of the Salish people. Garfield never convinced Charlo to sign, although the official treaty document voted on by Congress bore his forged mark. In 1876, Garfield developed a trapezoid proof of the Pythagorean theorem, which was published in the New England Journal of Education. Mathematics historian William Dunham wrote that Garfield's trapezoid work was "really a very clever proof." According to the Journal, Garfield arrived at the proof "in mathematical amusements and discussions with other members of congress." After his conversion experience in 1850, religious inquiry was a high priority for Garfield. He read widely and moved beyond the confines of his early experience as a member of the Disciples of Christ. His new, broader perspective was rooted in his devotion to freedom of inquiry and his study of history. The intensity of Garfield's religious thought was also influenced by his experience in combat and his interaction with voters. Presidential election of 1880 Republican nomination Having just been elected to the Senate with Sherman's support, Garfield was committed to Sherman for the 1880 Republican presidential nomination. Before the convention began, however, a few Republicans, including Wharton Barker of Philadelphia, thought Garfield the best choice for the nomination. Garfield denied any interest in the position, but the attention was enough to make Sherman suspicious of his lieutenant's ambitions. Besides Sherman, the early favorites for the nomination were Blaine, former President Grant; several other candidates attracted delegates as well. The Republican Party at the time was split into two factions: the "Stalwarts", who supported the existing federal government patronage system, and the "Half-Breeds", who wanted civil service reform. As the convention began, New York Senator Roscoe Conkling, floor leader for the Stalwarts, who supported former President Ulysses S. Grant, proposed that the delegates pledge to back the eventual nominee in the general election. When three West Virginia delegates declined to be so bound, Conkling sought to expel them from the convention. Garfield rose to defend the men, giving a passionate speech in defense of their right to reserve judgment. The crowd turned against Conkling, and he withdrew the motion. The performance delighted Garfield's boosters, who were then convinced he was the only one who could attract a majority of the delegates' votes. After speeches in favor of the other front-runners, Garfield rose to place Sherman's name in nomination; his speech was well-received, but the delegates mustered little excitement for Sherman as the