达了一种关系：整体与较大部分的比等于较大部分与较小部分的比，即 a+b : a = a : b。这一比例反复出现在自然界中，从鹦鹉螺壳到向日葵花盘，数百年来在艺术与建筑中被有意识地运用。
A Golden Rectangle, whose sides are in the ratio 1 : 1.618, is considered especially pleasing to the eye. You can construct one by starting with a square, halving it and swinging a diagonal down to form the longer side. Placing the focal point at a Golden Ratio division within the format often creates a balanced, dynamic tension.
边长为 1 : 1.618 的黄金矩形被认为在视觉上格外悦目。你可以从一个正方形出发，将其二等分，然后将对角线旋转下来形成长边，从而构建黄金矩形。将视觉焦点放置在画面按黄金比例分割的位置，常能营造出平衡且富有张力的动态感。
A simple approximation useful for fieldwork is the rule that a line divided into 5 and 8 parts locates the Golden Section near the 5/8 mark. Use φ ≈ 1.618 or the fraction 8/5 = 1.6 as a practical guide.
适合作业实践的简单近似法是：将线段分为 5 和 8 份，黄金分割点大致位于 5/8 标记处。可将 φ ≈ 1.618 或分数 8/5 = 1.6 作为实用指南。
2. Rule of Thirds | 三分法则
The Rule of Thirds is a compositional guideline that divides an image into nine equal parts using two equally spaced horizontal lines and two equally spaced vertical lines. Placing the main subject or points of interest along these lines or at their intersections tends to produce a more engaging and balanced composition than centring the subject.
三分法则是一种构图指导，用两条等距的水平线和两条等距的垂直线将画面分为九个相等的部分。将主要对象或趣味点放置在这些线上或其交叉点上，通常比将对象居中能够带来更具吸引力和平衡感的构图。
The intersections are often referred to as ‘power points’. Positioning an eye, a horizon or a key vertical element on a third line prevents the composition from feeling static. For landscapes, placing the horizon on the upper third line emphasizes the land, while placing it on the lower third emphasizes the sky.
这些交点常被称为“力量点”。将眼睛、地平线或关键垂直元素放在三分线上可以避免构图呆板。在风景画中，将地平线放在上三分线时突出大地，放在下三分线时则强调天空。
Modern cameras and editing software frequently offer a Rule of Thirds grid overlay, showing that this formula is deeply embedded in visual practice across all media.
现代相机与编辑软件常提供三分网格叠加，表明这一公式已深深嵌入各类媒介的视觉实践中。
3. Perspective Drawing Formulas | 透视绘制公式
Linear perspective relies on a simple mathematical principle: objects appear smaller as their distance from the viewer increases. In one-point perspective, all receding parallel lines converge at a single vanishing point on the horizon line. The apparent height (H’) of an object at distance D from the picture plane can be described by the proportion H’ / H = d / (d + D), where H is actual height and d is the distance from the viewer to the picture plane.
线性透视依赖一个简单的数学原理：物体随距离增加而看起来变小。在一点透视中，所有向后退去的平行线都汇聚于地平线上的一个消失点。距离画面平面 D 的物体，其表观高度 (H’) 满足比例 H’ / H = d / (d + D)，其中 H 为实际高度，d 为观察者到画面平面的距离。
Two-point perspective introduces two vanishing points on the horizon line, typically used when the object’s front corner faces the viewer. The steeper the angle of the receding edges, the closer the vanishing points move toward the centre. Keeping vanishing points far apart creates a more natural, wide-angle feel.
两点透视在地平线上引入两个消失点，通常在物体的前角朝向观看者时使用。后退边缘的角度越陡，消失点越向中心靠拢。将消失点保持较远距离能营造更自然、广角的感觉。
For quick sketches, remember: vertical lines stay vertical in one- and two-point perspective. The spacing of evenly spaced elements (such as fence posts or windows) decreases geometrically towards the vanishing point; the first interval is the largest, and each subsequent interval is multiplied by a constant factor derived from the perspective construction.
绘制速写时请记住：在一点和两点透视中，垂直线始终保持垂直。等距元素（如栅栏柱或窗户）的间距朝消失点按几何级数递减；第一个间隔最大，其后的每个间隔都乘以由透视构造得出的恒定因子。
4. Human Figure Proportions | 人体比例
Idealised human proportions use the head as the basic unit of measurement. In classical canons, the average adult body is about 7½ to 8 heads tall. The halfway point of the body is the pubic bone, not the waist. The arms, when extended horizontally, reach a span roughly equal to the total height – a relationship seen in Leonardo da Vinci’s Vitruvian Man.
