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@mathsvault.bsky.social Sep 30, 2026, 2:30 PM

Discuss — Three-Dimensional Shapes #maths #mathsteacher #UKMathsChat #GCSEMaths #MathsChat #Discussion #MathsDiscussion #TalkTasks #ThreeDimensionalShapes #SurfaceArea #Geometry #Area

@mathsvault.bsky.social Sep 28, 2026, 7:30 AM

Plenary — Three-Dimensional Shapes #maths #mathsteacher #UKMathsChat #GCSEMaths #Plenary #MathsDiscussion #RealLifeMaths #Applications #ThreeDimensionalShapes #SurfaceArea #Geometry #Area

@yrroi.bsky.social Sep 21, 2026, 12:34 AM

www.twitch.tv/videos/28797...
Just wrapped this week's stream on multivariable integration, featuring some live singing and bass - a cover of Billie Eilish's L'Amour de Ma Vie by myself!
#stream #twitch #math #calculus #integration #surfacearea #sphere #indiemusic #singing

Differentiation using the chain rule of the function 2x^3 + 5x + 7 = 6x^2 +5. Integration of the function 6x^2 + 5 dx = 2x^3 + 5x + c. Tetration is a function of stacking exponentials, a^a^a^a... well beyond my wheelhouse.
Double variable indefinite integration of the function x^2 y dy dx, separated into integral of x^2 dx times integral of y dy, resulting in the answer of (1/6)x^3 y^2.
Question asked by Sandels_45, represented here as a slightly shiny orb, of a double integral of y^x dydx is a nontrivial integrand, and cannot be evaluated this way, instead requiring a special function called the exponential integral, also something I've not prepared to discuss. Many special case integrals are only defined as "the solution to a difficult problem", so this may be all I can tell you about it, but please dig into this on your own. :)

Cartesian and spherical coordinates explained through diagrams. Rho (a curly P) is defined as the 3D radius of the sphere, phi as the polar angle running from 0 to pi, and theta as the azimuthal angle running from 0 to 2pi. A 2D slice of the sphere can be calculated by looking at the projection of the 3D radius rho into a circle in the 2D plane with a radius of r = rho sin phi.
A volume element can be described using the definition of radian angles and arc lengths, where the polar edge is given by rho delta phi, and the azimuthal edge is given by r delta theta = rho sin phi delta theta.
Using this description of a surface area element, the surface of a full sphere A can be calculated as the double integral from 0 to 2pi, from 0 to pi, of rho^2 sin theta dphi dtheta. This expression can be separated into A = rho^2 integral from 0 to 2pi dtheta integral from 0 to pi of sin phi dphi, then A = rho^2 (theta evaluated from 0 to 2pi) (-cosphi evaluated from 0 to pi) = 4 pi rho^2 = A.

@mathsvault.bsky.social Sep 8, 2026, 7:30 AM

Plenary — Three-Dimensional Shapes #maths #mathsteacher #UKMathsChat #GCSEMaths #Plenary #MathsDiscussion #Extension #Challenge #ThreeDimensionalShapes #SurfaceArea #Geometry #Area #Reasoning #ProblemSolving

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