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Discussion Imaginary numbers - okay I get them now

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Here's a stupidly simple video series that actually made me understand why imaginary numbers exist.

It also helps to understand that "imaginary numbers" is a buffoon's name. A goof's name. The wrong name for what they are. "Lateral numbers" is more accurate.

Anyway, I've always seen the introduction of imaginary numbers as the stopping point for my "grasp" of mathematics. I was a shit student so I never got to calculus. I dropped out of college, too, so I never got enough time to fuck around with these babies in precalc. So the concept has always mystified me.

 
Love that video, I've used it in the classroom.
Indeed "imaginary" is a poor choice for a name. So is "real" for that matter.
 
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Quick remark after viewing it again and refreshing my memory of it: the video kind of glosses over irrational numbers and omits them completely during the historical runthrough.

The Pythagoreans of ancient Greece are said to be the first to have learned of irrationals, supposedly somewhere around 500 B.C., give or take. This was way before the invention of the decimal system and the use of zero.
But the story goes that they found their existence to be so disturbing, people were murdered to prevent the secret from getting out.

Negative numbers, funnily enough, were written about seriously only much later, in India around 900 A.D.
 
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They've always made sense to me, but I knew someone who was apparently a math nerd as a kid who just noped out of math classes in high school once they came up lol.
 
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How many holes are there in the rational number line?
 
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The way they showed a 2d equation with no roots being moved to a 3d space that has roots was pretty cool

Btw, random fun fact, the 'i' symbol used for the imaginary unit conflicts with the 'i' used for electric currents, so in some courses the imaginary unit might sometimes be randomly changed to 'j' instead
 
Imaginary numbers took me a long time to grasp, and it was actually an electric circuits class that finally made them click - the whole idea of current phase and how to solve circuit problems involving that. I could use them in equations and solve problem with them, but they didn't really make actual sense to me until then.

I still think Euler's Identity is one of the most mind-blowing things in math: e^(iπ) + 1 = 0 . It's just so... clean
 
My older brother is ten years older than me and he taught me about negative numbers and imaginary numbers in kindergarten. I thought both were super cool.

I had a horrible 1st grade teacher and they got mad at me when I was asked to count backwards from ten and I started counting into negative numbers past zero lol.
 
chocolate_supra said:
The stopping point for my grasp of mathematics was teachers not up to the task.
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Fixed that for you.
It's such a terrible thing, what the standardized education programs have done to such a beautiful subject.

It's why I insist on having the freedom to customize my approach - and my curriculum - to my current students, wherever I go.

Allow me to link a well known essay by Mathematician Paul Lockhart about the poor state of mathematical education in schools.

Lockhart's Lament

www.maa.org
I urge anyone who ever had their interest in math extinguished to read the entire essay. It starts off with the most beautiful introduction: Imagine a horrible world, one without music!


This is a short preface to give you the general idea, written by Keith Devlin, another mathematician:

Lockhart's Lament​

This month's column is devoted to an article called A Mathematician's Lament, written by Paul Lockhart in 2002. Paul is a mathematics teacher at Saint Ann's School in Brooklyn, New York. His article has been circulating through parts of the mathematics and math ed communities ever since, but he never published it. I came across it by accident a few months ago, and decided at once I wanted to give it wider exposure. I contacted Paul, and he agreed to have me publish his "lament" on MAA Online. It is, quite frankly, one of the best critiques of current K-12 mathematics education I have ever seen. Written by a first-class research mathematician who elected to devote his teaching career to K-!2 education.
Paul became interested in mathematics when he was about 14 (outside of the school math class, he points out) and read voraciously, becoming especially interested in analytic number theory. He dropped out of college after one semester to devote himself to math, supporting himself by working as a computer programmer and as an elementary school teacher. Eventually he started working with Ernst Strauss at UCLA, and the two published a few papers together. Strauss introduced him to Paul Erdos, and they somehow arranged it so that he became a graduate student there. He ended up getting a Ph.D. from Columbia in 1990, and went on to be a fellow at MSRI and an assistant professor at Brown. He also taught at UC Santa Cruz. His main research interests were, and are, automorphic forms and Diophantine geometry.

After several years teaching university mathematics, Paul eventually tired of it and decided he wanted to get back to teaching children. He secured a position at Saint Ann's School, where he says "I have happily been subversively teaching mathematics (the real thing) since 2000."

He teaches all grade levels at Saint Ann's (K-12), and says he is especially interested in bringing a mathematician's point of view to very young children. "I want them to understand that there is a playground in their minds and that that is where mathematics happens. So far I have met with tremendous enthusiasm among the parents and kids, less so among the mid-level administrators," he wrote in an email to me. Now where have I heard that kind of thing before? But enough of my words. Read Paul's dynamite essay. It's a 25-page PDF file.
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FYI: Did you know that one of this year's winners of the Fields Medal - the highest honor in Math, more prestigious and more difficult to win than the Nobel Prize in other disciplines* - is a highschool dropout who originally studied poetry in college?

en.m.wikipedia.org

June Huh - Wikipedia

en.m.wikipedia.org en.m.wikipedia.org

*Because it is only awarded every four years, and only Mathematicians who are under 40 the year it is awarded are eligible. Yeah, it's a dumb and anachronistic rule. The original intention was for the prize to encourage young mathematicians to continue on their path of discovery rather than burn out, but the amount of knowledge required to advance the field has grown considerably since those days, and I suspect this requirement will be relaxed, sooner or later.
 
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In my language we refer to them as "complex numbers" which makes more sense because they're made of two parts (although the other numbers are still "real numbers").

I was okay with them cause I love math, but it was one of those subjects where I was having a hard time seeing any practical use for it. I guess they're a thing in programming and advanced physics?
 
Really good video. Mindblowing concepts expansion for me. Even though I used complex number before in statistics and fourier transform(jpeg compression algorithm for example) I always considered them a hack to solve the problem. Fuck this shit of Imaginary name convention.
 
I teach middle school, so we don’t usually mention these outside of fun trivia. I always have students ask, though, so I’m happy to have this at the ready.
 
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