The space of vertical and horizontal right hyperbolas and the lines tangent to these hyperbolas is considered in the double plane. It is proved that an injective map from the middle region of a considered hyperbola that takes hyperbolas and lines in this space to other hyperbolas and lines in this space must be a direct or indirect linear fractional transformation.

Author Bio

James Hays hails from Dayton, Ohio, and moved north to Grand Rapids, Michigan for his undergraduate study despite a desire to live in a warmer climate. James plans to graduate from Calvin College in the spring of 2011 with a major in Mathematics and minors in Spanish and Computer Science. He enjoys Ultimate, biking, games, word-play, recycling, and improvisational comedy.

Todd Mitchell is from Minneapolis, MN. He is a senior at Calvin College majoring in Mathematics with a minor in Psychology. Todd is planning to pursue a career in secondary education. He runs cross country and track at Calvin and enjoys backpacking. He hopes to live out west so that he can teach, coach, and enjoy the mountains.