Comments by "John Berry" (@user-ud6ui7zt3r) on "Why are the formulas for the sphere so weird? (major upgrade of Archimedes' greatest discoveries)" video.

  1. John Berry's perfect cube... 𝑤³ + 𝑥³ + 𝑦³ = 𝑧³; 3³ + 4³ + 5³ = 6³ 27 + 64 + 125 = 216 216 = 216 ✅ ...also... √(3² + 4² + 5²) = √50 √50 = sin(45°) × 10 √50 = (√2/2) × 10 √50 = 0.70710678118654752440084436210485 × 10 ✅
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  2. extra extra extra SPECIAL QUESTION... Can someone tell me why, when the notation for the LaPlace transform is written, you often see... ∫𝑑𝑥(expression to be transformed) ...instead of... ∫(expression to be transformed)𝑑𝑥 ??? In other words, when it comes to the LaPlace transform, why do they usually write the integrand FIRST (i.e. ∫𝑑𝑥) followed by the expression to be transformed? What special meaning does this notational practice indicate?
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