False position method ibn Luqa (10th century), an Arab mathematician from Baalbek, Lebanon. He justified the technique by a formal, Euclidean-style geometric proof. Within the tradition of medieval Muslim mathematics, double false position was known as "hisāb al-khaṭāʾayn" ("reckoning by two errors"). It was used for centuries to solve practical problems such as commercial and juridical questions (estate partitions according to rules of Quranic inheritance), as well as purely recreational problems. The algorithm was often memorized with the aid of mnemonics, such as a verse attributed to Ibn al-Yasamin and balance-scale diagrams explained by al-Hassar and Ibn al-Banna, all three being mathematicians of
Soccer in the United States effectively the amateur fifth division of soccer in the United States. The Lamar Hunt U.S. Open Cup is a knockout tournament in American soccer. The tournament is the oldest ongoing national soccer competition in the U.S. and was historically open to all United States Soccer Federation affiliated teams, from amateur adult club teams to the professional clubs of Major League Soccer. Since the 2016 edition, professional teams that are majority-owned, or whose playing staff is managed, by a higher-division outdoor professional team have been barred from the competition; all other U.S. Soccer-affiliated teams remain eligible to enter. The Open Cup