Two-Dimensional Diagram – Square, Rectangle, Ring, Divided Circle
The accurate and engaging presentation of geographical data is a cornerstone of cartography and practical geography, essential for visual analysis and communication. While one-dimensional diagrams rely solely on length (such as bar charts or line graphs), Two-Dimensional Diagrams, often referred to as Area Diagrams or Surface Diagrams, utilize two dimensions—length and breadth—to represent data. In these diagrams, the area of the figure is constructed to be proportional to the quantity of data it represents.
Two-dimensional diagrams hold a significant advantage over one-dimensional counterparts, particularly in that they occupy comparatively less space and are capable of showing greater variations in data magnitude. Common examples of two-dimensional statistical diagrams include squares, rectangles, and circles, as well as their subdivided forms, such as divided squares and divided circles (pie diagrams).
1. The Square Diagram (Proportional Squares)
The square diagram is a widely utilized two-dimensional figure in cartography. It is categorized as a proportional symbol map technique, where square symbols of varying sizes are employed to represent data quantities across geographical regions.
1.1 Principle and Construction
The construction of a square diagram is governed by the principle that the area of the square ($a^2$) is directly proportional to the magnitude or quantity ($x_i$) of the item being represented.
To ensure that the area, and not just the side length, is proportional to the value, the relationship used is: $$x_i = a^2$$
Where $x_i$ is the original data value (referent magnitude) and $a$ is the length of the side of the square symbol.
Consequently, the method for drawing a square diagram requires a critical initial step:
- Find the Square Root: The length of one side ($a$) of the square is derived by taking the square root of the value of the item to be shown in the diagram ($a = \sqrt{x_i}$).
- Scale Adoption: A suitable scale is then adopted to reduce the side length to an appropriate size for drawing. The chosen scale ensures the areal size of the symbols reflects the magnitude of the referent quantities.
- Visualization: Proportional square maps effectively communicate variations in data, such as economic metrics or population. Squares are commonly used to represent figures like the number of households or houses.
1.2 Types and Design Considerations
Square diagrams can generally be constructed in two ways:
- Simple Square Diagram (Proportional Square Diagram): This type is used when the data has only one component, and each square represents a single value.
- Compound Square Diagrams (Divided Squares): These are used when the data includes multiple components. The square is proportionally divided into rectangular segments to illustrate the constituent parts. However, subdivided squares are used rarely in practice.
In designing proportional squares for maps, modern cartographic studies suggest filling the symbol areas:
- Uniform Gray Area Fills: Used to overcome the limitations of open symbols (defined only by outlines), differentiating the enclosed area from the surrounding map plane.
- Graded Gray Area Fills: Adding a second graphic variable (value/shade) redundantly to the size variable. This modulation of size and value jointly corresponds to the variations in magnitude and has shown better results in discrimination tasks.
2. The Rectangle Diagram
Rectangular diagrams are another form of two-dimensional diagram. In this representation, the total area of the rectangle is kept in proportion to the value it represents. Rectangles are particularly useful when comparing two or more magnitudes that possess different components.
2.1 Types of Rectangular Diagrams
- Percentage Subdivided Rectangular Diagram: In this diagram, the total values are converted into percentages. The width of the rectangles is typically set in proportion to the total values being compared (e.g., $400:600$ is simplified to $2:3$). The height of the rectangles is often kept the same, representing 100 percent. The various components are then divided within this rectangle based on their proportional percentage values.
- Subdivided Rectangle: This is a general term for rectangles divided to show components of the quantity, often used to visualize related phenomena such as quantity of production or cost per unit.
3. The Circular Diagram (Ring and Divided Circle)
Circular diagrams use circles to represent data, wherein the area of the circle is proportional to the quantity shown. They are the most popular among two-dimensional diagrams because they are relatively simple to construct, cover less space, and provide a balanced appearance by spreading equally in all directions.
Circular diagrams are broadly classified into three types: the Pie or Wheel Diagram (Divided Circle), Proportional Circles, and the Ring Diagram.
3.1 Divided Circle Diagram (Pie Diagram)
The Divided Circle, often called the Pie Diagram, is constructed by dividing a circle into sectors (or segments) where the angle and area of each sector are proportional to the magnitude of the components it represents.
This technique ranks high in interpretability. It is particularly useful when attempting to compare parts of a whole, such as occupational categories, land use, or components of expenditure. When plotted onto maps, they are referred to as Proportional Divided Circles.
Construction Method for Divided Circles (Pie Diagrams)
The foundation of construction is converting the quantitative values or percentages into corresponding angular degrees, knowing that a full circle contains $360^\circ$.
- Calculate Total Value: Sum up the values of all sub-components to determine the total quantity.
- Determine Angular Value: Convert each component’s value into degrees using the following formula: $$\text{Angle value} = \left[ \frac{\text{Value of component}}{\text{Total value}} \right] \times 360^\circ$$ If the data is already in percentages, the angle of the sector can be calculated by multiplying the percentage by $3.6^\circ$ ($\frac{360^\circ}{100}$).
- Draw the Circle: Select a suitable radius (often between 3–5 cm) and draw the circle.
- Mark the Sectors: Using a protractor, draw the calculated angles at the center of the circle. It is conventional and convenient to start drawing the sectors from the vertical radius (12 o’clock position) and proceed in a clockwise direction.
- Final Touches: Represent each sector using distinct colors or shades. An index (legend) should be prepared to explain the meaning of these colors/shades.
Advantages and Disadvantages of Divided Circles
| Merits | Demerits |
|---|---|
| They are attractive and give a good visual impression. | They only provide a comparative picture, but the exact numerical value cannot be easily extracted from the figure alone. |
| They allow for easy interpretation and comparison of proportional parts of a whole. | They become less effective and interpretation becomes challenging when the number of component pieces is too large (e.g., exceeding 5-6 components). |
| They summarize large datasets visually and effectively demonstrate that the total sum equals 100%. | A series of pie charts must be used to compare multiple data sets over time or space. |
3.2 Proportional Circles (Graduated Circles)
Proportional circles are generally used for thematic mapping to show total quantity at specific geographical points. This method applies the area proportionality principle to the total magnitude before subdivision (if applicable).
- Principle: The area of the circle ($A = \pi r^2$) is proportional to the total value of the data quantity ($Q$).
- Method: To determine the correct size, the radius ($r$) of the circle is made proportional to the square root of the data value. This method is especially useful if the range of data values is very large, such as mapping population.
3.3 Ring Diagram
The Ring Diagram is explicitly listed as a method of diagrammatic data presentation in the Practical Geography syllabus for B.A./B.Sc. Part II students. It is also categorized as one of the types of circular diagrams.
Summary for Practical Application
In preparation for B.A. Geography practical file making and the viva, students must distinguish between the categories of diagrams. Two-dimensional diagrams—including squares, rectangles, and divided circles—are area diagrams where the area is the primary visual variable proportional to the data. For diagrams showing absolute totals that vary across space (Proportional Squares or Proportional Circles), remember the crucial step of using the square root of the data value to determine the correct linear dimension (side length or radius) for accurate visual representation. For representing components of a whole (Divided Circles/Pie Diagrams), the focus shifts to calculating proportional angles out of $360^\circ$.
Visual presentation of statistical facts simplifies complex data and aids comparison. Mastering the principles and construction techniques for these diagrams is essential for geographical analysis.