Common terminology is so lacking in some areas of mathematics. And topology uses words that have an entirely different meaning for a mathematician than it does for a non-mathematician. Take the word manifold. Topology can be considered a sub grouping of multi dimensional geometry. You know, a space that might have 3, 4, 5, or more dimension. Most people have been taught that we live in a 3 dimensional world. We don't, we just aren't equiped to "see" the higher dimension. Mathematical dimensions, not science fiction dimensions. Different animals, they are. Solid shapes that can be transformed into a different shape without damage or breaks to the material is the subject of topology. Topology rarely deals in pure numbers. That's why a lot of mathematicians have a problem with studying it. It's like in high school geometry when you did proofs. You didn't do it with numbers, you did it with using specialized language, and symbols that were beyond Greek. Topology carries this concept further, to the nth degree, so to speak. Some of you may now realize why I describe math as a language. Sorry if I haven't answered about the Poincaré conjecture. I don't know. Wednesdays are my true 9-to-9 days this semester. Didn't think it would leave me so tired.

I have been watching a number of female ruby throat hummingbirds, it's been raining for a couple days now, and a lone female ruby throat has started setting on one of the flower petal on the feeder for long lengths, last time for almost 7 minutes in the pouring rain. She has feed about six times during that time, I've never seen this kind of action, of course this is my first year with feeders for both hummingbirds and regular birds. Is this normal behavior, there is no shelter there? she has added hovering in front of the window that's in front of the feeders, it has a reflective coating on the windows to stop heat loss or to prevent heat coming in in the summer. she is testing the window with her beak not really pecking, at first I thought she was lick the water off the window. Looks like she wants in. This post was edited by plantnut65 on Sat, Jul 19, 14 at 23:44

Thanks Rachel - My only regret is that the photo is not more of a close-up, and not larger; but we were so taken by surprise by the whole thing, we were incredibly lucky! For someone new to birdwatching it was especially awe-inspiring.

Vinyl on that large of an empty field (the 'butterfly wing' on the left) will most likely show lots of waves and canning. I understand following the angle of the roof with the siding, but it usually is more successful on steeper angles. If it were me, I would be looking into alternative materials, like fibercement/Hardie, steel, or stucco (panels). I would separate the two wings visually with either horizontal and vertical lines mixed with solid. The front, and the garage (if that is what is on the other side of the swingset) I would "inadvertently" exclude from this design, just as the original designer did.