ackermann

Ackermann may refer to several topics in mathematics, engineering, and onomastics. It is a German surname and is associated with notable figures such as Wilhelm Ackermann, a German mathematician and logician active in the 20th century. The name is also attached to mathematical constructs and mechanical arrangements, most prominently the Ackermann function and Ackermann steering geometry.

The Ackermann function is a computable function of two nonnegative integers, defined by A(0,n) = n+1; A(m,0) = A(m-1,1) for m > 0; and A(m,n) = A(m-1, A(m, n-1)) for m > 0 and n > 0. It grows rapidly and is a standard example in computability theory because it is total for all inputs but not primitive recursive, illustrating the gap between general recursive functions and primitive recursion. The function is named after Wilhelm Ackermann, who studied it in early work on recursive functions.

Ackermann steering geometry refers to a steering linkage arrangement used in vehicle design to align the axes of the wheels during turning. If implemented correctly, it directs each wheel to pivot about a common instantaneous center, reducing tire scrubbing and wear. The arrangement is widely used in automobiles and other wheeled vehicles, and its geometric principle remains a reference point in steering design.