I had a large Peters world map on my classroom wall for years and used it to provoke discussion about how we see things. Like any 2D representation of the globe, it distorts shape, in this case the distortion getting ever greater the further from the 45-degree north and south parallels you moved. The most striking thing that hits you at first is that both Africa and the Americas are rendered "long and thin." The claimed advantage of the Peters map was that it showed countries in the correct area relationships with each other, ostensibly doing away with the potential for "cartographic imperialism." Of course, that depends also on who you put in the middle of the map :-) The controversy rumbles on!