Euler’s line

The incentre I does not, in general, lie on Euler’s line.

Fun fact — not syllabus. The same Euler also gave the identity

e^iπ + 1 = 0

In the complex plane, multiplying by e^iπ is a half-turn (a rotation of 180°). Starting at 1 and turning halfway around the origin lands at −1, so e^iπ + 1 = 0. This is a curiosity only — it is not part of the DSE work on Euler’s line.

Orthocentre →