First of a series of articles on that famous nexus.
A plug for good old Euclidean geometry.
The famous collection of propaedeutic exercises published in 1931 by Tatjana Ehrenfest-Afanassjewa (PDF).
An earlier view on intuition versus formalism by a French mathematician and teacher.
An incomplete sketch of what is (confusingly) called segment arithmetic.
Why light refracts as it does, if you assume (with Fermat) that it wants to minimise travel time.
Why the circumcircle of the orthic triangle contains the midpoints of the orginial sides and the points half-way between the orthocentre and the original vertices, and how this implies Euler's Theorem about the radii of incircle and circumcircle.