Eve McVeagh Jayne Meadows Lara Jill Miller Melba Moore John Moschitta Jr. Ron O'Neal Rex Reed Jack Riley Dick Sargent Ronnie Schell Madge Sinclair Yeardley Smith Arnold Stang McLean Stevenson Guy Stockwell Nedra Volz Marcia Wallace Dick Wilson William Windom Edward Winter "Weird Al" Yankovic In addition, real-life LAPD officers Sam Salazar and Steve Fellman have also appeared as themselves, as did head writers David D. Connell and Jim Thurman as various characters. Math and science Real principles of math and science and mathematical tools used by the detectives to solve crimes include: Alphanumerics ("The Case of the Unnatural") Fibonacci sequence and modular arithmetic (see also Pisano period) ("The Case of the Willing Parrot") Kinematics ("The Problem of the Missing Baseball") Chromatic scale ("The Problem of the Passing Parade") Displacement of fluids ("The Problem of the Trojan Hamburger") Hamiltonian path ("The Case of the Smart Dummy") Process of elimination ("The Case of the Great Car Robbery", "The View from the Rear Terrace") Number patterns ("The Case of the Missing Air") Bar charts and line charts ("The Case of the Purloined Policies", "The Case of the Great Car Robbery") Triangulation ("The Case of the Map With a Gap") Development and production After a successful first season, production began on six new episodes for the second season. By the time production ended on the third season and its six episodes in 1989, Beverly Leech (Kate Monday) left, and was replaced by a new character named Pat Tuesday, played by Toni DiBuono. Production on the first six episodes with the new character commenced in 1990, and ended in 1991, in time for Square One TV's fourth season. Production on the final season and its five episodes began taping in 1991, and the last episode aired in 1992. During production, the background music also changed. Originally, it had a synth score. Gradually, as the series progressed, it was replaced with an orchestral score. The exterior shots of the Los Angeles police station were filmed at the former LAPD Highland Park Police Station, which had closed in 1983. It now houses the Los Angeles Police Museum and is located at 6045 York Boulevard. The exterior shots of the New York City police station for seasons 3 and 4 were filmed at the Alexander Hamilton U.S. Custom House in Lower Manhattan. It now houses the George Gustav Heye Center of the National Museum of the American