Exhaustive Study Guide on Thematic Maps and Map Projections

Thematic maps are defined as maps that utilize exactly $1$ specific characteristic to create a THEME on the map.

Heat Map:
- A heat map is a representation of data in the form of a map or diagram.
- In this format, data values are represented as colors determined by the intensity of the observations.
Graduated Symbol Map:
  - This map type utilizes a specific symbol to display the frequency of an observation.
  - The relationship between symbol and data is proportional: the larger the symbol appears on the map, the higher the frequency of that observation discovered within the geographic unit.
  - Common geographic units used for these maps include counties, states, and similar divisions.
Cartogram Map:
- A cartogram uses proportionality, specifically the area on the map, to demonstrate the intensity of a particular observation.
- To reflect this intensity, the size of the geographic unit is adjusted, which results in the warping of the shape of the study area.
Choropleth Map:
  - This map type shows a pattern of occurrences within a geographic unit such as a county or state.
  - It is frequently used to represent data like population density or voting patterns.
  - The data is displayed by using various colors or different degrees of shading.
Dot Density Map:
- This format uses dots to represent the frequency of an occurrence.
- Each individual dot on the map represents a set number of occurrences.
Isoline Map:
- Isoline maps display lines that connect points of equal value.
- Crucially, every observation located along the same line will possess the same value.

Map projections represent the method by which a $3D$ sphere is represented over a $2D$ piece of paper.
No projection is perfect; they each have their own unique distortions.
Despite distortions, each projection has specific situations or contexts where they are best used.

Mercator/Cylindrical:
  - This projection fairly accurately shows direction and shape.
  - It is flawed in that it distorts the distance and size of land masses.
  - Accuracy is highest at the equator, but land areas around the poles are greatly exaggerated.
  - Named Example: In reality, Greenland is approximately the same size as Mexico, though the Mercator projection distorts this relationship significantly.
Conic:
- This follows the projection of the globe onto a cone, with the cone's point situated over one of the earth's poles.
- This projection is noted for being most accurate in the mid-latitudes.
Compromise/Robinson:
- This projection maintains overall shapes and relative positions without creating extreme distortion in any one area.
- This is achieved through a trade-off: every characteristic is slightly distorted in order to limit the overall distortion across the whole map.
Polar/Azimuthal:
  - This map shows true compass directions.
  - Grid layout: Longitude lines are represented as straight lines, while latitude lines are represented as circles.
  - The map is at its highest accuracy at the pole and distorts size and shape more as one moves toward the outer edges.
  - Definitional Note: The term "Azimuthal" means direction and is measured in $\text{degrees}$ , effectively functioning like an angle.

The Equal Area projection is designed to retain the relative size of the area throughout a map.
This means that at any given region in the map, the true size of features is maintained.
While these projections preserve area, they result in the distortion of shapes and angles.
The specific version discussed is identified as just one example of an equal area projection.