https://math.codidact.com/categories/41/tags/4732.rssNew Posts Tagged 'visualization' - MathematicsMathematics - Codidact2023-09-26T09:01:49Zhttps://math.codidact.com/posts/289758How can I improve contrast of red and green, to prove Reverse Triangle Inequality? Tortillahttps://math.codidact.com/users/656722023-09-20T05:48:28Z2023-09-26T09:01:49Z<p>I need to improve <a href="https://math.stackexchange.com/a/774233">this original diagram</a> to the one beneath, because this diagram reappears on standardized tests <em><strong>with different ...https://math.codidact.com/posts/289757Solely by eye, how can 16 year olds visually distinguish $\color{red}{\vec{b} - \vec{r}}$ from $\color{limegreen}{|\vec{b}| - |\vec{r}|}$ ?Tortillahttps://math.codidact.com/users/656722023-09-20T05:32:39Z2023-09-22T18:23:44Z<p>Yearly, I teach 16 year olds the diagram beneath (improvement of <a href="https://math.stackexchange.com/a/774233">this original</a>) that reappears on standardized tests <em><strong>with differ...https://math.codidact.com/posts/289760While pictorializing $|x - y| < |x + y|$, how can 1 picture simultaneously prove (Reverse) △ Inequalities, $|x-y| ≤ |x|+|y|, |x|-|y| ≤ |x-y|$? Tortillahttps://math.codidact.com/users/656722023-09-20T06:21:31Z2023-09-20T12:27:27Z<p>I shall improve <a href="https://math.codidact.com/posts/289496">this post</a>, because</p>
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<p>it overlooked Triangle Inequality, $|x + y| ≤ \color{darkgoldenrod}{|x| + |y|}$. Micha...https://math.codidact.com/posts/289495Picture proof for expansion of $x^n−y^n$ Estehttps://math.codidact.com/users/563032023-08-22T07:31:45Z2023-08-23T13:14:52Z<p>Most students fail to intuit <a href="https://math.stackexchange.com/a/117676">$x^n−y^n \equiv (x−y)(x^{n−1}+x^{n−2}y+...+xy^{n−2}+y^{n−1})$ </a> as substantiated by the glut of duplicates, at l...https://math.codidact.com/posts/2894961 picture proof for the triangle inequality and the reverse triangle inequality Estehttps://math.codidact.com/users/563032023-08-22T08:01:57Z2023-08-22T14:17:22Z<p>Michael Spivak's <em>Calculus</em> (2008 4 edn), Exercise 12, p 16.<br>
(vi) is the Reverse Triangle Inequality.</p>
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<p>(iv) $|x-y| ≤ |x| + |y|$. (Give a very short proof.)<br>
...https://math.codidact.com/posts/282888How can I visualize the Law of Total Probability with extra conditioning?DNBhttps://math.codidact.com/users/536282021-07-28T00:06:49Z2021-09-02T14:14:13Z<p>How can I pictorialized this Theorem 2.4.3? As you can see below, I edited a picture by drawing E inside B.. Is my edit correct? Can my edit be improved?</p>
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<p><strong>Theorem 2....https://math.codidact.com/posts/280850How to visualize division as splitting Dividend into B equal “partial groups”, then rounding up A partial groups to get a full group?Chgg Clouhttps://math.codidact.com/users/535642021-02-18T06:38:08Z2021-06-26T19:36:04Z<p>Because $10 \div \dfrac{4}{3}$ isn't an integer, <a href="https://old.reddit.com/r/learnmath/comments/ckv75r/why_multiplying_by_the_reciprocal_works_while/evurf0g/">I changed the numbers in thi...https://math.codidact.com/posts/280653How can I visualize $\lim\limits_{x \rightarrow \pm \infty} f(x) = \lim\limits_{t \rightarrow 0^{\pm}} f(1/t)$?TextKithttps://math.codidact.com/users/536962021-02-02T21:22:23Z2021-06-05T15:38:14Z<p>I'm not asking about <a href="https://math.stackexchange.com/a/3983012/872474">the proof</a> that I already understand. I'm longing to understand this graphically. As you can see, I added $1/t$...https://math.codidact.com/posts/280848How can I visualize this Compound Interest Chart with indefinite integrals?Chgg Clouhttps://math.codidact.com/users/535642021-02-18T06:36:11Z2021-02-18T20:09:22Z<p>How can I visualize <a href="https://betterexplained.com/articles/definitions-of-e-colorized/">the integrals below</a>? Can someone draw on the chart and point to where $\int 1 , dx = x$, $\int ...https://math.codidact.com/posts/280849How can I visualize dividing by a fraction as partial and full groups?Chgg Clouhttps://math.codidact.com/users/535642021-02-18T06:37:44Z2021-02-18T06:37:44Z<p>I can't visualize all these "full groups" and "partial groups." Can someone please picture them? Please see my questions red in-line. Please don't use the identity that $\dfr...https://math.codidact.com/posts/280663How can I generalize a picture for the Mean Value Theorem to the Generalized MVT?TextKithttps://math.codidact.com/users/536962021-02-04T02:22:15Z2021-02-11T22:16:44Z<p>How can I transmogrify this figure for the <a href="https://math.stackexchange.com/q/296176">Generalized MVT</a>? If $f$ and $g$ are continuous
on the closed interval $[a, b]$ and differentiabl...