tag:blogger.com,1999:blog-3071719252136968205.post6998983573933530713..comments2023-09-01T01:19:38.867-07:00Comments on Following Learning: How we write numbersSimon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-3071719252136968205.post-88874300275657093492015-12-28T12:18:38.903-08:002015-12-28T12:18:38.903-08:00Thanks Alan. Interesting thoughts.
I'm thinki...Thanks Alan. Interesting thoughts.<br /><br />I'm thinking, this Roman system continued up until Fibonacci's time. My impression from Keith Devlin's book about him is that a lot of the examples he gave in his book of what you could do with the new numbering involved multiplication and division.<br /><br />Things like:<br /><br />"If one hundredweight of linen or some other merchandise is sold near Syria or Alexandria for 4 Saracen bezants, and you will wish to know how much 37 rolls are worth, then..."<br /><br />"Three men made a company in which the first man put 17 pounds, and the second 29 pounds, the third 42 pounds, and the profit was 100 pounds."<br /><br />(And of course there's the famous rabbits!)<br /><br />I suppose it's possible that there wasn't so much trade before the 12th century, and so this kind of calculation wasn't needed so much. Perhaps trade took off, at least for places like Pisa, and the new numbers were more attractive?<br /><br />As for the base ten, thank you - that was a mistake that I was very likely to make, and yes, of course all bases are base 10. I did "new maths" at secondary school, so we learnt about different bases (along with a bit of modular arithmetic, and Boolean algebra); it was actually one of the parts of the curriculum that grabbed me most. We didn't do base negative two though - I'll have to check that out!Simon Gregghttps://www.blogger.com/profile/07751362728185120933noreply@blogger.comtag:blogger.com,1999:blog-3071719252136968205.post-58052151712784832312015-12-28T08:05:37.268-08:002015-12-28T08:05:37.268-08:00Is there any evidence the Romans ever did any mani...Is there any evidence the Romans ever did any manipulations with their number symbols? I was always told that if they needed to do any sort of meaty calculations they'd get a Greek slave to do it using their own number system.<br /><br />And I don't want to be picky, but surely our number system is base TEN rather than than base 10 ? No matter what number you're using as a base, 10 represents the value of the base. That's true whether you're working in base ten, base twelve, or - and this one's a lot of fun, I promise, base negative two.piogoldhttps://www.blogger.com/profile/09994830425092781110noreply@blogger.comtag:blogger.com,1999:blog-3071719252136968205.post-28296576731741438072015-12-28T05:25:29.914-08:002015-12-28T05:25:29.914-08:00Thanks Prof. I like the idea of exploring how mult...Thanks Prof. I like the idea of exploring how multiplication might work.<br /><br />Thinking about the abacus, I've come to the conclusion that the battle depicted between the abacists and the algorists wasn't quite the walkover the image presents. Expert users of the saroban, which seems very like the Roman system, are, I've heard, very fast.Simon Gregghttps://www.blogger.com/profile/07751362728185120933noreply@blogger.comtag:blogger.com,1999:blog-3071719252136968205.post-77400750090257608522015-12-28T04:31:38.004-08:002015-12-28T04:31:38.004-08:00I think we tend to be too quick to dismiss Roman n...I think we tend to be too quick to dismiss Roman numerals as unwieldy and difficult to calculate with, at least as far as multiplication is concerned. They don't provide such a powerful and extendable system as offered by our place-value system, but multiplying with Roman numerals, though limited to natural numbers perhaps, is easy to make sense of - it could be said to involve repeated addition, collecting like numerals and exchange, with some scaling (especially when multiplying by 10). It also calls for partitioning (and the distributive law) in a very 'natural' way and thus could provide a useful, if limited, model of multiplication for students. <br />@ProfSmudgeAnonymousnoreply@blogger.com