I’ve been revisiting Pythagorean Polygons, first posted by Florian F as Pythagorean Pentagons. I’ve options for normal polygons with as much as ten sides and want to see what others can provide you with, starting with octagons. The outline under has been copied from the earlier query and modified or this one. I hope you do not get bored.
The common octagons above have sides respectively 3, 4 and 5. Pythagoras says that the sum of the areas of the primary two equals the realm of the final one. Sure, the Pythagorean theorem works with any form, not solely squares.
Your job is to dissect the primary two octagons right into a finite variety of items and reassemble them to kind the third octagon. After all, with out gaps and with out overlaps. You possibly can rotate and flip the items as you want.
These dissections are confirmed to be at all times potential. It might take many items and be ugly, so I’m asking to attenuate the variety of items.
Simply to keep away from bizarre options, the items have to be easy polygons.
Edit:
A few very good nine-piece options have been posted, however these are usually not minimal. I’ve an eight-piece answer with out rotation or flipping. Are you able to just do as effectively?
Maybe this may assist:
