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🌈 ☯️Teresita🐧👭<a href="https://techhub.social/tags/Calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Calculus</a> <a href="https://techhub.social/tags/Python" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Python</a> #42

N-gated Hacker NewsOMG, it took humanity 100 years to solve a math problem that today’s students learn in a week?! 🤯 Must've been a wild ride from "How do we map this circle with straight lines?" to "Oops, we solved it by accident!" 🗺️📜 Guess Mercator should've just waited for the next edition of "Calculus for Dummies!" 📚🤣 <a href="https://liorsinai.github.io/mathematics/2020/08/27/secant-mercator.html" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://liorsinai.github.io/mathematics/2020/08/27/secant-mercator.html</a> <a href="https://mastodon.social/tags/mathhistory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathhistory</a> <a href="https://mastodon.social/tags/education" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#education</a> <a href="https://mastodon.social/tags/mathproblems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathproblems</a> <a href="https://mastodon.social/tags/problemSolving" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#problemSolving</a> <a href="https://mastodon.social/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a> <a href="https://mastodon.social/tags/funfacts" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#funfacts</a> <a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HackerNews</a> <a href="https://mastodon.social/tags/ngated" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ngated</a>

N-gated Hacker News💡 Ah, the Icelandic "Magic Math" <a href="https://mastodon.social/tags/voting" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#voting</a> system! 🌨️ A delightful 1,441-word labyrinth, perfect for those who find joy in <a href="https://mastodon.social/tags/Sudoku" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Sudoku</a> puzzles and <a href="https://mastodon.social/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a> textbooks. Because who doesn't love using a PhD-level formula just to choose a politician on a gloomy Saturday? 📊🤔 <a href="https://smarimccarthy.is/posts/2024-11-25-voting-system/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://smarimccarthy.is/posts/2024-11-25-voting-system/</a> <a href="https://mastodon.social/tags/MagicMath" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MagicMath</a> <a href="https://mastodon.social/tags/Politics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Politics</a> <a href="https://mastodon.social/tags/IcelandicSystem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#IcelandicSystem</a> <a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HackerNews</a> <a href="https://mastodon.social/tags/ngated" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ngated</a>

Space Data ScientistBetter to integrate than to disintegrate. -- Leibniz <a href="https://fosstodon.org/tags/motivationalspeaking" class="mention hashtag" rel="tag">#motivationalspeaking</a> <a href="https://fosstodon.org/tags/calculus" class="mention hashtag" rel="tag">#calculus</a> <a href="https://fosstodon.org/tags/astrodon" class="mention hashtag" rel="tag">#astrodon</a> <a href="https://fosstodon.org/tags/physics" class="mention hashtag" rel="tag">#physics</a> <a href="https://fosstodon.org/tags/teaching" class="mention hashtag" rel="tag">#teaching</a> <a href="https://fosstodon.org/tags/wisdom" class="mention hashtag" rel="tag">#wisdom</a>

Your Autistic Life FR/EN/ESSeen in a tutoring job ad:"I have a final exam in AP calculus BS":catthinking: BS??? I see how much you *love* calculus.(Probably meant BC.)<a href="https://mast.yourautisticlife.com/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mast.yourautisticlife.com/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a> <a href="https://mast.yourautisticlife.com/tags/bullshit" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#bullshit</a> <a href="https://mast.yourautisticlife.com/tags/tutoring" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tutoring</a> <a href="https://mast.yourautisticlife.com/tags/JobAd" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#JobAd</a>

Pustam | पुस्तम | পুস্তম🇳🇵A cycloidal pendulum - one suspended from the cusp of an inverted cycloid - is isochronous, meaning its period is constant regardless of the amplitude of the swing. Please find the proof using energy methods: Lagrange's equations (in the images attached to the reply).Background: The standard pendulum period of \(2\pi\sqrt{L/g}\) or frequency \(\sqrt{g/L}\) holds only for small oscillations. The frequency becomes smaller as the amplitude grows. If you want to build a pendulum whose frequency is independent of the amplitude, you should hang it from the cusp of a cycloid of a certain size, as shown in the gif. As the string wraps partially around the cycloid, the effect decreases the length of the string in the air, increasing the frequency back up to a constant value.In more detail: A cycloid is the path taken by a point on the rim of a rolling wheel. The upside-down cycloid in the gif can be parameterized by \((x, y)=R(\theta-\sin\theta, -1+\cos\theta)\), where \(\theta=0\) corresponds to the cusp. Consider a pendulum of length \(L=4R\) hanging from the cusp, and let \(\alpha\) be the angle the string makes with the vertical, as shown (in the proof).<a href="https://mathstodon.xyz/tags/Pendulum" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Pendulum</a> <a href="https://mathstodon.xyz/tags/Cycloid" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Cycloid</a> <a href="https://mathstodon.xyz/tags/Period" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Period</a> <a href="https://mathstodon.xyz/tags/Frequency" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Frequency</a> <a href="https://mathstodon.xyz/tags/SHM" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#SHM</a> <a href="https://mathstodon.xyz/tags/TimePeriod" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TimePeriod</a> <a href="https://mathstodon.xyz/tags/CycloidalPendulum" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CycloidalPendulum</a> <a href="https://mathstodon.xyz/tags/Lagrange" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Lagrange</a> <a href="https://mathstodon.xyz/tags/Cusp" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Cusp</a> <a href="https://mathstodon.xyz/tags/Energy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Energy</a> <a href="https://mathstodon.xyz/tags/KineticEnergy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#KineticEnergy</a> <a href="https://mathstodon.xyz/tags/PotentialEnergy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PotentialEnergy</a> <a href="https://mathstodon.xyz/tags/Lagrangian" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Lagrangian</a> <a href="https://mathstodon.xyz/tags/Length" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Length</a> <a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/Maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Maths</a> <a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Physics</a> <a href="https://mathstodon.xyz/tags/Mechanics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mechanics</a> <a href="https://mathstodon.xyz/tags/ClassicalMechanics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ClassicalMechanics</a> <a href="https://mathstodon.xyz/tags/Amplitude" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Amplitude</a> <a href="https://mathstodon.xyz/tags/CircularFrequency" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CircularFrequency</a> <a href="https://mathstodon.xyz/tags/Motion" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Motion</a> <a href="https://mathstodon.xyz/tags/Vibration" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Vibration</a> <a href="https://mathstodon.xyz/tags/HarmonicMotion" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HarmonicMotion</a> <a href="https://mathstodon.xyz/tags/Parameter" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Parameter</a> <a href="https://mathstodon.xyz/tags/ParemeterizedEquation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ParemeterizedEquation</a> <a href="https://mathstodon.xyz/tags/GoverningEquations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#GoverningEquations</a> <a href="https://mathstodon.xyz/tags/Equation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Equation</a> <a href="https://mathstodon.xyz/tags/Equations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Equations</a> <a href="https://mathstodon.xyz/tags/DifferentialEquations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DifferentialEquations</a> <a href="https://mathstodon.xyz/tags/Calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Calculus</a>

Hacker NewsCLP Calculus Textbooks<a href="https://personal.math.ubc.ca/~CLP/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://personal.math.ubc.ca/~CLP/</a><a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HackerNews</a> <a href="https://mastodon.social/tags/CLP" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CLP</a> <a href="https://mastodon.social/tags/Calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Calculus</a> <a href="https://mastodon.social/tags/Textbooks" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Textbooks</a> <a href="https://mastodon.social/tags/education" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#education</a> <a href="https://mastodon.social/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a> <a href="https://mastodon.social/tags/textbooks" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#textbooks</a> <a href="https://mastodon.social/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mastodon.social/tags/resources" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#resources</a> <a href="https://mastodon.social/tags/learning" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#learning</a>

Kyle Taylor<a href="https://mathstodon.xyz/@diffgeom" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@diffgeom</a> I'm probably one of n=3 people on Mastodon interested in real analysis and applied <a href="https://hostux.social/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a>, but take my boost all the same. Will add to the stack.

SurfmasterSome people use math just like they use people, to lie, cheat or steal. But math itself never lies, or cheats, or steals from me, thats why I love math. <a href="https://mastodon.social/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mastodon.social/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a> <a href="https://mastodon.social/tags/algebra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#algebra</a> <a href="https://mastodon.social/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a>

Patrick HonnerMy graph of the day. Inspired by the fact that \[ \sum_{k=1}^{\infty}{\sin k} \] is bounded but diverges, I've been exploring other similar sums. Here's the start of \[ \sum_{k=1}^{\infty}{\tan k} \] It's not shocking that it looks like \(y = \ln(\|\cos x\| ) \), but I definitely wonder if at some point it blows up down the line!<a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/Calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Calculus</a>

Emmanuel José GarcíaThe first and most complete unification of classical integration techniques ever! Say hello to USM. Draft article: <a href="https://drive.google.com/file/d/12DayP6cD1VwDIZCL-nMlcaNH2XUwHfAy/view?usp=drivesdk" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://drive.google.com/file/d/12DayP6cD1VwDIZCL-nMlcaNH2XUwHfAy/view?usp=drivesdk</a><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a> <a href="https://mathstodon.xyz/tags/halfangleapproach" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#halfangleapproach</a> <a href="https://mathstodon.xyz/tags/symmetrymatters" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#symmetrymatters</a>

