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Fill in each blank with an appropriate preposition: in, to, among, of, for, into, at. One preposition may be used several times.
1. Mathematics ranks ... the highest cultural developments of man.
2. Mathematical reasoning is ... the
highest level known ...man.
3. Mathematical style aims ... brevity and perfection.
4. Arithmetic, geometry,
and astronomy were to the classical Greece music ... the soul and art ... the mind.
5. Most
mathematicians claim that there is great beauty ... their science.
6. ...1933, George Birkhoff, one ... the
most distinguished mathematicians his generation, attempted to apply mathematics art.
7. Joseph Fourier showed that all sounds, vocal and instrumental, simple and complex, are completely describable ...
mathematical terms.
8. Each musical sound, however complex, is merely a combination ... simple
sounds.
9. Thus, thanks ... Fourier, the nature ... musical sounds is now clear ... us.
10. The role of mathematics ... music stretches even ...the composition itself.
11. Masters, such as Bach, constructed and advocated vast mathematical theories the composition ... music.
12. ... such theories, cold reason rather
than feeling and emotions produce the creative pattern.
13. Through Fourier's theorem, music leads
itself perfectly ... mathematical description.