We're starting on removing a big heavy ugly grill patio which will become a light covered patio, possibly enclosed and filled with mathematical plants. Insert your own "square roots" joke here. And before summer we'll have a 10 meter diameter geodesic frame in the garden for concerts and dancing!
OOOOOH BE REALLY REALLY CAREFUL There are few structures with acoustics as shitty as geodesic domes. If you leave it open, you'll be fine. If you put any panels in you're hosed. The acoustic response of circular and ellipsoidal structures are beyond counterintuitive. You can understand, for example, that standing at one locus of an ellipse and speaking will make for spooky gain at the other locus. However, a conversation within an ellipse is a maddening experience. Likewise, geodomes - had a friend who lived in one and you'd walk around the room and the stereo would go from "mute" to "too loud" and there were places you could stand and hear the bathroom entirely too well.
The dome will be an open skeletal structure. Probably with anchor points to hoist up a cover of sorts in the rain. Never thought of the acoustics inside a closed geodesic dome. I can easily see how it could be a nightmare! Frankly, I think geodesic dome houses are ugly. Here's a concept sketch. Dome might look like this. Or might not.
Not gonna lie. I LOVE that dome. A suggestion? Rather than have this big beautiful open thing that's going to require you to hang tarps in the weather, you could perhaps build it as the cupola of a gazebo... you'd have to sink footings, yeah, and you'd need some columns... but columns are just an excuse to decorate, as you've proven. And then you could shell 120 degrees or so of it (temporarily or permanently - dunno how much you care about wind loading where you're at) and have a legit performance space. A shell, a half dome and an acoustic guitar is a recital. No amplification needed. My mother used to hit 300-person weddings with a shell and a string quartet.
The dome will be an open skeletal structure. Probably with anchor points to hoist up a cover of sorts in the rain. Never thought of the acoustics inside a closed geodesic dome. I can easily see how it could be a nightmare! Frankly, I think geodesic dome houses are ugly. Here's a concept sketch. Dome might look like this. Or might not.
There is a guy named Gregg Fleishman who is building FASCINATING furniture and structures that use no nails - just slotted pieces of wood that fit together perfectly - and his structures are a fascinating look at some math I really don't understand. Some great ideas here: http://www.greggfleishman.com/structures.html Plus, his video on the "Lost Triangle of Pythagoras" plays nicely into your math camp: