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Version devBuilt at: 2026-10-10 01:38:52 EDT

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@mathify-dev.bsky.socialOct 2, 2026, 12:11 AM

Inside a Helical Vortex: Zero Divergence, Constant Curl

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#VectorCalculus #VectorField #Curl #Mathify

@yrroi.bsky.socialSep 9, 2026, 1:33 AM

www.twitch.tv/videos/28673...
Green boards from the stream this Sunday. Thanks for the live question! I'll be chatting more about divergence and doing some curl next week. Always happy to talk vector calculus any time! #math #stream #vectorcalculus #sciencecommunication

Notes explaining the vector operator Nabla, made of partial derivatives along each component of 3d space. Vector fields showing the gradient increasing along x in green and orthogonal to x in pink, notes suggest thinking of acceleration parallel to velocity will cause a pile up of whatever matter is flowing. Quick description of Gauss's Law in integral form, providing an electricity based use case for the divergence operator.Divergence of an unspecified vector A expanded. Diagram of a magnetic dipole with butterfly shaped magnetic field lines. Section of dense field lines is contrasted with section of sparse magnetic field lines, and related to magnetic force. Electron surrounded by radial, decreasing field lines, beside formal function for the electric field around a charge proportional to the reciprocal of the radius away from the charge.Trigonometry set up, showing Sine of theta as opposite over hypotenuse, Cosine of theta adjacent over hypotenuse, Tangent as opposite over hypotenuse which is equivalent to sine over cosine. This rapidly got dropped for a live question about divergence and green's theorem, special case of stoke's theorem, that any closed loop about a three dimensional shape will contain information about the enclosed shape, in integral form.