August Ferdinand Mobius was a renowned mathematician and astronomer who lived in the 19th century. Synonyms for his name include 'Mobius strip,' 'Mobius band,' and 'Mobius transformation.' The Mobius strip is a one-sided surface with only one boundary, while the Mobius band is a loop with a half-twist that can be used to represent infinity. The Mobius transformation is a mathematical transformation that preserves non-orientability. Mobius was also known for his work on topology, where he made significant contributions to the study of closed surfaces and manifolds. Overall, August Ferdinand Mobius was a brilliant mind whose name is synonymous with innovative mathematical concepts, theories, and transformations.