This page contains just a few extras to help you better understand ideas about projection methods and projected coordinate systems. Lots of times, when we read thing written by different authors, the concepts are really clarified.
An Article About Various Projection Methods - USGS
This article does a great job of explaining the uses of several common projection methods, which will later become projected coordinate systems. Like we learned earlier, the projection method is the means by which we transform the round Earth into a flat map after selecting a developable surface and an aspect. To get from a projection method to a projected coordinate system, one must first select either a single tangential line or two tangential lines and a linear unit of measure (metric, imperial, or international imperial) for that specific projected coordinate system. We learned that projection methods can be either secant either one parallel or Meridian (or tangent at two), and while that is indeed true, it's important to note that just because that is how we get a projection method, it's not creating a projected coordinate system until the line(s) - or single point, in the case of azimuthal projection method - of intersection AND pick a linear unit.
Projections Wizard - A Projection Selection Tool
Projection Wizard is a web application that helps cartographers select an appropriate projection for their map. Depending on the extent and the distortion property of the map, the application returns a list of appropriate map projections with additional projection parameters if necessary. The Projection Wizard is based on John P. Snyder’s selection guideline and on the extension to this guideline for world and hemisphere maps written by the Cartography and Geovisualization Group at Oregon State University.
The Projection Wizard displays a map preview on the right side of the list with appropriate projections. The preview shows how the projected data will look and in most cases does not show the correct geographic extent. The map preview is created using D3.
XKCD Web Comic - What your Favorite Map Projection Says About You
Just a few examples of visualizing projection from around the web.
XKCD A webcomic of romance, sarcasm, math, and language. http://xkcd.com/977/
V-Sauce: What Does Earth Look Like?
Another well done video by our friends over at V-Sauce