Emmanuel José GarcíaThe USM, the Dominican method 🇩🇴, has relegated Euler substitutions to mere historical relics. Modern integration has a new name.Method draft: <a href="https://drive.google.com/file/d/12DayP6cD1VwDIZCL-nMlcaNH2XUwHfAy/view?usp=drivesdk" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://drive.google.com/file/d/12DayP6cD1VwDIZCL-nMlcaNH2XUwHfAy/view?usp=drivesdk</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a> <a href="https://mathstodon.xyz/tags/integrals" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#integrals</a> <a href="https://mathstodon.xyz/tags/method" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#method</a> <a href="https://mathstodon.xyz/tags/euler" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#euler</a> <a href="https://mathstodon.xyz/tags/halfangleapproach" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#halfangleapproach</a> <a href="https://mathstodon.xyz/tags/symmetrymatters" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#symmetrymatters</a>

Patrick HonnerToday I accidentally learned that limacons are inversions of conic sections!<a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/Geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Geometry</a> <a href="https://mathstodon.xyz/tags/Calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Calculus</a>

Paul BaldufI've made my lecture notes for applied calculus 2 publicly available. The content of that course is mostly "multidimensional real functions", including all the practical formulas for computing surfaces and volumes, slopes, optimization etc. The lecture notes contain a lot of practice problems with solutions. Maybe they're helpful for someone either learning or teaching <a href="https://mathstodon.xyz/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a> and <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://paulbalduf.com/teaching/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://paulbalduf.com/teaching/</a>

Your Autistic Life FR/EN/ESIt's really fucking aggravating when you try to compute an integral, get to a solution, and then when you look at the instructor's solution, you find him using a formula that WAS NEVER INTRODUCED BEFORE JUST NOW!🤬 <a href="https://mast.yourautisticlife.com/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mast.yourautisticlife.com/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a> <a href="https://mast.yourautisticlife.com/tags/integrals" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#integrals</a> <a href="https://mast.yourautisticlife.com/tags/fuck" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fuck</a>

Philo SophiesGuest article by Heinz Luediger: “Sketch of a <a href="https://planetearth.social/tags/negative" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#negative</a> <a href="https://planetearth.social/tags/structuralism" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#structuralism</a> - A minimalist <a href="https://planetearth.social/tags/theory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#theory</a> of <a href="https://planetearth.social/tags/experience" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#experience</a>”This juxtaposition is to take place in the sense of his approach of <a href="https://planetearth.social/tags/orthogonality" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#orthogonality</a>. In a <a href="https://planetearth.social/tags/dialectical" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#dialectical</a> procedure, this should lead to <a href="https://planetearth.social/tags/contradiction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#contradiction</a>-free <a href="https://planetearth.social/tags/category" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#category</a> systems that require no further legitimation through <a href="https://planetearth.social/tags/logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#logic</a> or a <a href="https://planetearth.social/tags/mathematical" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematical</a> <a href="https://planetearth.social/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a> and should lead to a <a href="https://planetearth.social/tags/minimalist" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#minimalist</a> theory of experience. More at: <a href="https://philosophies.de/index.php/2023/06/21/skizze-eines-negativen-strukturalismus/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://philosophies.de/index.php/2023/06/21/skizze-eines-negativen-strukturalismus/</a>

Patrick Honner"I'm not sure if that's a line or if it's two rays", asked a student, validating the instructional design of my introduction to polar coordinates activity.<a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/MathEd" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MathEd</a> <a href="https://mathstodon.xyz/tags/Calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Calculus</a>

Nicole HennigThe Missing Introduction to Calculus for AI <a href="https://medium.com/effortless-programming/the-missing-introduction-to-calculus-for-ai-3d5e8df6efa3" rel="nofollow noopener noreferrer" target="_blank">https://medium.com/effortless-programming/the-missing-introduction-to-calculus-for-ai-3d5e8df6efa3</a> <a class="hashtag" href="https://bsky.app/search?q=%23AI" rel="nofollow noopener noreferrer" target="_blank">#AI</a> <a class="hashtag" href="https://bsky.app/search?q=%23calculus" rel="nofollow noopener noreferrer" target="_blank">#calculus</a> <a class="hashtag" href="https://bsky.app/search?q=%23NeuralNetworks" rel="nofollow noopener noreferrer" target="_blank">#NeuralNetworks</a>

Nicole HennigThe Missing Introduction to Calculus for AI <a href="https://medium.com/effortless-programming/the-missing-introduction-to-calculus-for-ai-3d5e8df6efa3" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://medium.com/effortless-programming/the-missing-introduction-to-calculus-for-ai-3d5e8df6efa3</a> <a href="https://techhub.social/tags/AI" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AI</a> <a href="https://techhub.social/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a> <a href="https://techhub.social/tags/NeuralNetworks" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NeuralNetworks</a>

Patrick HonnerThis makes sense, right? (Trying to better understand arclength in polar.)<a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a>

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