Final answer:
The 'Napoleon Sonata' designed to be played on one string was composed by Niccolò Paganini, a renowned 19th-century Italian violinist.
Step-by-step explanation:
The 19th-century Italian violinist who designed his "Napoleon Sonata" to be played on one string was Niccolò Paganini. Paganini was known for his extraordinary technical skills on the violin and was a famous virtuoso of his time.
This piece, more formally known as "Violin Sonata No. 6 in A minor", showcases his ability to produce a wide range of music on a single string, a feat that contributed to his legendary status among violinists and composers of the Romantic era.