http://betterexplained.com/articles/a-quirky-introduction-to-number-systems/ Learn Right, Not Rote. Fri, 03 Feb 2012 19:38:49 +0000 hourly 1 http://wordpress.org/?v=3.2.1 http://betterexplained.com/articles/a-quirky-introduction-to-number-systems/#comment-33942 Richard Ross-Langley Tue, 03 Jan 2012 13:55:16 +0000 http://betterexplained.com/articles/a-quirky-introduction-to-number-systems/#comment-33942 I believe the Romans used a simpler method to multiply two numbers a and b: halve a and double b until a reaches 1; then add the values of b where a was odd. Using your example (a=IX, b=XXXIV): odd IX XXXIV even IV LXVIII even II CXXXVI odd I CCLXXII then add XXXIV and CCLXXII to get CCCVI. Simples! If you examine the details, it is a binary-shift method used by digital computers, and works in any base including decimal. I believe the Romans used a simpler method to multiply two numbers a and b: halve a and double b until a reaches 1; then add the values of b where a was odd. Using your example (a=IX, b=XXXIV):
odd IX XXXIV
even IV LXVIII
even II CXXXVI
odd I CCLXXII
then add XXXIV and CCLXXII to get CCCVI. Simples!
If you examine the details, it is a binary-shift method used by digital computers, and works in any base including decimal.

]]> http://betterexplained.com/articles/a-quirky-introduction-to-number-systems/#comment-31588 kalid Thu, 29 Dec 2011 02:50:40 +0000 http://betterexplained.com/articles/a-quirky-introduction-to-number-systems/#comment-31588 @Jon: Thank you for the clarification! I'll amend the post. As you mention, our number system can be really, really bizarre :). @Jon: Thank you for the clarification! I’ll amend the post. As you mention, our number system can be really, really bizarre .

]]> http://betterexplained.com/articles/a-quirky-introduction-to-number-systems/#comment-31294 Jon Wed, 28 Dec 2011 10:34:09 +0000 http://betterexplained.com/articles/a-quirky-introduction-to-number-systems/#comment-31294 Not sure if anyone has pointed this out, but I think the sentence "Luckily, irrationals are at least algebraic" should be "luckily, *some* irrationals are algebraic" since the set of algebraic numbers is countable and thus has lebesgue measure zero in the reals, meaning "almost all" real numbers are *not* algebraic. Instead they are called trancendental. This is yet another bizarre property of our familiar real number system, I just figured the author would want to note. Not sure if anyone has pointed this out, but I think the sentence “Luckily, irrationals are at least algebraic” should be “luckily, *some* irrationals are algebraic” since the set of algebraic numbers is countable and thus has lebesgue measure zero in the reals, meaning “almost all” real numbers are *not* algebraic. Instead they are called trancendental. This is yet another bizarre property of our familiar real number system, I just figured the author would want to note.

]]> http://betterexplained.com/articles/a-quirky-introduction-to-number-systems/#comment-9393 A Visual, Intuitive Guide to Imaginary Numbers | BetterExplained Tue, 08 Nov 2011 03:30:00 +0000 http://betterexplained.com/articles/a-quirky-introduction-to-number-systems/#comment-9393 [...] Seeing complex numbers as an upgrade to our number system, just like zero, decimals and negatives were. [...] [...] Seeing complex numbers as an upgrade to our number system, just like zero, decimals and negatives were. [...]

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