UKC

Can someone tell me what an American climber means by an ''inside corner''?

A normal (open book) corner as opposed to an arête (aka outside corner).

But the one facing you isn't normally the arête!

It seems that in the early days of rock climbing in the UK (up to about the time of the first ascent of Cenotaph Corner), the term 'corner' was often used for something we'd now call an arete. Like the corner of house. E.g Birchden Corner, North-West Corner (at Harrisons) and Congo Corner at Stanage. The implication is that the Americans still use the term in both senses.

Americans use the terms "book", "inside corner" and "dihedral". I wonder what the differences are. Interestingly, there is an American asking in another thread what the difference is between a corner and a groove!

I think its as simple as corners tend to be 90 degrees and close to vertcal and traditionally were used for outside and inside versions, in the UK as well as the US, as Gordon correctly points out. Grooves tend to be more than 90 degrees and anything from slabby to overhanging but can be anything angle-wise from where flared chimneys end to something barely perceptable (but still usable by a skilled ascentionist).

PS wonderful point on an open book ...takes a mathematical mind to look at a book that way.

My perception of a groove is that it is a vertical gouge out of the rock that could be rounded or angular and probably doesn't have a crack in the back. A corner (inside) always has a crack in the back however thin it may be. A corner is usually formed where the rock is jointed a groove can be in a solid piece of rock even a slab.

But there are some nowhere near vertical, e.g. Hammer and Agony on the Etive Slabs.

I  know of one climb which is actually an arete, but has Corner as part of its name. Proud Corner (VS 4c)

Basically agree with you but I vaguely remember that by the the 60s and 70s Blackshaw's mountaineering "bible" classified all the "inside" features as open book formations in the first instance. Unfortunately I am unable to look up his doubtlessly definitive sub-divisions.

FWIW just looked at Ron James selected climbs book for (North) Wales (1970). North Buttress, Tryfan  is described as best started up the deepest groove next to North Gully: pitch 1 Climb the corner... ! There was a a photo ridiculously exaggerating its steepness. Keith-Ratcliffe may be perturbed to know that there is an obvious crack in the back! The then current comprehensive guide called it a groove.

To be fair, they're half vertical (the left wall). If the left side was the same angle as the right they'd maybe be grooves?