Spiral staircase / Helicoid

The picture shows a spiral staircase at the palace of Sintra (Portugal).

The following picture shows a spiral walk at the Round Tower (Kopenhagen).

See also http://www.rundetaarn.dk/engelsk/facts_om_rundetaarn.htm

Monkey saddle

The picture shows the entrance to the Museum of Welsh Life at Cardiff, UK.

Miquel's theorem