tag:blogger.com,1999:blog-2109150351375891279.post2490678910989780128..comments2023-05-26T13:58:00.927-07:00Comments on Mathie x Pensive: Variables May Vary - Part 2Gregory Taylorhttp://www.blogger.com/profile/06547180132612659893noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2109150351375891279.post-16686956406939294142013-03-16T11:32:58.585-07:002013-03-16T11:32:58.585-07:00So, capitals are out, and there's still too mu...So, capitals are out, and there's still too much cross-use of lower case letters, unless there's an unwritten rule about using the letters at the end of the alphabet for real variables (x, y, and z, though one can argue that those are based on the axes on graphs) and letters at the beginning for the placeholders for constants. (Not really. It got buried by university math where Greek letters became the norm.)<br /><br />The use of j as sqrt(-1) comes up in electrical engineering, for no reason I could discern at the time. It could be from the mix of i and j in some typeset. (What if you replaced the hats with berets?) It's an advantage in programming, and widely encouraged, even for counters (though you could get away with i, j, and k there. In programming, multiplication has to be explicit because the compiler isn't robust enough to tell the difference between IAmAVariable and xy (x * y, for readability here).<br /><br />The Greek letters start getting used for equations in university, especially with angles. It's a case where you might not want to add a layer of confusion later. And capital Greek letters tend to be used for new types of mathematical manipulations, such as the Greek capital sigma for the sum of a series.<br /><br />What if you used Japanese kana? Or letters from a made-up alphabet like Klingon or Aurabesh (http://starwars.wikia.com/wiki/Aurebesh)?Scott Delahunthttps://www.blogger.com/profile/06735796666483741699noreply@blogger.comtag:blogger.com,1999:blog-2109150351375891279.post-46954441231333414182013-03-15T19:34:11.497-07:002013-03-15T19:34:11.497-07:00Nice try. Capitals are taken. Ax + By = C is the e...Nice try. Capitals are taken. Ax + By = C is the equation of a line in standard form, where A, B and C are arbitrary (albeit related to slope and an item total). Different from y = mx + b. Similarly, Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 is the general form of a conic. Probably don't want to cross the streams there. (Don'tcha remember high school math? ;) )<br /><br />Incidentally, where is j used as an imaginary number? Programming? I figured a case of 'looked too similar to i'. (Now, I know i, j and k are all used as unit vectors in three space. But then they have the little hats.) I will buy that computer programming has the advantage, since your variables are allowed to be more than one letter in length. More than one letter in math means invisible multiplication.<br /><br />Of course, all that said, there is another alphabet available -- the greek one, and I've seen use of those symbols for transformations on the site of a UK teacher. Except from what I know of North America, the convention tends to be to use those to refer to angles only.Gregory Taylorhttps://www.blogger.com/profile/06547180132612659893noreply@blogger.comtag:blogger.com,1999:blog-2109150351375891279.post-20013325689370308762013-03-14T15:30:48.093-07:002013-03-14T15:30:48.093-07:00Math needs at least three separate alphabets, one ...Math needs at least three separate alphabets, one for variables, one for placeholders of constants, one for defined constants, like e (Euler's constant) and i (square root of negative one). I can understand needing to avoid confusion, thus not touching i and j (both used for imaginary numbers), but that leaves 24 other letters in use.<br /><br />Would it help to designate placeholders of constants using capital letters? The only place I can see that causing an issue is determining the period (T) of a cycle.<br /><br />As an example, I'll take your classic y=ax^2 + bx +c and apply the above changes to get y=Ax^2 + Bx +C. Does that make it clearer?<br /><br />In programming, you get to declare the variables at the beginning. (This is where good commenting helps, incidentally.) You can declare the user-supplied parameters A, B, and C as apple, bark, and congaline for all the computer cares, as long as the documentation explains what each one is for. This changes the above equation to f(x)=apple*x*x + bark*x + congaline. (Okay, not so clear, but it splits the variables and the constants a little.)<br /><br />Maybe math needs a new grammar when it comes to letter use?Scott Delahunthttps://www.blogger.com/profile/06735796666483741699noreply@blogger.com