理想化的人体比例以头部为基本测量单位。在古典法则中，成年人的身体平均约为 7½ 到 8 个头长。身体的中点位于耻骨而非腰部。双臂水平伸展时，臂展大致等于全身高度——达芬奇的《维特鲁威人》中便可看到这一关系。
Key landmarks for figure drawing: eyes sit halfway down the head; the nose is halfway between eyes and chin; the mouth is approximately one-third of the way down from the nose to the chin. Hands are roughly the length of the face from chin to hairline, and the foot length is roughly equal to the head height.
人体素描的关键标记点：眼睛位于头部一半处；鼻子在眼睛与下巴的中间；嘴巴大约在鼻子到下巴距离的三分之一处。手的长度约等于从下巴到发际线的面部长度，脚长约等于头高。
When drawing children, proportions shift: a one-year-old is about four heads tall, while a six-year-old is around six heads tall. These proportional formulas help artists avoid common errors even when working in expressive or stylised modes.
画儿童时比例会发生变化：一岁儿童约四个头高，六岁儿童约六个头高。这些比例公式有助于艺术家即使在表现性或风格化创作中也避免常见错误。
5. Colour Theory Formulas | 色彩理论公式
Colour theory provides systematic ‘formulas’ for achieving harmony and contrast. The traditional colour wheel arranges hues in a circle, with primary, secondary and tertiary colours. Key colour schemes based on geometric relationships on the wheel can be treated as recipes for mixing and designing.
色彩理论提供了实现和谐与对比的系统“公式”。传统色轮将色相排列成圆，包含原色、间色和复色。基于色轮上几何关系的关键色彩搭配方案，可以作为调色与设计的配方来使用。
| Scheme / 搭配 | Wheel Geometry / 色轮几何 | Intended Effect / 预期效果 |
|---|---|---|
| Complementary / 互补色 | Opposite colours (180° apart) / 相对180° | High contrast, vibrant / 高对比，鲜艳 |
| Analogous / 类似色 | Three neighbours (e.g. 30° spreads) / 三个邻近色 | Harmonious, serene / 和谐，宁静 |
| Triadic / 三角色 | Three equally spaced (120°) / 三等分120° | Balanced yet lively / 平衡而活泼 |
| Split Complementary / 分裂互补 | Base + two adjacent to its complement / 基色加补色两侧色 | Contrast with less tension / 张力较小的对比 |
Designers also use mathematical tints, shades and tones: a tint is a hue mixed with white, a shade with black, and a tone with grey. The perceived warmth or coolness of a colour can be adjusted by adding a small amount of its complementary colour, gradually neutralising its intensity.
设计师还会使用数学化的淡色、暗色和浊色：淡色是色相加白调成，暗色加黑，浊色加灰而得到。通过加入少量互补色，可以调整色彩的冷暖感，并逐渐中和其强度。
6. Fibonacci Spiral and Growth Patterns | 斐波那契螺旋与生长模式
The Fibonacci sequence, where each term is the sum of the two preceding ones (1, 1, 2, 3, 5, 8, 13, …), generates a spiral that appears widely in living forms. When squares with these side lengths are arranged, the resulting curve approximates the Golden Spiral and can be used as a dynamic compositional device.
斐波那契数列中每一项是前两项之和（1, 1, 2, 3, 5, 8, 13, …），它产生了一种在生命形态中广泛出现的螺旋。将这些边长的正方形排列起来，所得曲线近似黄金螺旋，可作为动态构图工具来使用。
Artists often overlay a Fibonacci spiral on a canvas to guide the placement of elements along a flowing curve, leading the eye from a detail towards the main subject or out into the space. Many classical paintings and contemporary photographs use this hidden spiral to create a sense of natural movement.
艺术家常在画布上叠加斐波那契螺旋，引导元素沿流动曲线布置，使视线从细节移向主体或进入空间深处。许多古典绘画和当代摄影都利用这一隐形螺旋营造自然的运动感。
You can quickly construct an approximation by drawing quarter circles inside a series of squares with dimensions following the sequence: 1, 1, 2, 3, 5, 8 units. The spiral nestles into the composition more organically than a rigid grid.
