The geometric interpretation of sin x = x - x³/3! + x⁵/5! -...

Comments · 635

• MA

  @mathemaniac · 4 years ago (edited) · pinned

  Update: proof of donation: <a href="https://www.youtube.com/post/UgkxMsm-mzZc9a-gD8cmiygHPBC62vcf1pdM">https://www.youtube.com/post/UgkxMsm-mzZc9a-gD8cmiygHPBC62vcf1pdM</a><br><br>I might change the title to &quot;Without calculus...&quot; because... how else do you combine &quot;differentiation and integration&quot; so that the title is snappier?<br><br>The only thing that held me back from making this video a fundraiser is the fear of political comments, or any comment that seeks to create conflict, so please do me a favour by not making those comments. Anyway, donate if you can; if not, like, comment and share this video so that this gets more people’s attention.<br><br>This video is a lot slower than my usual videos, but it might be better for understanding. If somehow you think this is too slow, you can always speed it up. The hope is that you don’t need any university-level maths to understand this video.<br><br>NOTE: In the last part, k is supposed to be fixed, so each bracket do go to 1 when n tends to infinity.

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• AN

  @anwyl42 · 4 years ago (edited)

  This feels like tricking kids into eating vegetables. &quot;Oh, taylor series is too complicated? Okay we&apos;ll just add up a bunch of lines tangent to curves!&quot; I love it.

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• HE

  @henrymarkson3758 · 4 years ago

  Your content rivals that of 3b1b and there is no greater praise in the world of YouTube maths.

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• NA

  @nathanwestfall6950 · 4 years ago

  This is what I needed 20 years ago! A very satisfying approach that gives meaning to an otherwise non-intuitive result. &nbsp;Keep it up! :-)

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• GL

  @glarynth · 4 years ago

  Great illustration! Also, e^x is hidden in there, as the total length of the spiral (including the horizontal segment from the origin to (1, 0)). &nbsp;This shows an intimate connection between the exponential and the sine/cosine, which typically isn&apos;t apparent without invoking the complex numbers.

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• BL

  @blackpenredpen · 4 years ago

  <a href="https://www.youtube.com/watch?v=x09IsbVZeXo&amp;t=179">2:59</a> 😮<br>thanks for an amazing video!!!

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• CO

  @coffeecup1196 · 4 years ago (edited)

  More of a &quot;How to sneak calculus into a &apos;without calculus&apos; explanation&quot; video<br><br>I love it, keep it up. There are a lot of people who will have a better intuition for calculus when they get to their intro class if they watch this stuff.

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• TI

  @timermens350 · 4 years ago

  Very nice. Sice 3Blue1Brown and Mathologer their &quot;moving average probability&quot; of uploading content seems to be in a downwards trend, this might be the next channel showing the beauty of math. Pls keep doing these kinds of videos!

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• PH

  @physicsboy1234 · 4 years ago

  This is an interesting video and the showing of the proof is simple &nbsp;enough that even I can understand you explained it well

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• AN

  @anhthiensaigon · 4 years ago

  dude this is so perfectly well done that it seems like a weapon by itself already.

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• BE

  @been_shaded · 4 years ago

  Another beauty of these videos are that: They make u feel jealous in a very positive way and u start thinking as to why I couldn&apos;t think of this masterpiece!!! Love for yet another beautiful channel

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• TH

  @therealAQ · 4 years ago

  Tangent lines to curves, inifinite processes and &apos;epsilons&apos; going to zero, all that is calculus-ey enough for me. Complex analysis is quite geometric actually. 👌

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