A common requirement in many emerging applications is the ability to process, in real time, a continuous high-volume stream of data. Consequently, data stream monitoring in a distributed system is the focus of much research in recent years. Examples of such applications are sensor networks, real-time analysis of financial data and intrusion detection. We present a novel geometric approach utilizing naive, centralized algorithms for efficient arbitrary threshold functions monitoring over distributed data streams without requiring the very high communication overhead common in other methods.