你可以快速构造一个近似螺旋：在一系列尺寸为 1, 1, 2, 3, 5, 8 单位的正方形内分别画出四分之一圆。这样形成的螺旋比呆板的网格更有机地融入构图。
7. Dynamic Symmetry and Root Rectangles | 动态对称与根号矩形
Dynamic symmetry uses root rectangles (such as √2, √3, √5 rectangles) rather than static, rational proportions. A √2 rectangle has sides in the ratio 1 : √2 (approx. 1 : 1.414); when folded in half, it produces a smaller √2 rectangle, a property used in paper sizes like A4. These rectangles generate intricate diagonal networks that help artists place elements along lines of inherent visual energy.
动态对称采用根号矩形（如 √2、√3、√5 矩形）而非静态的有理比例。√2 矩形两边之比为 1 : √2（约 1 : 1.414）；对折后依然产生更小的 √2 矩形，这一特性体现在 A4 等纸张尺寸中。这些矩形生成复杂的对角线网络，帮助艺术家将元素放置在充满内在视觉能量的线上。
The armature of a rectangle is created by drawing both diagonals, plus lines from the corners to the midpoints of opposite sides. Overlaying this on a canvas reveals a web of interconnecting segments; compositional nodes where these lines cross naturally attract the eye and can anchor key visual points.
矩形的框架线由两条对角线以及从角连接到对边中点的线构成。将此框架覆盖在画布上，会显示出相互连接的线段网络；这些线段交叉所形成的构图节点自然吸引视线，可用于锚定关键视觉点。
Try constructing a √3 rectangle from a square by extending one side using the diagonal of the square. The resulting proportions offer alternatives to the Golden Ratio and can bring a subtle, structured rhythm to your layouts.
试试利用正方形的对角线延伸一边，从正方形构造 √3 矩形。这样得到的比例为黄金比例提供了替代方案，能为你的版式带来微妙而有结构的韵律。
8. Composition Grids and Aspect Ratios | 构图网格与长宽比
Every artwork exists within a framing ratio that affects the distribution of visual weight. Common ratios include 1:1 (square), 3:2 (classic 35mm), 4:3, 5:4 and 16:9. Each ratio favours certain compositional schemes: a square often suits centred, symmetrical arrangements, while a wide panoramic canvas invites layered foreground, middle ground and background.
每一件作品都处于某个画幅比例之内，这一比例影响着视觉重量的分布。常见的长宽比包括 1:1（正方形）、3:2（经典 35mm）、4:3、5:4 和 16:9。每种比例适合不同的构图方案：正方形常适合居中、对称的布局，而宽阔的全景画布则邀请层叠的前景、中景和背景。
The ‘golden’ aspect ratio of 1:1.618 and the 5:8 ratio derived from the fifth and sixth Fibonacci numbers are often used in art and graphic design to create a balanced but not overly static frame. Checking the ratio with a simple formula: width ÷ height = desired aspect value, helps you prepare supports and crop images more intentionally.
1:1.618 的“黄金”长宽比以及基于第五、第六个斐波那契数推导出的 5:8 比例，常被用于艺术和平面设计之中，以营造平衡又不至过度呆板的画面。用一个简单公式核验比例（宽度 ÷ 高度 = 期望的长宽值），有助于你更自觉地准备画材与裁剪图像。
When drawing a live scene, you can form a quick grid by measuring the subject’s dimensions with a pencil at arm’s length and transferring proportional relationships to your paper using a basic scaling formula: drawing size = actual size × desired scale factor.
在写生时，你可以在手臂伸直处用铅笔测量对象的尺寸，然后将比例关系通过基本缩放公式（画面尺寸 = 实际尺寸 × 所需比例尺）转换到纸上，以此快速形成网格。
9. Gestalt Principles of Visual Unity | 格式塔视觉统一原理
Gestalt psychology describes how we tend to perceive whole forms rather than isolated parts. These principles act as ‘theorems’ for visual grouping and are fundamental in graphic design, logo creation and painting. The law of proximity states that objects close together are seen as a group; the law of similarity groups elements that look alike.
格式塔心理学描述了我们如何倾向于感知整体形式而非孤立的部分。这些原则充当了视觉分组的“定理”，在平面设计、标志制作和绘画中具有基础作用。接近律指出，相近的物体被视为一组；相似律将外观相似的元素归为一个整体。
Continuity suggests the eye follows smooth paths and prefers to see aligned elements as a single line or curve. Closure allows the viewer to complete incomplete shapes – a principle exploited in minimalist art and logo designs. The figure-ground relationship defines what we perceive as the main object and what recedes as background.
