A visual, bite-sized mini-lesson for elementary school kids that bridges the gap between counting and algebra.
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Code available at https://github.com/zombimann/Mathematical-video-animations-and-visualization/blob/main/Kids_Elementary_Multiplication_Using_Circle_Grids.ipynb
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This visualizes the reduction of control systems block diagrams into their equivalent transfer functions.
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Code available at https://github.com/zombimann/Mathematical-video-animations-and-visualization/blob/main/Control_Systems_Block_Diagram_Simplification.ipynb
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This video demonstrates a high-fidelity 2D simulation of the Magnus effect by modelling the trajectories of spinning spheres falling through a fluid medium.
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For code click https://github.com/zombimann/Mathematical-video-animations-and-visualization/blob/main/Bernoulli_Equations_Magnus_Effect.ipynb
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I’ve been thinking about the sample mean from a linear algebra perspective.
If y is a data vector and 1 is the vector of all ones, then the average can be seen as the scalar you get when projecting y onto span(1).
So the projection has the form:
y-hat = y-bar · 1
where y-bar is the usual sample average.
I like this because it makes the average feel like the simplest possible least-squares problem: find the constant vector closest to the data vector.
It also connects naturally to ordinary least squares regression, where y gets projected onto the column space of X instead of just the one-dimensional space spanned by 1.
Does this seem like a good way to introduce projections/least squares, or would you teach it differently?