see Gallery of Map Projections
see Thematic Maps

Projecting a 3D sphere onto a 2D map results in distortions.

Place a lamp in the center of a translucent sphere. Let it project a shadow onto a sheet, hanging flat or curled in a cylinder.

All 2D maps are distorted. Distortion occurs in:

• shapes
• areas
• distances
• directions
• angles

Types of distortion correction:

• conformal - preserves angles
• equal-area - preserves areas

Each type of map projection has a different approach to distortion correction.

Three projection types, with variations:

• conic
  • Albers
  • Equidistant
  • Lambert Conformal
• cylindrical
  • Equirectangular
  • Mercator
• planar
  • azimuthal perspective
    • orthographic

In 2005, Google Maps introduced a modification to the Mercator to allow faster calculations.

Web Mercator uses a spheroid model instead of Mercator's ellipsoid model.
This allows a faster calculation but sacrifices some accuracy at low scales.

Web Mercator also introduces “zoom level”. Explained here at TomTom.

Web Mercator is now used in most online street mapping systems.

\begin{align} x &= \lambda && \text{longitude} \\ y &= \varphi && \text{latitude} \\ \end{align}

This projection is mathematically simple and is used sometimes for raw data, like altitude data for instance.

\begin{align} x &= R\left (\lambda - \lambda _{0} \right ) && \text{longitude} \\ y &= R \text{ln} \left [ \text{tan} \left( \frac{\pi}{4} + \frac{\varphi}{2}\right )\right ] && \text{latitude} \\ \end{align}

This is the Web Mercator variation used by Google Maps and most other online street mapping programs because of the speed of calculation.

Demonstrate the expansion of life forms from Africa outwards to the rest of the world.
see Out of Africa

• circular shape, 86 mm diameter, to fit in a petri dish
• origin in Lake Victoria
• maintain relationship between eastern Russia and Alaska
• equal-area

Types of Map Projections by Elizabeth Borneman

A Guide to Understanding Map Projections by Caitlin Dempsey, plagiarized from the Borneman article

Projection Wizard by Bojan Šavrič