连续律表明眼睛会沿着平滑路径移动，并倾向于将排成一列的元素看作一条线或曲线。闭合律使观者补全不完整的形状——极简艺术与标志设计常利用此原理。图底关系则界定我们将何者感知为主要对象，何者退为背景。
Applying Gestalt formulas helps you control emphasis and rhythm without overcomplicating compositions. For instance, placing several similar marks with one contrasting element instantly creates a focal point through the combination of similarity and anomaly.
运用格式塔公式能帮你控制重点与节奏，而不会使构图过于复杂。例如，放置数个相似笔触并在其中一个上引入变化，便能结合相似与异常原理立刻营造出视觉焦点。
10. Leading Lines and Vanishing Point Networks | 引导线与消失点网络
Leading lines are literal or implied lines that direct the viewer’s gaze toward a principal area. Roads, fences, rivers and even a figure’s sightline can serve as leading lines. The geometric formula for a line converging at a vanishing point ensures perspective accuracy: all physically parallel lines that recede in space meet at the same vanishing point on the horizon.
引导线是真实或隐含的线条，将观者的视线引向主要区域。道路、栅栏、河流甚至人物的视线都可以充当引导线。消失点汇聚的几何公式可确保透视准确：所有在空间中后退且实际平行的线，都会汇聚于地平线上同一个消失点。
You can construct a network of diagonals from each vanishing point to the edges of the frame, creating a ‘perspective grid’. This grid acts as a formula for placing multiple objects at consistent spatial depths. In three-point perspective, you add a third vanishing point above or below the horizon to control vertical convergence for dramatic worm’s-eye or bird’s-eye views.
你可以从每个消失点向画框边缘构建对角线网络，形成“透视网格”。这一网格如同公式，可将多个对象放置在一致的空间深度上。在三点透视中，你在视平线上方或下方添加第三个消失点，以控制垂直线的汇聚，实现极具戏剧性的虫瞰或鸟瞰效果。
Curvilinear perspective, though more complex, uses curved lines and multiple vanishing points to replicate the spherical nature of human vision, where straight lines at the periphery appear slightly bent. Even in freehand drawing, awareness of these guiding formulas adds credible depth.
曲线透视虽然更复杂，但使用曲线和多个消失点来再现人类视觉的球形特性，使得周边区域的直线显得微微弯曲。即使在徒手绘画中，对这些指引公式的意识也能增加可信的深度感。
11. Shading and Value Scale Formulas | 明暗与明度等级公式
A value scale shows the gradual transition from pure white to pure black, typically divided into 9 or 11 even steps. The formula for maintaining contrasts in a composition often references ‘key’ – high key (mostly light values), low key (mostly dark values) and full contrast (spanning at least 7 steps). The human eye tends to read the area of highest contrast as the focal point.
明度等级表现从纯白到纯黑的渐变过渡，通常分为 9 或 11 个均匀等级。维持构图对比的公式常引用“调子”——高调（以亮调为主）、低调（以暗调为主）和全对比（至少跨越 7 个等级）。人眼倾向于将对比最强的区域视为焦点。
When rendering form, the classic formula identifies five tones: highlight, light, mid-tone, core shadow and reflected light. Cast shadow adds a sixth. You can calculate approximate tonal steps by observing that the lightest light on a matte surface rarely exceeds 90% white, and the darkest dark under normal lighting remains above 5% black – extremes are reserved for specular highlights and deep crevices.
在表现形体时，经典公式界定出五个色调：高光、亮部、中间调、明暗交界线和反光。投影则增加了第六个。你可以计算大致色调阶梯：通常情况下，哑光表面最亮处极少超过 90% 白，最暗处则保持在 5% 黑以上——极端值只留给高光点和深缝。
Chiaroscuro, the strong use of light and dark, can be thought of as a ‘contrast ratio’ formula. Caravaggio’s paintings, for instance, often compress large sections into dark values while spotlighting the narrative core with a narrow band of high values.
明暗对照法（Chiaroscuro）对光暗的强烈运用，可视为一种“对比率”公式。例如卡拉瓦乔的画作，常将大面积压缩至暗调，同时以狭窄的高调范围照亮叙事核心。
12. Typeface and Layout Ratios | 字体与版式比例
In graphic design and mixed-media art, type proportions follow mathematical relationships to achieve readability and elegance. The baseline grid, where leading (line spacing) is often set at 1.414× (√2) or 1.618× the type size, ensures consistent vertical rhythm. A common
Published by TutorHao | Year 10 艺术 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Cancel reply