Napoleon Theorem is classical theorem of Plane Geometry. Here we are giving it's Generalisation and wanted to see an easy method to prove it and also check whether it is old or new.
Generalisation of Napoleon Theorem:
Let ABCD and CDEF be two Parallelogram as shown in this figure. Let G be the apex of equilaterial triangle constructed on segment BF such that GBF is clockwise.
Similarly , H and I are apices of equilaterial triangle constructed on segment EC and DA such that HEC and IDA are clockwise.
Then Centroid of equilaterial triangle ∆GBF; ∆HEC and ∆IDA form Equilaterial triangle.
Note:
- When A=B , This reduce to Napoleon Theorem.
- The construction also produced equilaterial triangle if clockwise replaced by counter clockwise.
We have also published the same results on Euclid group.io