Cali (US$0.99) is a clever variation on the traditional computer calculator. Rather than aim for buttons for particular functions, the basic ones are gesture-based. Swipe up to add, down to subtract, right to multiply and left to divide. It seems like a trivial feature, but if you have a lot of numbers to enter, I found it much faster than poking around the screen.
In addition to the gesture controls, the app is graphically pleasing, although I'm not thrilled with the loud sounds when you enter numbers. I think the app needs a volume control. Hearing the entries is important; I just think the sounds are too loud. I'd also like to see a gesture for equals -- maybe a diagonal swipe.
The app also has more complex functions, like tangent, sine and cosine. Finally, help is included when you click on the page that has additional mathematical functions.
Cali gesture based calculator
Cali was written by 15-year-old Austin Valleskey, and I think he's got some promise as a programmer. It's universal, requires iOS 7 or greater and is optimized for the iPhone 5. It's nice to see a worthwhile app come from a young programmer.