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A delta wing, for starters, is a triangle shaped wing (Delta, like the triangle-shaped letter in the Greek alphabet). You frequently see this shape of wing in fighter jets.

In a compound delta (or double delta, or cranked arrow) the inner part of the wing has a very sharp angle, while the outer part has a wider angle, which makes it look like a thin and then fat triangle. This helps the pilot control the lift, reduce drag, and land better.