Category: Mathematics
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An adult friend is getting tested to see if she has a formal neurological problem that would account for her struggles with mathematics. She asked how it could be that she might make it all the way through public education without being tested for such a learning disability (LD). Here were my thoughts; keep in…
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[mathjax]Because mathematical terminology developed piecemeal over time, there are many inconsistencies which prove to be a challenge to students. One of the more obvious examples is what is called the “standard form” of the quadratic. A quadratic equation has three common forms: \(ax^2 + bx + c = 0\) \(a(x – h)^2 + k =…
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[mathjax]Several of my math teacher colleagues are of the opinion that calculators have destroyed math sense. I am not convinced that this is directly true: Calculators are a tool, nothing more. A few months ago, I saw a video by the mythically amazing Vi Hart which led me to an epiphany: Perhaps the problem isn’t…
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[mathjax]This is my translation of Meyl’s 1878 proof that a triangular pyramid of balls will only have a square number of balls if the base side is two or forty-eight. “Solutions to questions posed in The New Annals: Question 1194.” A. J. J. Meyl, former artillary captain at the Hague, Nouvelles annales de mathématiques. Journal…
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[mathjax]This is my translation of Lucas’s 1877 proof that a square pyramid of balls will only have a square number of balls if the base side is twenty-four. “Solutions to questions posed in The New Annals: Question 1180.” M. Édouard Lucas, Nouvelles annales de mathématiques. Journal des candidats aux écoles polytechnique et normale, second series,…
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[mathjax]This is my translation of Gerono’s 1877 proof listing all the possible solutions (x, y) for the equation \(y^2 = x^3 + x^2 + x + 1\). “Solutions to questions posed in The New Annals: Question 1177.” MM. Gerono, Nouvelles annales de mathématiques. Journal des candidats aux écoles polytechnique et normale, second series, volume 16…
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[mathjax]I have been spending my free time the last few days on the task of working backwards through three proofs in a 19th century French language mathematics journal. This started with a simple question in the G+ Mathematics community, posted by Jeremy Williams: “Who can find the largest tetrahedral number that is also a square?”…
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Effective mathematics involves two distinct acts: Parsing and writing mathematical symbols to create meaningful messages Applying an understanding of mathematical relations and objects It seems to me that we have two terms at our disposal: Numeracy and mathematical literacy. It also seems to me that these two terms are used somewhat interchangeably. (“What is numeracy?”)…
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[mathjax]In my last post, I pointed out that SSA is in fact sufficient for determining all three sides and angles under certain conditions. In this post, I will specify those conditions, with illustrations. Given two noncollinear segments \(\overline{S_1}\) and \(\overline{S_2}\) and angle \(\angle A\), where \(\overline{S_1}\)’s two endpoints are the vertex of \(\angle A\) and an…
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[mathjax]There is a standard litany of theorems involving proving triangle congruence that has remained largely unchanged since my high school days. I was told that, to prove that two triangles are congruent, we need three pieces of information. The abbreviations were given as SSS, SAS, AAS, and ASA. Astute students would ask about SSA (or…