It is proved that among the regular polygons with prime edges, only the regular polygons with Fermat prime edges are constructable with compass and straightedge. As 17 is a Fermat prime number, the construction of hep...It is proved that among the regular polygons with prime edges, only the regular polygons with Fermat prime edges are constructable with compass and straightedge. As 17 is a Fermat prime number, the construction of heptadecagon has been discussing all the time. Many different construction methods are proposed although they are based on the same theory. Simplification of the construction is still a sensible problem. Here, we propose a simple method for constructing regular heptadecagon with the fewest steps. The accumulation of construction errors is also avoided. This method is more applicable than the previous construction.展开更多
文摘It is proved that among the regular polygons with prime edges, only the regular polygons with Fermat prime edges are constructable with compass and straightedge. As 17 is a Fermat prime number, the construction of heptadecagon has been discussing all the time. Many different construction methods are proposed although they are based on the same theory. Simplification of the construction is still a sensible problem. Here, we propose a simple method for constructing regular heptadecagon with the fewest steps. The accumulation of construction errors is also avoided. This method is more applicable than the previous construction.
