I was just looking at the perfect fit for your room the other day, and of course can't find the image now. Ikea has an amazing option for something like this, and you can sort of see the idea in this image: http://www.ikea.com/us/en/catalog/categories/departments/Textiles/tools/textiles_rooms_ideas/#/20121_txsv04a_01/379450/

Basically their Kvartal system is an inexpensive, simplistic track system that can go around corners, lending a continuity to corner windows. Additionally, you can put tracks on the floor and use their panel curtains for a more modern or streamlined look.

Hopefully that gives you a place to start!

with windows like these who needs "treatments"? Leave them alone!!

Cool windows :D, Venetian blinds may suit and would go with the period of the residence. For some reason I have yellow in my head, weird but hey that's life I guess.

As much as I appreciate ANNA's suggestion for the Ikea track system, I've read reviews that they are hard to install and fall apart. I wanted to use that system inplace of closet doors You can purchase a 'track' system from other companies but a much higher cost.

You actually can buy rods that 'curve' around the window; check the internet but I believe Penny's or Sears carry them.

I agree with LITTLECAT, they are great windows and maybe hang simple sheers so you don't lose the character of the windows.

Good Luck.

sorry...IN PLACE and PENNYS
It's good to QA before submitting...YIKES.

They are pretty great windows, so I suggest not doing anything too fusy.

Shutters are a great option. The only problem is you're in an apartment, and you either have to leave them when you move, thereby losing your money, taking them with you, where it is unlikely they will fit anywhere else, or selling them--either to your landlord, or the new tenant, which is unlikely.

If you can get the landlord to pay for them, great! Otherwise stick to removable--and reuseable-curtains.

Wide blinds are perfect for the era. Wooden 2 inch are widely available.

Treat them as if they are 2 separate windows, The trick is to use the same width of drapery in the middle as is used on each end. That is, if the draperies on each end are say 10" wide when open, try to achieve approximately 10" of fabric in the middle. With that said, you also need to decide if you need draperies and/or blinds for privacy. Doing w/out might not be an option. And, we very much believe in taking the eye away from something weird in our homes...we all have those - perhaps a great arch lamp and fun chair in the corner will minimize your angst with the drapery situation.

PS - here is an image that shows you the look: http://www.blakemaninteriors.com/portfolio/living-spaces.html

I love those metal casement windows and the blue wall and the scene beyond. Or maybe the wall isn't blue and it's just the light. Could you do nothing or would it be too hot? Maybe shades, something Raymond Chandler, which is the look I'm always going for.

What a stunning window - please don't treat it as two windows. I would suggest semi-sheer curtains, gathered one at each side and when necessary pulled to meet in the middle. I have Ikea curtains like this on very sunny, south facing patio doors and they are perfect for when the light is too bright in the daytime. They are light enough that I suspect you could suspend them from tension wires (again Ikea do fittings that go around corners).

With windows like that it's a shame to put curtains up. The blinds (slats) would be true to the period but bulky and obtrusive. For a timeless look and much more aesthetic appeal I would put in Japanese screens, which are already hinged at the corner and can easily fold back in place when you want more light/less privacy. You can shop for these in many styles online, and the price is much less than other options. I have a house with 5 clear-glazed corner windows, now 30 years old, so have long researched this problem. Good luck!