Unformatted text preview: • By 100 AD, the Chinese were handling fractions much as we do today. • The use of decimal fractions really got entrenched in the West around 1600. (This late date would help explain the old British monetary system, etc.) Irrationals • That 2 and other integers weren’t the square of any positive rational number was discovered by the Greeks around 400 BC. ◦ Arguably precipitated by their lousy number system. (Compare to epicycles.) ◦ Evidence seems to indicate that our standard algebraic proof (known to Aristotle) wasn’t used. ◦ Possibly a geometric proof based on a diagram like: and a calculation like p 2 = 2 q 2 ⇒ p/q = ( 2 q − p)/(p − q) . • This indicated that there were irrational lengths, but it didn’t explain what all lengths do look like....
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- Fall '10
- Fractions, Decimal, Rational number, unit fractions