Comments on: The Fourth Bunch of Ways to Multiply http://threesixty360.wordpress.com/2009/06/17/the-fourth-bunch-of-ways-to-multiply/ 12 tables, 24 chairs, and plenty of chalk Thu, 30 May 2013 02:26:42 +0000 hourly 1 http://wordpress.com/ By: Bob Bergen http://threesixty360.wordpress.com/2009/06/17/the-fourth-bunch-of-ways-to-multiply/#comment-9878 Sun, 28 Jun 2009 17:56:14 +0000 http://threesixty360.wordpress.com/?p=2584#comment-9878 Don’t know if this qualifies, but before I learned algebra I discovered what are known as the Associative and Communtative Laws, and found they worked very well for me when I mentally multiplied two and three digit numbers. In later years, as a Professor of Science, I tried to teach this to my students so they could make relatively accurate estimates. Most didn’t get it – but then, I was teaching freshman and sophomore level courses, probably the last science courses any of these students would ever experience.

]]> By: Ξ http://threesixty360.wordpress.com/2009/06/17/the-fourth-bunch-of-ways-to-multiply/#comment-5728 Fri, 19 Jun 2009 23:41:27 +0000 http://threesixty360.wordpress.com/?p=2584#comment-5728 Hmmm. I really like the ruler as a visual and have no trouble believing that it gives good accuracy, but I don’t see how the prosthaphaeretic formulas fit into it. The way I’m looking at it, it’s similar triangles and not trigonometry at all, although they clearly reference the trig formulas.

]]> By: Jason Dyer http://threesixty360.wordpress.com/2009/06/17/the-fourth-bunch-of-ways-to-multiply/#comment-5545 Fri, 19 Jun 2009 14:27:02 +0000 http://threesixty360.wordpress.com/?p=2584#comment-5545 It looks like someone made a slide rule version of that Greek multiplication you posted about:

http://en.wikipedia.org/wiki/File:Prosthaphaeretic_Slide_Rule2.svg

although they called it a Prosthaphaeretic slide rule for some strange reason:

http://findarticles.com/p/articles/mi_qa3950/is_200401/ai_n9372466/

]]> By: Ξ http://threesixty360.wordpress.com/2009/06/17/the-fourth-bunch-of-ways-to-multiply/#comment-5541 Thu, 18 Jun 2009 22:40:17 +0000 http://threesixty360.wordpress.com/?p=2584#comment-5541 Jason, I only know one way to multiply on an abacus. I’ll post it in a few days (probably early next week: these weekends are all Birthday Party weekends in our house) but I’m curious about what the differences are!

]]> By: Jason Dyer http://threesixty360.wordpress.com/2009/06/17/the-fourth-bunch-of-ways-to-multiply/#comment-5540 Thu, 18 Jun 2009 22:31:12 +0000 http://threesixty360.wordpress.com/?p=2584#comment-5540 which also explains how to Get off the couch to Change Channels on the TV set

Not entirely outdated. Occasionally I lose the remote!

Also, I’ve been looking up abacuses (abacii?) after the comment about the Roman abacus on the other thread and there are some differences in historical abacuses severe enough to qualify as different methods of multiplication. I think we could reach 35.

]]> By: Mr. H http://threesixty360.wordpress.com/2009/06/17/the-fourth-bunch-of-ways-to-multiply/#comment-5456 Thu, 18 Jun 2009 16:08:44 +0000 http://threesixty360.wordpress.com/?p=2584#comment-5456 it’s a wonder to me that this method was so popular for so long when so many other ways are even more accurate. Maybe I’m missing something

Speed. If you’re an astronomer with no calculators, would you want to multiply piles of numbers using the standard multiplication algorithm or would you want to (1)lookup tables (2)add the logs and (3)do a reverse lookup?

Addition is less prone to errors than the multiplication and addition together.

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