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A Simple Proof of the Quadratic Formula

Po-Shen Loh

2019 · arXiv

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From the abstract

This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the potential to demystify quadratic equations for students worldwide.

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5 selected excerpts · 5 total mentions

Worf
Neutral mention · rule
I understand your point that you want a fixed presentation layout and pagination. I prefer to be able to responsively resize the document and to follow the ToC instead of pages. I've yet to see documentation that's thousands of pages long that doesn't include a very detailed ToC. For me remembering "section 8.3.16.2" is better and makes more sense than remembering "page 1292". I've had to read scanned math books years ago and I remember using some PDF reader to put bookmarks that correspond to the ToC, so I'd put "2.5.1.2 - Theorem about X" in the sidebar. That's how I was able to actually go back and forth easily. With just pages it would've taken me tens of seconds to…
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locate a theorem (or lemma, proof, definition, whatever). And it was a dense book, so I had to constantly go back and reread stuff. But I agree that PDFs can, and often do, have ToCs, too. > the size ratios between various elements may be inappropriate I can't recall having this issue on websites or on EPUBs. What kinds of elements are we talking about? HTML and CSS are pretty good at keeping sizes from what I've seen. I agree that there are many EPUB readers, most of them very unpolished. And perhaps there aren't EPUB readers that are good at everything, yet. For formulas, MathML and other tech has been satisfactory. I was able to find this basic math paper arXiv uses as a demo for their HTML papers: https://ar5iv.labs.arxiv.org/html/1910.06709 It doesn't have figures, but the math is rendered perfectly. I can easily remove the "justify" style and increase and decrease the letters. If it was a long paper, it would've been nice to have a clickable ToC, but most EPUBs have one. I think that right now most EPUB readers and some HTML renderings are bad, but I believe they'll get better.
Original comment The surprisingly complex journey to text-selectable client-side generated PDFs
dginev
Neutral mention · rule
If you are already using LaTeXML, it is also easy to get the ar5iv rendering (example article: https://ar5iv.labs.arxiv.org/html/1910.06709) You can either copy the CSS asset from: https://github.com/dginev/ar5iv-css and add "--css=ar5iv.css --nodefaultresources" to the command line options for latexmlpost (or latexmlc). Or alternatively, for people not interested in learning how to install and configure latexml, they can try the self-contained Dockerfile at: https://github.com/dginev/ar5ivist/
Original comment The Stacks Project: A Wikipedia of algebraic geometry (2022)
svat
Neutral mention · rule
If this is indeed not new, one should be able to find a published source anywhere in the world's literature from before 2019 that does it this way, correct? The author mentions in his blog post / paper that he has looked for this exact method in many sources and not found it anywhere: can someone find it? See section 3.3 "Brief historical context" of the paper: https://arxiv.org/abs/1910.06709v2 — he also mentions on his website of many attempts to find this exact derivation somewhere earlier: https://www.poshenloh.com/quadratic/ > In summary, the author has not yet found a previously-existing book or paper which states the same pedagogical method as this present article…
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and precisely justifies the steps, but there exist independent references that contain the key ideas and can be adapted to achieve this. That said, it is entirely possible that the method in this present article was previously observed by people who did not share their findings.
Original comment A new way to make quadratic equations easy (2019)
finite_jest
Neutral mention · rule
I don't think this is new at all. This looks like just a standard proof of the quadratic formula. I believe most people probably have seen a variation of this in high school. Depending on your preferences, this might be a slightly better or worse presentation than what you have seen before. The fact that they couldn't (or haven't) publish it in a journal also supports this. [1]. (The ArXiv pre-print [2] is dated December 16, 2019) [1]: https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&q=%22A... [2]: https://arxiv.org/pdf/1910.06709.pdf
Original comment A new way to make quadratic equations easy (2019)

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