**SLR 511F: 10 MATHEMATICAL IDEAS EVERYONE SHOULD KNOW and their everyday applications in the real world **

** John Clements. **

** SESSION #3, Sept. 29/11. **

** SESSION #3 looked at TOPIC #4: Numbers and their interesting quirks. **

** TOPIC #4: Numbers and their interesting quirks: **

** ***Solving Equations using Algebra (particularly the QUADRATIC EQUATION ax² + bx + c = 0 ) drove the need for ever more complete number system. **

** e.g. the ancient Egyptians (approx 200 AD) could solve x² = 4 and the ancient Babylonians considered the problem x² - x = 870. Diophantus (" Father of Algebra " - approx. 270 AD) major treatise " Arithmetica " consisted of 13 books. He could solve ax² + bx - c = 0 where a,b,c were all positive. The first book to include the full solution did not appear until the 12th century (approx. 1120 AD). **

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