I’ve always been fascinated with electromagnetism and its connection to geometry. There’s a geometrical concept called the Flower of Life that hides the same rotational symmetry that governs magnetic flux. Another example is Faraday’s law of induction, $\mathcal{E} = -\frac{d\Phi_B}{dt}$, tracing the same closed loops you find in Metatron’s Cube. I went ahead and created 16 chapters of geometry and Maxwell’s equations rendered in 3D — each one interactive, with real mathematics. You can orbit a torus, twist a vortex, drag sliders to reshape field lines in real time, and explore the beauty of electromagnetism and its mathematical and physical effects.

I was watching a video on the mathematics and physics of an electron and electromagnetism. One of the things it mentioned was that an electron needs 720° to fully rotate around its axis — not 360°. This isn’t a quirk. The reason is because SU(2) double-covers SO(3). SU(2) is the special unitary group: the set of all 2×2 unitary matrices with determinant 1, $\mathrm{SU}(2) = \{ U \in \mathbb{C}^{2 \times 2} \mid U^\dagger U = I,\; \det U = 1 \}$. The mapping $\mathrm{SU}(2) \to \mathrm{SO}(3)$ sends every pair of opposite elements $\pm U$ to the same physical rotation, which is exactly why a spinor needs two full turns to return to its original state. Drag a slider through the full rotation and watch the phase flip at 360° before it finally returns at 720°. Includes a simulated neutron interferometer and the mathematics of quaternion lifts.