See: List of castles Castles in England
Angus
Argyll and Bute
Dumfries and Galloway
Dundee
Edinburgh
Fife
Highland
Moray
Perthshire
Scottish Borders
Stirling
... as "either of those element(s) of the field whose square equals b2 - 4ac". In some fields, some elements have no square roots and some have two; only zero has just one ...