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One crank expands this wooden lattice into an equiangular spiral. r = a e^(bθ) keeps the angle φ = cot⁻¹(b) fixed between radius vector and tangent. Growth is pure differential geometry; no motors. Same curve used in deployable satellite solar arrays.

One crank expands this wooden lattice into an equiangular spiral. r = a e^(bθ) keeps the angle φ = cot⁻¹(b) fixed between radius vector and tangent. Growth is pure differential geometry; no motors. Same curve used in deployable satellite solar arrays.

65,950 views • 24 days ago

Only straight bars and pivots. Still draws a perfect circle. One end stays fixed. The chain of rods and joints keeps folding through triangles, squares and other shapes while the free tip traces the entire green path.

Only straight bars and pivots. Still draws a perfect circle. One end stays fixed. The chain of rods and joints keeps folding through triangles, squares and other shapes while the free tip traces the entire green path.

20,055 views • 19 days ago

What does a hydrogen atom’s |ψ|² actually look like as the quantum numbers change? This animation shows the electron probability density morphing in real time through superpositions α|nlm⟩ + β|n′l′m′⟩ while n, l, and m shift between allowed values.

What does a hydrogen atom’s |ψ|² actually look like as the quantum numbers change? This animation shows the electron probability density morphing in real time through superpositions α|nlm⟩ + β|n′l′m′⟩ while n, l, and m shift between allowed values.

10,305 views • 21 days ago

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