Kind of weird that no consensus have emerged for multiplication (·, ×, *, or horizontal juxtaposition) or division (÷, /, or vertical juxtaposition with horizontal line between) yet.
Everybody uses juxtaposition for multiplication (or dot when some separation is required) and horizontal line for division. * and / are poor man's substitutes when all you have is ASCII. × is used for vector products, Cartesian products and products of algebraic structures in general. The only place I've ever seen × or ÷ being used in arithmetics was primary school. No idea why they use them.
Where and When Did the Symbols "+" and "–" Originate?
21–30 of 90 posts
Re: Where and When Did the Symbols "+" and "–" Originate?
#22Earlier quoted context omitted.
Everybody uses juxtaposition for multiplication (or dot when some separation is required) and horizontal line for division. * and / are poor man's substitutes when all you have is ASCII. × is used for vector products, Cartesian products and products of algebraic structures in general. The only place I've ever seen × or ÷ being used in arithmetics was primary school. No idea why they use them.
In primary school in the Netherlands (and maybe elsewhere?), : is used for division.
Re: Where and When Did the Symbols "+" and "–" Originate?
#23Several earliest known uses of other mathematical notations can be found at: http://jeff560.tripod.com/mathsym.html
Re: Where and When Did the Symbols "+" and "–" Originate?
#24Several earliest known uses of other mathematical notations can be found at: http://jeff560.tripod.com/mathsym.html
Interesting. The close parentheses form of division from 1540 looks like the basis of the long division form of division, i.e. 2)6 with a bar or vinculum, extending from the top of the parentheses over the 6. The long division form finally takes its modern form in 1888. The transformation of that symbol seems somewhat obvious and natural. I wonder if we are likely to see further changes, as modern typesetting should…
Re: Where and When Did the Symbols "+" and "–" Originate?
#25Re: Where and When Did the Symbols "+" and "–" Originate?
#26Earlier quoted context omitted.
Everybody uses juxtaposition for multiplication (or dot when some separation is required) and horizontal line for division. * and / are poor man's substitutes when all you have is ASCII. × is used for vector products, Cartesian products and products of algebraic structures in general. The only place I've ever seen × or ÷ being used in arithmetics was primary school. No idea why they use them.
In primary school in the Netherlands (and maybe elsewhere?), : is used for division.
Re: Where and When Did the Symbols "+" and "–" Originate?
#27I always felt the origin of the equals sign was wonderful: "I will sette as I doe often in woorke use, a paire of parralles, or Gemowe lines of one lengthe, thus : ==, bicause noe 2, thynges, can be moare equalle."
The opposite of something. It's only when we can separate nothing, that we can begin to describe something.
(And is the universe the mathematical manifestation of everything that isn't nothing?) /stoner
Re: Where and When Did the Symbols "+" and "–" Originate?
#28That's interesting. The Silk Road (http://en.wikipedia.org/wiki/Silk_Road) was in full swing at that time. This is pure guesswork, but multiple classical Chinese characters now pronounced yu (予,与,餘,逾,與) meant something close to addition. I wonder if there's a link?
There were a great many languages in operation there, and the Chinese were primarily interested in trade. It wouldn't surprise me at all if there were a regional patois language of business utilizing Chinese idiom that the subcontinent and others were able to borrow from.
Likewise, the borrowing may have gone in the other direction.
Note that some of the above symbols are not so dissimilar from the + symbol, allowing some minor scope for simplification.
On further investigation, http://www-history.mcs.st-and.ac.uk/PrintHT/Bakhshali_manusc... claims the Bakshali manuscript yu was "for yuta" (apparently Sanskrit/Devanagari: युत). Apparently yu is a well recognized word root meaning "to mix" or "(equipped) with" within Sanskrit, yuta being some kind of derived or more expanded/standalone form. (Sources: http://www.hindunet.org/hindu_history/sarasvati/dictionary/9... http://vedabase.net/y/yuta http://dictionary.tamilcube.com/sanskrit-dictionary.aspx?ter... http://www.hinduwebsite.com/sacredscripts/sanskrit_dictionar...)
That yu is apparently the same Sanskrit / proto Indo-European root as yoga, or even the far-western-Barbarian modern derivation in English, yoke. http://dictionary.reference.com/browse/yoke https://en.wiktionary.org/wiki/Appendix:List_of_Proto-Indo-E...
Hrrm... there must be something published on this already. Anyone with academic library access? :) I'm up in the Himalayan foothills, hehehe.
Re: Where and When Did the Symbols "+" and "–" Originate?
#29Kind of weird that no consensus have emerged for multiplication (·, ×, *, or horizontal juxtaposition) or division (÷, /, or vertical juxtaposition with horizontal line between) yet.
Everybody uses juxtaposition for multiplication (or dot when some separation is required) and horizontal line for division. * and / are poor man's substitutes when all you have is ASCII. × is used for vector products, Cartesian products and products of algebraic structures in general. The only place I've ever seen × or ÷ being used in arithmetics was primary school. No idea why they use them.
Perhaps because the other prominent use is on the buttons of every single calculator in the world.
Re: Where and When Did the Symbols "+" and "–" Originate?
#30In Czech Republic we would write
453: 12 = 37.75
In Netherlands:
12/453\37.75
In Russia:
453 | 12
| 37.75
all of them are listed on Wikipedia