So I am working on a project that requires me to join multiple thin pieces of wood (10mm in thickness) together to form 45 degree angles (examples below). We would like to avoid brackets as this is a visual prototype that needs to remain as visually pleasing as possible. Also, we would like to avoid joining techniques that require special tools or equipment. If you have any suggestions, please help. Thanks!
You could use a Splined Mitre Joint, such as shown in this question: Should I use one large spline or multiple smaller ones for a miter joint?
It doesn't require specialized tools over a handsaw or circular/table saw, and some chisels/sandpaper to clean it up.
A finger joint is relatively easy to make without requiring special tools, only a saw and chisels, and does not need too complicated woodworking. One of the other answers has a great suggestion of using a splined mitre joint, which also could be done without power/special tools.
However you could also use a simple dowelling system. Using a drill and careful calculations you could drill holes into both pieces of wood, then use a correctly sized dowel with wood glue to strengthen the joints. Easier would be to drill straight through both wood pieces, then cut off and sand down the exposed dowel end.(See diagram below)
To keep the piece looking relatively clean it may be advisable to use a box joint to create a strong interconnecting joint. To visualize this just interconnect your hands with your fingers. Cut the pieces to allow for the extra length needed to make the joint. Trim and sand to complete the work. Hope this helps.