21–30 of 163 posts
In 2017 we just do: $ perl6 -e 'say Ⅻ / Ⅲ' 4
care to explain why this works?
That Perl allows them in integer literals is strange, but also logical in a weird way. (Now I wonder what other number systems it supports.)
EDIT: Ok, so I installed perl6 (rakudo) just to test this out, and it apparently doesn't work out of the box. Pity.
It's interesting how the notation used can encourage or retard progress. For example, Leibniz's calculus notation was vastly superior to Newton's, and calculus theory advanced much more quickly where Leibniz's notation was used. https://en.wikipedia.org/wiki/Leibniz%27s_notation
I prefer Mathematica's notation over Leibniz's, because it is not as ambiguous (dx can also mean d TIMES x, as a simple example, but also dy^2 can mean d(y^2) and (dy)^2)
The derivative w.r.t. x of f(x) is D_x f in Lagrange notation. It looks a bit like matrix multiplication for a good reason—a matrix is just a representation of a linear operator on a finite dimensional vector space.
> the Romans greatly preferred the simpler IIII to IV, XXXX to XL, and so on. (The IIII-for-4 notation survives today on the faces of clocks.) looks at watch Well, damn, it's IIII. However my watch does use IX over VIIII, what's up with that?
I, II, III, IIII (consisting of I only)
V, VI, VII, VIII (consisting of I and V)
IX, X, XI, XII (consisting of I and X)
[1] https://www.hautehorlogerie.org/en/encyclopaedia/glossary-of...
Since we have a lot of math experts here I thought I'd ask a question I was always wondering about: Is there an inherent advantage or disadvantage to using the decimal system as we do? Somehow I think octal or hexadecimal would be easier but I am not sure.
Since we have a lot of math experts here I thought I'd ask a question I was always wondering about: Is there an inherent advantage or disadvantage to using the decimal system as we do? Somehow I think octal or hexadecimal would be easier but I am not sure.
I speak a language (Mende) that has no formal mathematics but counting is done in base 10; there are 10 individual words for 1 to 10 , the word for one is "yaella", the word for 10 is "poo", the word (really expression) for 11 is "poo mahun yaella", which literally translates to 10 on top of 1 ie 10+1...I can only think they stopped at 10 words because there are ten fingers to do elementary arithmetic?? granted there are other words for high magnitudes...there are apparently other languages with other bases besides 10 so who knows...possibly due to using other cultural artifacts to serve as digits.
Since we have a lot of math experts here I thought I'd ask a question I was always wondering about: Is there an inherent advantage or disadvantage to using the decimal system as we do? Somehow I think octal or hexadecimal would be easier but I am not sure.
http://www.dozenal.org/drupal/content/brief-introduction-doz...
These people believe that base 12 would be superior to base 10. And they do make good points, expressing fractions like those in 3rds become easier. Is it superior in the grand scheme? I'll leave that debate to actual experts. Will people see the utility and switch? I'm going to keep my base 10 skills up, you know, just in case duodecimal doesn't catch on. ;-)
It's interesting how the notation used can encourage or retard progress. For example, Leibniz's calculus notation was vastly superior to Newton's, and calculus theory advanced much more quickly where Leibniz's notation was used. https://en.wikipedia.org/wiki/Leibniz%27s_notation
I prefer Mathematica's notation over Leibniz's, because it is not as ambiguous (dx can also mean d TIMES x, as a simple example, but also dy^2 can mean d(y^2) and (dy)^2)
It's interesting how the notation used can encourage or retard progress. For example, Leibniz's calculus notation was vastly superior to Newton's, and calculus theory advanced much more quickly where Leibniz's notation was used. https://en.wikipedia.org/wiki/Leibniz%27s_notation
An important facet to mathematics in general, that most are unaware of before studying it, is that the majority of proofs, especially those done in bachelor university courses, are purely notation. Other problems often become trivial to solve by using a different notation (e.g. polar form vs. points on the complex plane) as well.
To the extent that this is true, how much do you think that is due to the notation itself, and how much is due to someone identifying the essential underlying concepts and then making those the basis for a good notation?
I had, for some reason, never thought of that directly. Although I do remember some joke on arithmetics in one of the Asterix comic books. But reading this article and trying out a few things, I found it was great fun!
...which is funny (the Asterix thing), because spoken French isn't exactly brilliant with numbers either: 99 for example is expressed as "eighty nineteen", 70 as "sixty ten". My friends lived in France a while and said their landlady could never count their rent (paid in cash) correctly first time. Always stumbled somewhere between 100x+60 and 100x+100 for integer values of x. The Swiss have corrected this in Swiss F…
I speak a language that does this as well (Georgian), where say 54 is ormotsdatotxmeti (two times twenty and fourteen.)
I didn't find maths particularly different difficulty wise, when thinking about it in Georgian or not. What did trip me up, was the times! Up to x:29 it's 29 minutes past x, but at x:30 it is 30 minutes to ++x. Weird.