Seventeen equations.
A new way to see.

The right angle lies between a and b. Babylonian knowledge predates the traditional association with Pythagoras.

The example x³ = 15x + 4 has x = 4. The paired complex cube roots 2+i and 2−i add to 4.

For x,y > 0 and a common base b > 0, b ≠ 1.

Newton and Leibniz independently developed calculus. The visual example uses position f(t)=t².

The inverse-square expression applies to point masses; the orbit illustration is schematic.

The animation compares 100 fair coin tosses with a normal approximation: mean 50, standard deviation 5.

An ideal one-dimensional linear wave model; fixed ends introduce standing waves.

For convex polyhedra. Adding a diagonal across one face increases both E and F by one.

The demonstration combines three harmonics. The displayed transform uses frequency ν and the 2π convention.

Incompressible Newtonian fluid with constant density and viscosity, ∇·u=0. The streamlines are illustrative, not a numerical PDE solution.

Modern SI notation. In vacuum, c=1/√(μ₀ε₀); the electric and magnetic fields in a plane wave are transverse and in phase.

For an isolated system. The example conserves energy while the total entropy of two bodies increases.

Equal opposite light pulses carry energy away without net momentum; the body loses mass.

The free wave packet and hydrogen energy levels are separate examples. Hydrogen n=3→2 emits about 1.89 eV, near 656 nm.

Base-two logarithms give entropy in bits. A binary source with probabilities .95 and .05 has about .286 bits of entropy.

Lorenz’s continuous convection system is distinct from the logistic map. The latter illustrates stable, periodic and chaotic behaviour.

European options under the Black–Scholes assumptions. An illustrative model price is not a forecast or investment recommendation.