A constant interface anti-pattern describes the use of an interface solely to define constants, and having classes implement that interface in order to achieve convenient syntactic access to those constants. According to Effective Java:
The constant interface pattern is a poor use of interfaces. That a class uses some constants internally is an implementation detail. Implementing a constant interface causes this implementation detail to leak into the class's exported API. It is of no consequence to the users of a class that the class implements a constant interface. In fact, it may even confuse them. Worse, it represents a commitment: if in a future release the class is modified so that it no longer needs to use the constants, it still must implement the interface to ensure binary compatibility. If a nonfinal class implements a constant interface, all of its subclasses will have their namespaces polluted by the constants in the interface.
In this example, we designed a Circle class which implements Constants interface to access the constant PI. This implementation violates the intention of an interface since Constants does not define any behavior for Circle class.