Printable View
Japanese multiplication technique.
<video controls autoplay loop> <source src="https://diqn32j8nouaz.cloudfront.net/japan_multiplication.mp4" type="video/mp4"> Your browser does not support the video tag. </video>
Previously:
https://www.homemadetools.net/forum/...013#post207216
https://www.homemadetools.net/forum/...015#post179894
https://www.homemadetools.net/forum/...1787#post94713
https://www.homemadetools.net/forum/...896#post108875
https://www.homemadetools.net/forum/...166#post115788
Jethro from the Beverely Hillbillies, naught and naught and naught plus naught equals 42. Now haw he ever came up with 42 is anybody's guess
He was prescient about HHGTTG?
Yep, but his brain probably ran on granny's rheumatiz medicine not lemonsQuote:
Originally Posted by kb4mdz
Looks nice. Try 76x47...
https://youtu.be/TjIcoiP1vEc shows how numbers over 10 intersections are dealt with
So basically abacusless abacus? ;)
Or 99 x 99.Quote:
Originally Posted by jarekp
Gonna be drawing a lot of lines and counting a lot of intersections. I fail to see any advantages to their system.
99 x 99 = (100 -1) x (100 -1) = 100 x 100 - 200 + 1 = 9800 + 1 = 9801
would seem a lot simpler - can even do that one in your head.
76 x 47 = (80 - 4) x (50 - 3) = 4000 - 240 - 200 + 12 = 3560 +12 = 3572
Ok, a bit more difficult but still simpler than drawing all those lines.
Or having paper, "western" oldschool method:
76
47
--------
532
304
-------
3572
At least no limits of digits.
Btw
Have you imagined that Copernicus was able to do quite complicated calculations?
Try to do above using roman numbers (he did not know other)....
J.
The awkwardness of computation using Roman numerals probably accounts for the Romans' use of the abacus.Quote:
Originally Posted by jarekp
The Roman abacus was similar to modern ones but had some additional columns at the right...
Attachment 43338
The Wikipedia article provides a full description of the device and its use...
https://en.wikipedia.org/wiki/Roman_abacus
Actually, I'm not so sure that Copernicus knew only Roman numerals. Two figures from the Wikipedia article on the man here...
This figure from a surviving AUTOGRAPH copy of De Revolutionibus...
Attachment 43340
shows him using Arabic numerals
which were converted to Roman in the published version...
Attachment 43341
Copernicus lived 1473-1543. As this extract from Wikipedia...
The reception of Arabic numerals in the West was gradual and lukewarm, as other numeral systems circulated in addition to the older Roman numbers. As a discipline, the first to adopt Arabic numerals as part of their own writings were astronomers and astrologists, evidenced from manuscripts surviving from mid-12th century Bavaria. Reinher of Paderborn (1140 - 1190) used the numerals in his calendrical tables to calculate the dates of Easter more easily in his text Compotus emendatus.
shows, Arabic numerals were already well known and in use during Copernicus' life. Given that he was a polymath, he would have been well aware of the simplicity afforded by the decimal system expressed with Arabic numerals.
As soon as one starts using an abacus, with its neat columns representing powers of ten, one is already driven to a positional number representation. The only thing missing is separate symbols for the digits zero to nine. The Arabic numerals provided just that.
Although the positional number system had spread from Arabia to Europe at the beginning of the second millennium (hundreds of years before Copernicus' birth), I believe that the use of abacus-like devices provided a lot of encouragement to its wide-spread adoption.
