How I approximated 68-1 Hadi Rihawi 2025-09-18 | This video first appeared on my TikTok at hadi_sr.I approximated 68-1 using the Taylor series centered at 0 (or Maclaurin series) of (1+x)^(1/2), plugging in -1/68 for x. This is also known as the binomial series, the extension of the binomial theorem to non-integer powers. Then I approximated the square root of 68 using the Newton Raphson method. Combining these results, we can multiply to find an approximate value for 68-1.
How to Integrate 1/sin(x) Hadi Rihawi 2025-08-02 | Finding the antiderivative of 1/sin(x) (or csc(x)) using three different methods. Full video to accompany the shorter cut on my TikTok @ hadi_sr.Minor error: At 11:01, the numerator should be -sin(x) based on what I said and I preemptively got rid of the negative sign due to the absolute value. This, however, ends up messing up the tangent half-angle identity which is corrected in post editing (at 11:30, I should say "one minus cosine x")Chapters:00:00 Standard Trick01:18 Pythagorean Identity04:26 Weierstrass Substitution08:03 Solution Analysis11:45 Outro
Integrating 1/(x^2+1)^n Hadi Rihawi 2024-12-28 | Integrating 1/(x^2+1)^n from -infinity to infinity using complex analysis (the residue theorem). Additional resources:Complex order derivatives: arxiv.org/pdf/1209.0400Legendre duplication formula: mathworld.wolfram.com/LegendreDuplicationFormula.htmlChapters00:00 Setting up the Contour02:41 Bounding the Integral06:20 Sending R to Infinity07:42 Applying Cauchy's Residue Theorem09:13 Computing the Derivative11:30 Simplifying the Expression14:14 Final Answer14:54 Using the Legendre Duplication Formula16:35 "Nicer" Final AnswerFilmed on September 29th, 2024.
How to Factor x⁴+1 Hadi Rihawi 2024-08-14 | Three different ways to factor x⁴+1. FULL video to accompany the sped-up version posted on my TikTok @ hadi_sr.
How I Approximated 256+1 Hadi Rihawi 2024-07-01 | READ DESCRIPTION: This is a trial video first released on my Tiktok page to gauge metrics on more educational content. Future releases on Youtube will be filmed in landscape mode. My explanation was condensed to keep the video at around 2 minutes for Tiktok; future uploads here will likely be at least 5 minutes long. How I approximated 256+1 using the Taylor series centered at 0 (or Maclaurin series) of (1+x)^(1/8). This is also known as the binomial series, the extension of the binomial theorem to non-integer powers.
Newton’s Pi Approximation Method (extended) Hadi Rihawi 2024-03-14 | Happy Pi Day! Here’s an approximation of π rounded up to the 11th decimal place using the method Newton used. Time spent: ~π hours (~190 minutes).While I used the first 14 terms, Newton, in 1666, used the first 22 terms to obtain an approximation of π to 14 decimal places. Notably, Newton wrote, “I am ashamed to tell you to how many figures I carried these computations, having no other business at the time.” The computations did in fact take much longer than I thought they would…
