The Planiverse; Computer Contact with a Two-Dimensional World by A.K. Dewdney is a book which explores the hypothetical science of living in a 2D world. Written a century after the godfather of all 2D fiction Flatland (which is wonderful story about shapes acting as a mask for actually talking about Victorian class systems and morals) it aims to explore how things would actually work in such a world.
For example here is our protagonist Yendred (which is suspiciously close to the author's name backwards):
So... some things to note here. First of all there is no digestive tract because in 2D creature that would cut you in half. The creatures in this world solve this in different ways; either by having just a mouth which absorbs nutrients and then regurgitates, or by having a digestive system which works like a zip; sealing itself behind the food.
Also there are two arms on each side because you can't just turn around in 2D. If you wanted to sit you could just squat because the air pocket between your legs can't escape and would act as a cushion.
Related to that concept, think about how you can use a piece of string as a balloon in the Planiverse. Weird right?
There is a loose story built into the book, but it mostly just serves to show off different scientific principles. The planet is a circle and there are towns. But a problem arises if you build a house because it would block everyone's path. How do you solve this? Well you can build underground like this:
As long as you have a door which can swing back up to complete the path then you won't obstruct anyone. Ok, problem number two: you are trying to head East and you meet someone coming towards you, what do you do?
Well if it is a low traffic area then the solution is that one of you lies down and the other one walks over you. But if you have lots of people then you can use a traffic pit made out of a piece of string like this:
This book started as a short monograph by Dewdney back in 1979, but it completely blew up the next year when Martin Gardner wrote his most popular article ever about it in his long running Mathematical Games column in Scientific America. Gardner received literally thousands of letters and emails from scientists all expanding how their particular specialism would work in 2D. Based on this Dewdney collated this knowledge into what became The Planiverse.
There are sections explaining, for example, the 2D period table (hint you can fit 6 elections in the outer shell rather than 8 and the equivalent of carbon would have a periodic number 5 and would form a hexagon lattice), quantum mechanics for the Hydrogen atom, fluid dynamics and 1D art.
Here's an illustration of cells diffusing substances between themselves:
Notice the zip like structure and the double layer which act as air locks.
Or how about transport? Cars are pretty rubbish because you can't have axles, but the book goes into how planes work. Also here is a beautifully designed steam engine which works in 2D which I'll let you figure out yourself:
What I love about this book is that once you start thinking about it, you start wondering about how everything would work in 2D. After introducing it to a class I'll have a solid two weeks of people bring me designs for submarines, nuclear fusion reactors, or all manner of other crazy things. As a challenge see if you can design a hinge which has a range of more than 180 degrees. Or perhaps a sport? Or a musical instrument? Or a book?
I love this stuff.