TTT vs Top Tube length

I am confused - not that I am worried. Waterford certainly knows their stuff, for sure, so I am not really questioning - just trying to understand.

My optimal reach is 500 mm, and my beloved LHT is just a tad longer than that but we made her work. My custom Gunnar design has a TTT length of 500mm and an actual TT of 479.2 mm with a slope of 14 degrees. My hips will like that slope, but shouldn't a sloping TT be actually longer than the theoretical length? Geometry was never my strong point in school so I am confused...

I might also be confused, but with the seat tube at an angle, the longest side of this triangle should still be the TTT, right?

Imagine your bike in your photo, but with the top tube slanted downwards it would be shorter b/c of where it connected.

Jess is right. If it were a right triangle (seat tube would have to be perpendicular to the ground), then the TT would have to be the longest side of that triangle. With a sloping top tube and an angled seat tube, the seat tube forms the short leg, and the TT the other leg, and provided that the TTT is shorter than the sum of these (it is), your geometry teacher will be happy.
:)
Here's a picture with a sloping top tube.
http://montgomerycyclery.com/product...22-1-22955.htm

Edit: Durr, that's also a right triangle. It's just not the one you were expecting!

Actually the TTT is longer than the TT - and both fitters at my LBS today took quite some time to help me to understand this :) I may not be able to understand it clearly myself, but it seemed to make great sense to them - and they work with this stuff all of the time - so I accepted it.

It is the same way with my LHT, and also with my very first bike that I sold.

I then signed off on the design and put down my deposit - my beautiful new frame will be delivered and ready for building in about 5-6 weeks:D